%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP164^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:01 AM UTC 2026
% Result : Theorem 22.59s 6.42s
% Output : Refutation 24.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 350
% Syntax : Number of formulae : 702 ( 337 unt; 0 typ; 0 def)
% Number of atoms : 2241 ( 669 equ; 40 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 5589 ( 42 ~; 1 |; 96 &;4518 @)
% ( 0 <=>; 932 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 260 ( 260 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 9 con; 0-3 aty)
% Number of variables : 1979 ( 132 ^;1835 !; 12 ?;1979 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr451126599t_unit_type,type,
set_Pr451126599t_unit: $tType ).
thf(refine787176636t_unit_type,type,
refine787176636t_unit: $tType ).
thf(produc971140967t_unit_type,type,
produc971140967t_unit: $tType ).
thf(set_Pr1628433942t_unit_type,type,
set_Pr1628433942t_unit: $tType ).
thf(set_Pr1720557880unit_a_type,type,
set_Pr1720557880unit_a: $tType ).
thf(refine424419629nres_a_type,type,
refine424419629nres_a: $tType ).
thf(produc1767851702t_unit_type,type,
produc1767851702t_unit: $tType ).
thf(produc884009688unit_a_type,type,
produc884009688unit_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(if_Ref1369692790t_unit_decl,type,
if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(if_Ref1724547303nres_a_decl,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(bot_bo658782032t_unit_decl,type,
bot_bo658782032t_unit: refine787176636t_unit ).
thf(bot_bo529555393nres_a_decl,type,
bot_bo529555393nres_a: refine424419629nres_a ).
thf(bot_bo1087887705t_unit_decl,type,
bot_bo1087887705t_unit: set_Product_unit ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_le1051254044t_unit_decl,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(ord_le519537037nres_a_decl,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(ord_le2035129575t_unit_decl,type,
ord_le2035129575t_unit: set_Pr451126599t_unit > set_Pr451126599t_unit > $o ).
thf(ord_le2070001880unit_a_decl,type,
ord_le2070001880unit_a: set_Pr1720557880unit_a > set_Pr1720557880unit_a > $o ).
thf(ord_le1977877942t_unit_decl,type,
ord_le1977877942t_unit: set_Pr1628433942t_unit > set_Pr1628433942t_unit > $o ).
thf(ord_le1824328871od_a_a_decl,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_le1023748749t_unit_decl,type,
ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(order_453013155t_unit_decl,type,
order_453013155t_unit: ( refine787176636t_unit > $o ) > refine787176636t_unit ).
thf(order_1714329108nres_a_decl,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(top_to177290092t_unit_decl,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(top_to231829469nres_a_decl,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(partia1658438072t_unit_decl,type,
partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
thf(partia906949161nres_a_decl,type,
partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
thf(produc1076565719t_unit_decl,type,
produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
thf(produc1799512520unit_a_decl,type,
produc1799512520unit_a: product_unit > a > produc884009688unit_a ).
thf(produc1776699686t_unit_decl,type,
produc1776699686t_unit: a > product_unit > produc1767851702t_unit ).
thf(product_Pair_a_a_decl,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(refine1420258419t_unit_decl,type,
refine1420258419t_unit: product_unit > refine787176636t_unit ).
thf(refine2063221604TURN_a_decl,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine838861686t_unit_decl,type,
refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(refine364464487unit_a_decl,type,
refine364464487unit_a: set_Pr1720557880unit_a > refine787176636t_unit > refine424419629nres_a ).
thf(refine341651653t_unit_decl,type,
refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit ).
thf(refine1136779702un_a_a_decl,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine681446406t_unit_decl,type,
refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(refine119808503unit_a_decl,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine96995669t_unit_decl,type,
refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
thf(refine436832838nd_a_a_decl,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine944483349t_unit_decl,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(refine2043866374unit_a_decl,type,
refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
thf(refine2021053540t_unit_decl,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(refine1441824853un_a_a_decl,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine558004794t_unit_decl,type,
refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
thf(refine1001002027nres_a_decl,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(refine983493746t_unit_decl,type,
refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
thf(refine1312857699nres_a_decl,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(refine579265252t_unit_decl,type,
refine579265252t_unit: refine787176636t_unit > $o ).
thf(refine412683989fail_a_decl,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(refine1777164439t_unit_decl,type,
refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
thf(refine1198353288_RES_a_decl,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(refine230495195t_unit_decl,type,
refine230495195t_unit: ( refine787176636t_unit > refine787176636t_unit ) > ( refine787176636t_unit > refine787176636t_unit ) > $o ).
thf(refine2089046860nres_a_decl,type,
refine2089046860nres_a: ( refine787176636t_unit > refine424419629nres_a ) > ( refine424419629nres_a > refine787176636t_unit ) > $o ).
thf(refine327276970t_unit_decl,type,
refine327276970t_unit: ( refine424419629nres_a > refine787176636t_unit ) > ( refine787176636t_unit > refine424419629nres_a ) > $o ).
thf(refine2004812827nres_a_decl,type,
refine2004812827nres_a: ( refine424419629nres_a > refine424419629nres_a ) > ( refine424419629nres_a > refine424419629nres_a ) > $o ).
thf(domain2090798924t_unit_decl,type,
domain2090798924t_unit: set_Pr451126599t_unit > set_Product_unit ).
thf(domain822362941unit_a_decl,type,
domain822362941unit_a: set_Pr1720557880unit_a > set_Product_unit ).
thf(domain799550107t_unit_decl,type,
domain799550107t_unit: set_Pr1628433942t_unit > set_a ).
thf(domain_a_a_decl,type,
domain_a_a: set_Product_prod_a_a > set_a ).
thf(single330234563t_unit_decl,type,
single330234563t_unit: set_Pr451126599t_unit > $o ).
thf(single249782708unit_a_decl,type,
single249782708unit_a: set_Pr1720557880unit_a > $o ).
thf(single226969874t_unit_decl,type,
single226969874t_unit: set_Pr1628433942t_unit > $o ).
thf(single_valued_a_a_decl,type,
single_valued_a_a: set_Product_prod_a_a > $o ).
thf(collect_Product_unit_decl,type,
collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(insert_Product_unit_decl,type,
insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
thf(insert_a_decl,type,
insert_a: a > set_a > set_a ).
thf(member1423014800t_unit_decl,type,
member1423014800t_unit: produc971140967t_unit > set_Pr451126599t_unit > $o ).
thf(member1211819009unit_a_decl,type,
member1211819009unit_a: produc884009688unit_a > set_Pr1720557880unit_a > $o ).
thf(member2095661023t_unit_decl,type,
member2095661023t_unit: produc1767851702t_unit > set_Pr1628433942t_unit > $o ).
thf(member449909584od_a_a_decl,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_Product_unit_decl,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(f_decl,type,
f: product_unit > refine424419629nres_a ).
thf(141,axiom,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ ( refine364464487unit_a @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_abs__trans) ).
thf(892,plain,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ ( refine364464487unit_a @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(250,axiom,
! [A: set_Pr1628433942t_unit] :
( ( refine341651653t_unit @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_abs__fun__simps_I1_J) ).
thf(1322,plain,
! [A: set_Pr1628433942t_unit] :
( ( refine341651653t_unit @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(212,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ ( refine838861686t_unit @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_abs__trans) ).
thf(1168,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ ( refine838861686t_unit @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(41,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__subst2) ).
thf(518,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(192,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: refine424419629nres_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ A @ C ) @ ( refine1441824853un_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_conc__fun__R__mono) ).
thf(1083,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: refine424419629nres_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ A @ C ) @ ( refine1441824853un_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(109,axiom,
! [A: product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( member_Product_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_nres__order__simps_I21_J) ).
thf(777,plain,
! [A: product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( member_Product_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(77,axiom,
! [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( refine230495195t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_galois__connection_Ogalois) ).
thf(666,plain,
! [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( refine230495195t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(315,axiom,
! [A: set_a] :
( ( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_nres__more__simps_I1_J) ).
thf(1549,plain,
! [A: set_a] :
( ( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1,conjecture,
( ( refine119808503unit_a @ bot_bo658782032t_unit @ f )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( refine119808503unit_a @ bot_bo658782032t_unit @ f )
!= bot_bo529555393nres_a ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(352,plain,
( ( refine119808503unit_a @ bot_bo658782032t_unit @ f )
!= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(64,axiom,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit,C: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ C )
=> ( ord_le2035129575t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order_Otrans) ).
thf(628,plain,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit,C: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ C )
=> ( ord_le2035129575t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(176,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nres__order__simps_I3_J) ).
thf(1031,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(218,axiom,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( refine412683989fail_a @ ( refine2021053540t_unit @ A @ B ) )
= ( refine579265252t_unit @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_pw__conc__nofail) ).
thf(1200,plain,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( refine412683989fail_a @ ( refine2021053540t_unit @ A @ B ) )
= ( refine579265252t_unit @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(221,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine96995669t_unit @ A @ C )
= ( refine96995669t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_bind__cong) ).
thf(1211,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine96995669t_unit @ A @ C )
= ( refine96995669t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(169,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( ( refine1441824853un_a_a @ A @ B )
= top_to231829469nres_a )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_conc__fun__fail__iff_I1_J) ).
thf(1005,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( ( refine1441824853un_a_a @ A @ B )
= top_to231829469nres_a )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(98,axiom,
! [A: refine787176636t_unit,B: refine424419629nres_a,C: a > refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le1051254044t_unit @ ( C @ D ) @ A ) ) )
=> ( ord_le1051254044t_unit @ ( refine96995669t_unit @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_pw__bind__leI) ).
thf(730,plain,
! [A: refine787176636t_unit,B: refine424419629nres_a,C: a > refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le1051254044t_unit @ ( C @ D ) @ A ) ) )
=> ( ord_le1051254044t_unit @ ( refine96995669t_unit @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(187,axiom,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ ( refine341651653t_unit @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_abs__trans) ).
thf(1068,plain,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ ( refine341651653t_unit @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(339,axiom,
refine579265252t_unit @ bot_bo658782032t_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nofail__simps_I4_J) ).
thf(1618,plain,
refine579265252t_unit @ bot_bo658782032t_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(275,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ A )
=> ( ord_le519537037nres_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_dual__order_Otrans) ).
thf(1401,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ A )
=> ( ord_le519537037nres_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(100,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1136779702un_a_a @ A @ B ) )
= ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( member_a @ C @ ( domain_a_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_pw__abs__nofail) ).
thf(741,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1136779702un_a_a @ A @ B ) )
= ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( member_a @ C @ ( domain_a_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(28,axiom,
( ( (=) @ set_Pr451126599t_unit )
= ( ^ [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
& ( ord_le2035129575t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_order__class_Oorder_Oeq__iff) ).
thf(449,plain,
( ( (=) @ set_Pr451126599t_unit )
= ( ^ [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
& ( ord_le2035129575t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(234,axiom,
! [A: product_unit] :
( top_to177290092t_unit
!= ( refine1420258419t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_nres__inequalities_I3_J) ).
thf(1269,plain,
! [A: product_unit] :
( top_to177290092t_unit
!= ( refine1420258419t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(57,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ord__le__eq__subst) ).
thf(597,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(42,axiom,
! [A: set_Product_unit] :
( ( collect_Product_unit
@ ^ [B: product_unit] : ( member_Product_unit @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Collect__mem__eq) ).
thf(523,plain,
! [A: set_Product_unit] :
( ( collect_Product_unit
@ ^ [B: product_unit] : ( member_Product_unit @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(53,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Collect__cong) ).
thf(582,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(136,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_order__class_Oorder_Oantisym) ).
thf(878,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(73,axiom,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ ( refine364464487unit_a @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_abs__trans) ).
thf(655,plain,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ ( refine364464487unit_a @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(301,axiom,
! [A: product_unit,B: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ ( refine1420258419t_unit @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nres__monad1) ).
thf(1497,plain,
! [A: product_unit,B: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ ( refine1420258419t_unit @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(283,axiom,
! [A: refine424419629nres_a,B: refine787176636t_unit > refine424419629nres_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ord__eq__le__subst) ).
thf(1426,plain,
! [A: refine424419629nres_a,B: refine787176636t_unit > refine424419629nres_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(9,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_antisym__conv) ).
thf(384,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(116,axiom,
! [A: set_Product_unit] :
( ( refine558004794t_unit @ ( refine1777164439t_unit @ A ) )
= ( ^ [B: product_unit] : ( member_Product_unit @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_inres__simps_I2_J) ).
thf(797,plain,
! [A: set_Product_unit] :
( ( refine558004794t_unit @ ( refine1777164439t_unit @ A ) )
= ( ^ [B: product_unit] : ( member_Product_unit @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(34,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order__subst2) ).
thf(472,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(120,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( single_valued_a_a @ A )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ A @ C ) )
= ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_conc__abs__swap) ).
thf(814,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( single_valued_a_a @ A )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ A @ C ) )
= ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(155,axiom,
( refine558004794t_unit
= ( ^ [A: refine787176636t_unit,B: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_inres__def) ).
thf(945,plain,
( refine558004794t_unit
= ( ^ [A: refine787176636t_unit,B: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(78,axiom,
! [A: set_Product_unit,B: set_Pr1720557880unit_a] :
( ~ ( ord_le1023748749t_unit @ A @ ( domain822362941unit_a @ B ) )
=> ( ( refine364464487unit_a @ B @ ( refine1777164439t_unit @ A ) )
= top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_abs__fun__simps_I3_J) ).
thf(670,plain,
! [A: set_Product_unit,B: set_Pr1720557880unit_a] :
( ~ ( ord_le1023748749t_unit @ A @ ( domain822362941unit_a @ B ) )
=> ( ( refine364464487unit_a @ B @ ( refine1777164439t_unit @ A ) )
= top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(257,axiom,
! [A: refine787176636t_unit,B: refine424419629nres_a > refine787176636t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_order__subst1) ).
thf(1342,plain,
! [A: refine787176636t_unit,B: refine424419629nres_a > refine787176636t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(102,axiom,
! [A: a] :
( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ A ) )
= ( (=) @ a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_inres__simps_I3_J) ).
thf(747,plain,
! [A: a] :
( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ A ) )
= ( (=) @ a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(146,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Pr1628433942t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ C @ B ) @ D )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_abs__trans__additional_I1_J) ).
thf(913,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Pr1628433942t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ C @ B ) @ D )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(124,axiom,
! [A: a,B: a > refine787176636t_unit] :
( ( refine96995669t_unit @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_nres__monad1) ).
thf(829,plain,
! [A: a,B: a > refine787176636t_unit] :
( ( refine96995669t_unit @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(143,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nres__order__simps_I4_J) ).
thf(898,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(324,axiom,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ bot_bo529555393nres_a @ A )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bind__SUCCEED) ).
thf(1576,plain,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ bot_bo529555393nres_a @ A )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(111,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_dual__order_Oantisym) ).
thf(782,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(126,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_ord__le__eq__subst) ).
thf(841,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(163,axiom,
! [A: refine424419629nres_a,B: refine787176636t_unit > refine424419629nres_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_order__subst1) ).
thf(973,plain,
! [A: refine424419629nres_a,B: refine787176636t_unit > refine424419629nres_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(337,axiom,
top_to177290092t_unit != bot_bo658782032t_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_nres__inequalities_I2_J) ).
thf(1613,plain,
top_to177290092t_unit != bot_bo658782032t_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(333,axiom,
top_to231829469nres_a != bot_bo529555393nres_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_nres__inequalities_I2_J) ).
thf(1601,plain,
top_to231829469nres_a != bot_bo529555393nres_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(264,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( refine579265252t_unit @ B )
=> ( refine579265252t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pwD1) ).
thf(1366,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( refine579265252t_unit @ B )
=> ( refine579265252t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(306,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_bot_Oextremum) ).
thf(1518,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(298,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ord__le__eq__subst) ).
thf(1482,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(229,axiom,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
& ( ord_le1051254044t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_order__class_Oorder_Oeq__iff) ).
thf(1254,plain,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
& ( ord_le1051254044t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(96,axiom,
! [A: product_unit,B: set_Product_unit] :
( ( ( refine1420258419t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( ( insert_Product_unit @ A @ bot_bo1087887705t_unit )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_nres__more__simps_I5_J) ).
thf(724,plain,
! [A: product_unit,B: set_Product_unit] :
( ( ( refine1420258419t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( ( insert_Product_unit @ A @ bot_bo1087887705t_unit )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(51,axiom,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst) ).
thf(570,plain,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(112,axiom,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit] :
( ( single226969874t_unit @ A )
=> ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ A @ C ) )
= ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_conc__abs__swap) ).
thf(785,plain,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit] :
( ( single226969874t_unit @ A )
=> ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ A @ C ) )
= ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(233,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_pw__leI) ).
thf(1264,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(184,axiom,
! [A: refine424419629nres_a,B: a > refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ A @ B ) @ C )
= ( ( ( refine579265252t_unit @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le1051254044t_unit @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_pw__bind__le__iff) ).
thf(1059,plain,
! [A: refine424419629nres_a,B: a > refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ A @ B ) @ C )
= ( ( ( refine579265252t_unit @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le1051254044t_unit @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(205,axiom,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_conc__trans__additional_I1_J) ).
thf(1132,plain,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(249,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_order__trans) ).
thf(1319,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(297,axiom,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_less__eq__nres_Osimps_I2_J) ).
thf(1479,plain,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(200,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_order__subst2) ).
thf(1115,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(348,axiom,
! [A: set_Pr1628433942t_unit] :
( ( refine341651653t_unit @ A @ bot_bo529555393nres_a )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_abs__fun__strict) ).
thf(1641,plain,
! [A: set_Pr1628433942t_unit] :
( ( refine341651653t_unit @ A @ bot_bo529555393nres_a )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(300,axiom,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( ( refine2043866374unit_a @ A @ B )
= top_to177290092t_unit )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_conc__fun__fail__iff_I1_J) ).
thf(1494,plain,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( ( refine2043866374unit_a @ A @ B )
= top_to177290092t_unit )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(224,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
=> ( ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_pw__eqI) ).
thf(1232,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
=> ( ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(58,axiom,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a,C: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ C )
=> ( ord_le2070001880unit_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order_Otrans) ).
thf(606,plain,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a,C: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ C )
=> ( ord_le2070001880unit_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(258,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_top_Oextremum__unique) ).
thf(1347,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(274,axiom,
! [A: refine787176636t_unit,B: product_unit > refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine681446406t_unit @ A @ B ) )
= ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine579265252t_unit @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_pw__bind__nofail) ).
thf(1398,plain,
! [A: refine787176636t_unit,B: product_unit > refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine681446406t_unit @ A @ B ) )
= ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine579265252t_unit @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(137,axiom,
! [A: set_Product_unit,B: product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1420258419t_unit @ B ) )
= ( A
= ( insert_Product_unit @ B @ bot_bo1087887705t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_nres__more__simps_I3_J) ).
thf(881,plain,
! [A: set_Product_unit,B: product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1420258419t_unit @ B ) )
= ( A
= ( insert_Product_unit @ B @ bot_bo1087887705t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(113,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__mono__setup_Orefl) ).
thf(789,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(267,axiom,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_pw__eq__iff) ).
thf(1373,plain,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(345,axiom,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ bot_bo529555393nres_a )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_conc__fun__strict) ).
thf(1632,plain,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ bot_bo529555393nres_a )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(254,axiom,
( refine1312857699nres_a
= ( ^ [A: refine424419629nres_a,B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_nf__inres__def) ).
thf(1334,plain,
( refine1312857699nres_a
= ( ^ [A: refine424419629nres_a,B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(122,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_meta__le__everything__if__top) ).
thf(821,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(36,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ord__eq__le__subst) ).
thf(480,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(165,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord__le__eq__subst) ).
thf(981,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(14,axiom,
! [A: refine787176636t_unit,B: set_a > refine787176636t_unit,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ord__eq__le__subst) ).
thf(397,plain,
! [A: refine787176636t_unit,B: set_a > refine787176636t_unit,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(288,axiom,
~ ( refine412683989fail_a @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_nofail__simps_I1_J) ).
thf(1447,plain,
~ ( refine412683989fail_a @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(132,axiom,
! [A: product_unit] :
( ( refine558004794t_unit @ ( refine1420258419t_unit @ A ) )
= ( (=) @ product_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_inres__simps_I3_J) ).
thf(866,plain,
! [A: product_unit] :
( ( refine558004794t_unit @ ( refine1420258419t_unit @ A ) )
= ( (=) @ product_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(309,axiom,
( ( refine558004794t_unit @ bot_bo658782032t_unit )
= ( ^ [A: product_unit] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_inres__simps_I4_J) ).
thf(1526,plain,
( ( refine558004794t_unit @ bot_bo658782032t_unit )
= ( ^ [A: product_unit] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(75,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( top_to177290092t_unit
= ( refine944483349t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_conc__fun__fail__iff_I2_J) ).
thf(660,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( top_to177290092t_unit
= ( refine944483349t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(22,axiom,
( ( (=) @ set_Pr1628433942t_unit )
= ( ^ [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
& ( ord_le1977877942t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_order__class_Oorder_Oeq__iff) ).
thf(428,plain,
( ( (=) @ set_Pr1628433942t_unit )
= ( ^ [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
& ( ord_le1977877942t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(227,axiom,
! [A: refine787176636t_unit,B: refine424419629nres_a > refine787176636t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_ord__eq__le__subst) ).
thf(1242,plain,
! [A: refine787176636t_unit,B: refine424419629nres_a > refine787176636t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(39,axiom,
( ( (=) @ set_Pr451126599t_unit )
= ( ^ [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
& ( ord_le2035129575t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_eq__iff) ).
thf(507,plain,
( ( (=) @ set_Pr451126599t_unit )
= ( ^ [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
& ( ord_le2035129575t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(320,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ bot_bo658782032t_unit )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_conc__fun__strict) ).
thf(1564,plain,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ bot_bo658782032t_unit )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(220,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_order__subst2) ).
thf(1206,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(148,axiom,
! [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit] :
( ! [C: refine424419629nres_a,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ C @ ( A @ D ) )
= ( ord_le1051254044t_unit @ ( B @ C ) @ D ) )
=> ( refine327276970t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_galois__connection_Ointro) ).
thf(925,plain,
! [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit] :
( ! [C: refine424419629nres_a,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ C @ ( A @ D ) )
= ( ord_le1051254044t_unit @ ( B @ C ) @ D ) )
=> ( refine327276970t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(244,axiom,
! [A: refine424419629nres_a,B: a > refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine96995669t_unit @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine579265252t_unit @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_pw__bind__nofail) ).
thf(1306,plain,
! [A: refine424419629nres_a,B: a > refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine96995669t_unit @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine579265252t_unit @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(294,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(1470,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(93,axiom,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a,C: refine424419629nres_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ord_le1051254044t_unit @ ( refine2043866374unit_a @ A @ C ) @ ( refine2043866374unit_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_conc__fun__R__mono) ).
thf(714,plain,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a,C: refine424419629nres_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ord_le1051254044t_unit @ ( refine2043866374unit_a @ A @ C ) @ ( refine2043866374unit_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(183,axiom,
( refine2089046860nres_a
= ( ^ [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit] :
! [C: refine787176636t_unit,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_galois__connection__def) ).
thf(1057,plain,
( refine2089046860nres_a
= ( ^ [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit] :
! [C: refine787176636t_unit,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(189,axiom,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ ( refine944483349t_unit @ A @ C ) @ ( refine944483349t_unit @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_conc__fun__R__mono) ).
thf(1074,plain,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ ( refine944483349t_unit @ A @ C ) @ ( refine944483349t_unit @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(334,axiom,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ bot_bo658782032t_unit )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_conc__fun__strict) ).
thf(1604,plain,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ bot_bo658782032t_unit )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(154,axiom,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit,C: refine787176636t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ord_le519537037nres_a @ ( refine2021053540t_unit @ A @ C ) @ ( refine2021053540t_unit @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_conc__fun__R__mono) ).
thf(942,plain,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit,C: refine787176636t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ord_le519537037nres_a @ ( refine2021053540t_unit @ A @ C ) @ ( refine2021053540t_unit @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(24,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_order__class_Oorder_Oeq__iff) ).
thf(439,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(145,axiom,
! [A: set_a,B: a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine2063221604TURN_a @ B ) )
= ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_nres__more__simps_I3_J) ).
thf(910,plain,
! [A: set_a,B: a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine2063221604TURN_a @ B ) )
= ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(194,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nres__order__simps_I4_J) ).
thf(1091,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(260,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_conc__trans__additional_I1_J) ).
thf(1355,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(202,axiom,
! [A: a > refine787176636t_unit] :
( ( refine96995669t_unit @ top_to231829469nres_a @ A )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_bind__FAIL) ).
thf(1123,plain,
! [A: a > refine787176636t_unit] :
( ( refine96995669t_unit @ top_to231829469nres_a @ A )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(322,axiom,
! [A: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= bot_bo658782032t_unit )
= ( A = bot_bo1087887705t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_nres__more__simps_I2_J) ).
thf(1570,plain,
! [A: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= bot_bo658782032t_unit )
= ( A = bot_bo1087887705t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(303,axiom,
! [A: product_unit] :
( bot_bo658782032t_unit
!= ( refine1420258419t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nres__inequalities_I5_J) ).
thf(1502,plain,
! [A: product_unit] :
( bot_bo658782032t_unit
!= ( refine1420258419t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(12,axiom,
( ( (=) @ set_Pr1628433942t_unit )
= ( ^ [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
& ( ord_le1977877942t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_eq__iff) ).
thf(392,plain,
( ( (=) @ set_Pr1628433942t_unit )
= ( ^ [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
& ( ord_le1977877942t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(86,axiom,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_bind__FAIL) ).
thf(693,plain,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(180,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: a] :
( ( refine1001002027nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
= ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ A @ B ) )
=> ? [D: a] :
( ( refine1001002027nres_a @ B @ D )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_pw__abs__inres) ).
thf(1042,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: a] :
( ( refine1001002027nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
= ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ A @ B ) )
=> ? [D: a] :
( ( refine1001002027nres_a @ B @ D )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(158,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nres__order__simps_I3_J) ).
thf(952,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(340,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nres__order__simps_I1_J) ).
thf(1619,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(266,axiom,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_conc__trans__additional_I1_J) ).
thf(1370,plain,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(63,axiom,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_antisym__conv) ).
thf(625,plain,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(215,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1441824853un_a_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_pw__conc__nofail) ).
thf(1178,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1441824853un_a_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(243,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [C: product_unit] :
( ( refine579265252t_unit @ A )
=> ( ( refine558004794t_unit @ B @ C )
=> ( refine558004794t_unit @ A @ C ) ) )
=> ( ord_le1051254044t_unit @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pw__leI_H) ).
thf(1296,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [C: product_unit] :
( ( refine579265252t_unit @ A )
=> ( ( refine558004794t_unit @ B @ C )
=> ( refine558004794t_unit @ A @ C ) ) )
=> ( ord_le1051254044t_unit @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(342,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_bot_Oextremum) ).
thf(1624,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(140,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_top_Oextremum__uniqueI) ).
thf(889,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(238,axiom,
! [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit,D: refine424419629nres_a] :
( ( refine2089046860nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_galois__connection_Ogalois) ).
thf(1281,plain,
! [A: refine787176636t_unit > refine424419629nres_a,B: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit,D: refine424419629nres_a] :
( ( refine2089046860nres_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(272,axiom,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit] :
( ( refine412683989fail_a @ ( refine364464487unit_a @ A @ B ) )
= ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( member_Product_unit @ C @ ( domain822362941unit_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_pw__abs__nofail) ).
thf(1392,plain,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit] :
( ( refine412683989fail_a @ ( refine364464487unit_a @ A @ B ) )
= ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( member_Product_unit @ C @ ( domain822362941unit_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(241,axiom,
! [A: product_unit,B: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ A ) @ ( refine1420258419t_unit @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_nres__order__simps_I20_J) ).
thf(1291,plain,
! [A: product_unit,B: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ A ) @ ( refine1420258419t_unit @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(30,axiom,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_antisym) ).
thf(456,plain,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(323,axiom,
bot_bo529555393nres_a != top_to231829469nres_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_nres__inequalities_I4_J) ).
thf(1573,plain,
bot_bo529555393nres_a != top_to231829469nres_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(147,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_ord__le__eq__subst) ).
thf(916,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(33,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__subst2) ).
thf(467,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(128,axiom,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ ( refine2021053540t_unit @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_conc__trans) ).
thf(852,plain,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ ( refine2021053540t_unit @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(317,axiom,
bot_bo658782032t_unit != top_to177290092t_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_nres__inequalities_I4_J) ).
thf(1555,plain,
bot_bo658782032t_unit != top_to177290092t_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(82,axiom,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: product_unit] :
( ( refine558004794t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
= ( ( refine579265252t_unit @ ( refine341651653t_unit @ A @ B ) )
=> ? [D: a] :
( ( refine1001002027nres_a @ B @ D )
& ( member2095661023t_unit @ ( produc1776699686t_unit @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pw__abs__inres) ).
thf(682,plain,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: product_unit] :
( ( refine558004794t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
= ( ( refine579265252t_unit @ ( refine341651653t_unit @ A @ B ) )
=> ? [D: a] :
( ( refine1001002027nres_a @ B @ D )
& ( member2095661023t_unit @ ( produc1776699686t_unit @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(277,axiom,
! [A: refine424419629nres_a] :
( ( refine436832838nd_a_a @ A @ refine2063221604TURN_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_nres__monad2) ).
thf(1407,plain,
! [A: refine424419629nres_a] :
( ( refine436832838nd_a_a @ A @ refine2063221604TURN_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(330,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_abs__fun__strict) ).
thf(1592,plain,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(252,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_antisym__conv) ).
thf(1328,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(268,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1051254044t_unit @ ( refine96995669t_unit @ A @ C ) @ ( refine96995669t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1375,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1051254044t_unit @ ( refine96995669t_unit @ A @ C ) @ ( refine96995669t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(198,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_flat__ord__compat_I2_J) ).
thf(1111,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(207,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_top__greatest) ).
thf(1138,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(133,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_conc__fun__FAIL) ).
thf(869,plain,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(20,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(420,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(262,axiom,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ ( refine341651653t_unit @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_abs__trans) ).
thf(1360,plain,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ D @ ( refine341651653t_unit @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(259,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ A )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1051254044t_unit @ ( refine681446406t_unit @ A @ C ) @ ( refine681446406t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1350,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ A )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1051254044t_unit @ ( refine681446406t_unit @ A @ C ) @ ( refine681446406t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(88,axiom,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_nres__order__simps_I5_J) ).
thf(697,plain,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(313,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine119808503unit_a @ A @ C ) @ ( refine119808503unit_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1541,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine119808503unit_a @ A @ C ) @ ( refine119808503unit_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(321,axiom,
! [A: a > refine787176636t_unit] :
( ( refine96995669t_unit @ bot_bo529555393nres_a @ A )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_bind__SUCCEED) ).
thf(1567,plain,
! [A: a > refine787176636t_unit] :
( ( refine96995669t_unit @ bot_bo529555393nres_a @ A )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(138,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_pwD1) ).
thf(884,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(175,axiom,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a] :
( ( refine579265252t_unit @ ( refine341651653t_unit @ A @ B ) )
= ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( member_a @ C @ ( domain799550107t_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_pw__abs__nofail) ).
thf(1028,plain,
! [A: set_Pr1628433942t_unit,B: refine424419629nres_a] :
( ( refine579265252t_unit @ ( refine341651653t_unit @ A @ B ) )
= ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( member_a @ C @ ( domain799550107t_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(151,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: set_Pr451126599t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ C @ B ) @ D )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_abs__trans__additional_I1_J) ).
thf(933,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: set_Pr451126599t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ C @ B ) @ D )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(291,axiom,
! [A: set_Pr1720557880unit_a] :
( ( single249782708unit_a @ A )
=> ( refine2089046860nres_a @ ( refine364464487unit_a @ A ) @ ( refine2043866374unit_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_ac__galois) ).
thf(1461,plain,
! [A: set_Pr1720557880unit_a] :
( ( single249782708unit_a @ A )
=> ( refine2089046860nres_a @ ( refine364464487unit_a @ A ) @ ( refine2043866374unit_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(144,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ B )
=> ( ! [C: refine424419629nres_a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ C @ B ) )
=> ( ( order_1714329108nres_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_Greatest__equality) ).
thf(901,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ B )
=> ( ! [C: refine424419629nres_a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ C @ B ) )
=> ( ( order_1714329108nres_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(282,axiom,
( refine2063221604TURN_a
= ( ^ [A: a] : ( refine1198353288_RES_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_RETURN__def) ).
thf(1424,plain,
( refine2063221604TURN_a
= ( ^ [A: a] : ( refine1198353288_RES_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(67,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_antisym__conv) ).
thf(637,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(37,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_ord__le__eq__subst) ).
thf(489,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(349,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nres__order__simps_I1_J) ).
thf(1644,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(91,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( B = C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ord__le__eq__trans) ).
thf(706,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( B = C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(280,axiom,
( refine2004812827nres_a
= ( ^ [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a] :
! [C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_galois__connection__def) ).
thf(1419,plain,
( refine2004812827nres_a
= ( ^ [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a] :
! [C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(279,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_order__subst1) ).
thf(1414,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(43,axiom,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order__subst1) ).
thf(526,plain,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(173,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [D: product_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine558004794t_unit @ B @ D )
=> ( ord_le1051254044t_unit @ ( C @ D ) @ A ) ) )
=> ( ord_le1051254044t_unit @ ( refine681446406t_unit @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_pw__bind__leI) ).
thf(1016,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [D: product_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine558004794t_unit @ B @ D )
=> ( ord_le1051254044t_unit @ ( C @ D ) @ A ) ) )
=> ( ord_le1051254044t_unit @ ( refine681446406t_unit @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(55,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_eq__refl) ).
thf(590,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(81,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine944483349t_unit @ A @ B ) )
= ( refine579265252t_unit @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_pw__conc__nofail) ).
thf(679,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine944483349t_unit @ A @ B ) )
= ( refine579265252t_unit @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(162,axiom,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_nres__order__simps_I21_J) ).
thf(970,plain,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(62,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_antisym) ).
thf(622,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(70,axiom,
( ord_le1051254044t_unit
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine558004794t_unit @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_pw__le__iff) ).
thf(647,plain,
( ord_le1051254044t_unit
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine558004794t_unit @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(328,axiom,
( ( refine1001002027nres_a @ bot_bo529555393nres_a )
= ( ^ [A: a] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_inres__simps_I4_J) ).
thf(1588,plain,
( ( refine1001002027nres_a @ bot_bo529555393nres_a )
= ( ^ [A: a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(316,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
= ( A = bot_bo658782032t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_bot_Oextremum__unique) ).
thf(1552,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
= ( A = bot_bo658782032t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(7,axiom,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( A = B )
=> ( ord_le1977877942t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_eq__refl) ).
thf(371,plain,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( A = B )
=> ( ord_le1977877942t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(193,axiom,
! [A: refine787176636t_unit,B: product_unit > $o,C: product_unit > $o] :
( ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) )
=> ( ! [D: product_unit] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_SPEC__cons__rule) ).
thf(1086,plain,
! [A: refine787176636t_unit,B: product_unit > $o,C: product_unit > $o] :
( ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) )
=> ( ! [D: product_unit] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(182,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ E @ A @ C ) @ ( if_Ref1724547303nres_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order__mono__setup_Omono__if) ).
thf(1054,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ E @ A @ C ) @ ( if_Ref1724547303nres_a @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(178,axiom,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ B @ A )
& ( ord_le1051254044t_unit @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_dual__order_Oeq__iff) ).
thf(1035,plain,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ B @ A )
& ( ord_le1051254044t_unit @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(338,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ bot_bo529555393nres_a @ A @ B )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_flat__ord__compat_I1_J) ).
thf(1616,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ bot_bo529555393nres_a @ A @ B )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(115,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_dual__order_Oantisym) ).
thf(794,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(48,axiom,
! [A: refine787176636t_unit,B: set_a > refine787176636t_unit,C: set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_order__subst1) ).
thf(558,plain,
! [A: refine787176636t_unit,B: set_a > refine787176636t_unit,C: set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(188,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order_Otrans) ).
thf(1071,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(237,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ ( refine1136779702un_a_a @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_abs__trans) ).
thf(1278,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine341651653t_unit @ D @ ( refine1136779702un_a_a @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(103,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ord__eq__le__trans) ).
thf(750,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(23,axiom,
! [A: set_Pr451126599t_unit,B: refine424419629nres_a > set_Pr451126599t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le2035129575t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_ord__eq__le__subst) ).
thf(430,plain,
! [A: set_Pr451126599t_unit,B: refine424419629nres_a > set_Pr451126599t_unit,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le2035129575t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(235,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pwD2) ).
thf(1273,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(331,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ bot_bo658782032t_unit )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_abs__fun__strict) ).
thf(1595,plain,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ bot_bo658782032t_unit )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(26,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_eq__iff) ).
thf(444,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__le__eq__subst) ).
thf(375,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > set_a,D: set_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(206,axiom,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_bind__FAIL) ).
thf(1135,plain,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(351,axiom,
! [A: a] :
( bot_bo529555393nres_a
!= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nres__inequalities_I5_J) ).
thf(1648,plain,
! [A: a] :
( bot_bo529555393nres_a
!= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(17,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_antisym) ).
thf(412,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(228,axiom,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( refine579265252t_unit @ ( refine2043866374unit_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_pw__conc__nofail) ).
thf(1251,plain,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( refine579265252t_unit @ ( refine2043866374unit_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(60,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_eq__iff) ).
thf(618,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(21,axiom,
! [A: set_a,B: set_a,C: set_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_order__subst2) ).
thf(423,plain,
! [A: set_a,B: set_a,C: set_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(271,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: product_unit] :
( ( refine558004794t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
= ( ( refine579265252t_unit @ ( refine838861686t_unit @ A @ B ) )
=> ? [D: product_unit] :
( ( refine558004794t_unit @ B @ D )
& ( member1423014800t_unit @ ( produc1076565719t_unit @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_pw__abs__inres) ).
thf(1389,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: product_unit] :
( ( refine558004794t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
= ( ( refine579265252t_unit @ ( refine838861686t_unit @ A @ B ) )
=> ? [D: product_unit] :
( ( refine558004794t_unit @ B @ D )
& ( member1423014800t_unit @ ( produc1076565719t_unit @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(107,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine436832838nd_a_a @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine412683989fail_a @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_pw__bind__nofail) ).
thf(772,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine436832838nd_a_a @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine412683989fail_a @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(52,axiom,
! [A: product_unit,B: product_unit > $o] :
( ( member_Product_unit @ A @ ( collect_Product_unit @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mem__Collect__eq) ).
thf(579,plain,
! [A: product_unit,B: product_unit > $o] :
( ( member_Product_unit @ A @ ( collect_Product_unit @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(307,axiom,
! [A: refine787176636t_unit,B: product_unit > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine119808503unit_a @ A @ B ) @ C )
= ( ( ( refine412683989fail_a @ C )
=> ( refine579265252t_unit @ A ) )
& ! [D: product_unit] :
( ( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ D ) )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_pw__bind__le__iff) ).
thf(1520,plain,
! [A: refine787176636t_unit,B: product_unit > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine119808503unit_a @ A @ B ) @ C )
= ( ( ( refine412683989fail_a @ C )
=> ( refine579265252t_unit @ A ) )
& ! [D: product_unit] :
( ( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ D ) )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(230,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_order__mono__setup_Orefl) ).
thf(1256,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(135,axiom,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_conc__trans) ).
thf(875,plain,
! [A: refine787176636t_unit,B: set_Pr1720557880unit_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(123,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_order__class_Oorder_Oantisym) ).
thf(826,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(92,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ~ ( ord_less_eq_set_a @ A @ ( domain_a_a @ B ) )
=> ( ( refine1136779702un_a_a @ B @ ( refine1198353288_RES_a @ A ) )
= top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_abs__fun__simps_I3_J) ).
thf(711,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ~ ( ord_less_eq_set_a @ A @ ( domain_a_a @ B ) )
=> ( ( refine1136779702un_a_a @ B @ ( refine1198353288_RES_a @ A ) )
= top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(152,axiom,
! [A: a,B: set_a] :
( ( ( refine2063221604TURN_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( ( insert_a @ A @ bot_bot_set_a )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_nres__more__simps_I5_J) ).
thf(936,plain,
! [A: a,B: set_a] :
( ( ( refine2063221604TURN_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( ( insert_a @ A @ bot_bot_set_a )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(246,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_dual__order_Oeq__iff) ).
thf(1312,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(38,axiom,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__le__eq__subst) ).
thf(498,plain,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(346,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ bot_bo529555393nres_a @ A @ B )
= ( ? [C: a] : ( refine1001002027nres_a @ A @ C )
=> ( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_pw__flat__le__iff) ).
thf(1635,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ bot_bo529555393nres_a @ A @ B )
= ( ? [C: a] : ( refine1001002027nres_a @ A @ C )
=> ( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(197,axiom,
! [A: a] :
( top_to231829469nres_a
!= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nres__inequalities_I3_J) ).
thf(1107,plain,
! [A: a] :
( top_to231829469nres_a
!= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(231,axiom,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ ( refine2043866374unit_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_conc__trans) ).
thf(1258,plain,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ ( refine2043866374unit_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(156,axiom,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ ( refine2043866374unit_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_conc__trans) ).
thf(947,plain,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: set_Pr1720557880unit_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ ( refine2043866374unit_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(347,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nres__order__simps_I2_J) ).
thf(1638,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(45,axiom,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( A = B )
=> ( ord_le2035129575t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_eq__refl) ).
thf(540,plain,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( A = B )
=> ( ord_le2035129575t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(105,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( refine558004794t_unit @ A @ C ) ) ) )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_pw__leI) ).
thf(764,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( refine558004794t_unit @ A @ C ) ) ) )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(15,axiom,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_antisym__conv) ).
thf(406,plain,
! [A: set_Pr451126599t_unit,B: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ A @ B )
=> ( ( ord_le2035129575t_unit @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(171,axiom,
! [A: product_unit,B: product_unit] :
( ( ( refine1420258419t_unit @ A )
= ( refine1420258419t_unit @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nres__more__simps_I6_J) ).
thf(1011,plain,
! [A: product_unit,B: product_unit] :
( ( ( refine1420258419t_unit @ A )
= ( refine1420258419t_unit @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(166,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_abs__trans__additional_I1_J) ).
thf(990,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(285,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
= ( ( refine412683989fail_a @ A )
=> ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_pw__flat__ge__iff) ).
thf(1439,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
= ( ( refine412683989fail_a @ A )
=> ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(29,axiom,
! [A: set_a,B: refine787176636t_unit > set_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_order__subst1) ).
thf(451,plain,
! [A: set_a,B: refine787176636t_unit > set_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order_Otrans) ).
thf(567,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(40,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le2035129575t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ord__le__eq__subst) ).
thf(509,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le2035129575t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(71,axiom,
! [A: refine424419629nres_a] :
( ( top_to231829469nres_a != A )
= ( refine412683989fail_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_intro__nofail_I2_J) ).
thf(649,plain,
! [A: refine424419629nres_a] :
( ( top_to231829469nres_a != A )
= ( refine412683989fail_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(131,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > $o] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) )
=> ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_SPEC__trans) ).
thf(863,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > $o] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) )
=> ( ord_le1051254044t_unit @ A @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(214,axiom,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( top_to177290092t_unit
= ( refine2043866374unit_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_conc__fun__fail__iff_I2_J) ).
thf(1175,plain,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( top_to177290092t_unit
= ( refine2043866374unit_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(35,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_antisym__conv) ).
thf(477,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(191,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order_Otrans) ).
thf(1080,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(65,axiom,
! [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a,D: refine787176636t_unit] :
( ( refine327276970t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_galois__connection_Ogalois) ).
thf(631,plain,
! [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a,D: refine787176636t_unit] :
( ( refine327276970t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(256,axiom,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_conc__trans__additional_I1_J) ).
thf(1339,plain,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(59,axiom,
! [A: set_a,B: set_a,C: set_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ord__le__eq__subst) ).
thf(609,plain,
! [A: set_a,B: set_a,C: set_a > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(56,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order_Otrans) ).
thf(594,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(89,axiom,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nres__order__simps_I20_J) ).
thf(700,plain,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(251,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit,E: $o] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ E @ A @ C ) @ ( if_Ref1369692790t_unit @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order__mono__setup_Omono__if) ).
thf(1325,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit,E: $o] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ E @ A @ C ) @ ( if_Ref1369692790t_unit @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(142,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
= ( ( refine579265252t_unit @ A )
=> ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_pw__flat__ge__iff) ).
thf(895,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
= ( ( refine579265252t_unit @ A )
=> ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(106,axiom,
! [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a] :
( ! [C: refine787176636t_unit,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ C @ ( A @ D ) )
= ( ord_le519537037nres_a @ ( B @ C ) @ D ) )
=> ( refine2089046860nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_galois__connection_Ointro) ).
thf(769,plain,
! [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a] :
( ! [C: refine787176636t_unit,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ C @ ( A @ D ) )
= ( ord_le519537037nres_a @ ( B @ C ) @ D ) )
=> ( refine2089046860nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(119,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(811,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(10,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Collect__mem__eq) ).
thf(387,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(130,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_meta__le__everything__if__top) ).
thf(858,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(6,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_eq__refl) ).
thf(367,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(160,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_dual__order_Orefl) ).
thf(959,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(110,axiom,
! [A: set_Pr1628433942t_unit] :
( ( single226969874t_unit @ A )
=> ( refine327276970t_unit @ ( refine341651653t_unit @ A ) @ ( refine2021053540t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_ac__galois) ).
thf(780,plain,
! [A: set_Pr1628433942t_unit] :
( ( single226969874t_unit @ A )
=> ( refine327276970t_unit @ ( refine341651653t_unit @ A ) @ ( refine2021053540t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(13,axiom,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_antisym) ).
thf(394,plain,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(284,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( single330234563t_unit @ A )
=> ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ A @ C ) )
= ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_conc__abs__swap) ).
thf(1435,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( single330234563t_unit @ A )
=> ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ A @ C ) )
= ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(196,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_order__subst2) ).
thf(1102,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1051254044t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(74,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ B )
=> ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_pw__le__iff) ).
thf(658,plain,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ B )
=> ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(83,axiom,
! [A: refine787176636t_unit] :
( ( refine681446406t_unit @ A @ refine1420258419t_unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_nres__monad2) ).
thf(685,plain,
! [A: refine787176636t_unit] :
( ( refine681446406t_unit @ A @ refine1420258419t_unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(213,axiom,
! [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( refine2004812827nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_galois__connection_Ogalois) ).
thf(1171,plain,
! [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( refine2004812827nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le519537037nres_a @ ( A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(287,axiom,
( refine983493746t_unit
= ( ^ [A: refine787176636t_unit,B: product_unit] :
( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_nf__inres__def) ).
thf(1445,plain,
( refine983493746t_unit
= ( ^ [A: refine787176636t_unit,B: product_unit] :
( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(310,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( A = B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine119808503unit_a @ A @ C )
= ( refine119808503unit_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_bind__cong) ).
thf(1528,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( A = B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine119808503unit_a @ A @ C )
= ( refine119808503unit_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(199,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_pw__eq__iff) ).
thf(1113,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(49,axiom,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( A = B )
=> ( ord_le2070001880unit_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_eq__refl) ).
thf(563,plain,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( A = B )
=> ( ord_le2070001880unit_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(343,axiom,
! [A: set_a] :
( ( ( refine1198353288_RES_a @ A )
= bot_bo529555393nres_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_nres__more__simps_I2_J) ).
thf(1626,plain,
! [A: set_a] :
( ( ( refine1198353288_RES_a @ A )
= bot_bo529555393nres_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(219,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( refine558004794t_unit @ A @ C )
=> ( refine558004794t_unit @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_pwD2) ).
thf(1203,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( refine558004794t_unit @ A @ C )
=> ( refine558004794t_unit @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(44,axiom,
! [A: set_a,B: refine787176636t_unit > set_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst) ).
thf(531,plain,
! [A: set_a,B: refine787176636t_unit > set_a,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(76,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_conc__trans) ).
thf(663,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(305,axiom,
! [A: refine424419629nres_a,B: refine787176636t_unit,C: product_unit > refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [D: product_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine558004794t_unit @ B @ D )
=> ( ord_le519537037nres_a @ ( C @ D ) @ A ) ) )
=> ( ord_le519537037nres_a @ ( refine119808503unit_a @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_pw__bind__leI) ).
thf(1509,plain,
! [A: refine424419629nres_a,B: refine787176636t_unit,C: product_unit > refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine579265252t_unit @ B ) )
=> ( ! [D: product_unit] :
( ( refine579265252t_unit @ B )
=> ( ( refine558004794t_unit @ B @ D )
=> ( ord_le519537037nres_a @ ( C @ D ) @ A ) ) )
=> ( ord_le519537037nres_a @ ( refine119808503unit_a @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(153,axiom,
! [A: refine787176636t_unit] :
( ( top_to177290092t_unit != A )
= ( refine579265252t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_intro__nofail_I2_J) ).
thf(939,plain,
! [A: refine787176636t_unit] :
( ( top_to177290092t_unit != A )
= ( refine579265252t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(209,axiom,
! [A: refine787176636t_unit > $o,B: refine787176636t_unit,C: refine787176636t_unit > $o] :
( ( A @ B )
=> ( ! [D: refine787176636t_unit] :
( ( A @ D )
=> ( ord_le1051254044t_unit @ D @ B ) )
=> ( ! [D: refine787176636t_unit] :
( ( A @ D )
=> ( ! [E: refine787176636t_unit] :
( ( A @ E )
=> ( ord_le1051254044t_unit @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_453013155t_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_GreatestI2__order) ).
thf(1145,plain,
! [A: refine787176636t_unit > $o,B: refine787176636t_unit,C: refine787176636t_unit > $o] :
( ( A @ B )
=> ( ! [D: refine787176636t_unit] :
( ( A @ D )
=> ( ord_le1051254044t_unit @ D @ B ) )
=> ( ! [D: refine787176636t_unit] :
( ( A @ D )
=> ( ! [E: refine787176636t_unit] :
( ( A @ E )
=> ( ord_le1051254044t_unit @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_453013155t_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(47,axiom,
! [A: refine424419629nres_a,B: set_Pr451126599t_unit > refine424419629nres_a,C: set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le2035129575t_unit @ C @ D )
=> ( ! [E: set_Pr451126599t_unit,F: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_order__subst1) ).
thf(553,plain,
! [A: refine424419629nres_a,B: set_Pr451126599t_unit > refine424419629nres_a,C: set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le2035129575t_unit @ C @ D )
=> ( ! [E: set_Pr451126599t_unit,F: set_Pr451126599t_unit] :
( ( ord_le2035129575t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(216,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a > $o] :
( ( A @ B )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ord_le519537037nres_a @ D @ B ) )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ! [E: refine424419629nres_a] :
( ( A @ E )
=> ( ord_le519537037nres_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1714329108nres_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_GreatestI2__order) ).
thf(1181,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a > $o] :
( ( A @ B )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ord_le519537037nres_a @ D @ B ) )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ! [E: refine424419629nres_a] :
( ( A @ E )
=> ( ord_le519537037nres_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1714329108nres_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(168,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_flat__ord__compat_I2_J) ).
thf(1003,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(129,axiom,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( ( refine2021053540t_unit @ A @ B )
= top_to231829469nres_a )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_conc__fun__fail__iff_I1_J) ).
thf(855,plain,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( ( refine2021053540t_unit @ A @ B )
= top_to231829469nres_a )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(68,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_antisym) ).
thf(640,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(174,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_less__eq__nres_Osimps_I2_J) ).
thf(1025,plain,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(134,axiom,
! [A: refine424419629nres_a,B: a] :
( ~ ( refine412683989fail_a @ A )
=> ( refine1001002027nres_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_not__nofail__inres) ).
thf(872,plain,
! [A: refine424419629nres_a,B: a] :
( ~ ( refine412683989fail_a @ A )
=> ( refine1001002027nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(159,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_order__subst2) ).
thf(954,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(99,axiom,
! [A: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_nofail__simps_I3_J) ).
thf(739,plain,
! [A: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(265,axiom,
~ ( refine579265252t_unit @ top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_nofail__simps_I1_J) ).
thf(1368,plain,
~ ( refine579265252t_unit @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(16,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_mem__Collect__eq) ).
thf(409,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(167,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [C: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pw__leI_H) ).
thf(993,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [C: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(85,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
=> ( ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pw__eqI) ).
thf(690,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
= ( refine412683989fail_a @ B ) )
=> ( ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
= ( refine1001002027nres_a @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(332,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B )
= ( ? [C: product_unit] : ( refine558004794t_unit @ A @ C )
=> ( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_pw__flat__le__iff) ).
thf(1598,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B )
= ( ? [C: product_unit] : ( refine558004794t_unit @ A @ C )
=> ( ( ( refine579265252t_unit @ A )
= ( refine579265252t_unit @ B ) )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
= ( refine558004794t_unit @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(79,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ ( refine838861686t_unit @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_abs__trans) ).
thf(673,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ A @ B ) @ C )
=> ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ C ) @ E )
=> ( ord_le1051254044t_unit @ ( refine838861686t_unit @ D @ ( refine838861686t_unit @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(290,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ord__eq__le__subst) ).
thf(1452,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(114,axiom,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ ( refine944483349t_unit @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_conc__trans) ).
thf(791,plain,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ ( refine944483349t_unit @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(25,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(441,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(54,axiom,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__subst2) ).
thf(585,plain,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(94,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: set_Pr1720557880unit_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_abs__trans__additional_I1_J) ).
thf(717,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: set_Pr1720557880unit_a,D: refine424419629nres_a] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine364464487unit_a @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(225,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [D: a] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_SPEC__cons__rule) ).
thf(1235,plain,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [D: a] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(248,axiom,
( refine1420258419t_unit
= ( ^ [A: product_unit] : ( refine1777164439t_unit @ ( insert_Product_unit @ A @ bot_bo1087887705t_unit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_RETURN__def) ).
thf(1317,plain,
( refine1420258419t_unit
= ( ^ [A: product_unit] : ( refine1777164439t_unit @ ( insert_Product_unit @ A @ bot_bo1087887705t_unit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(312,axiom,
! [A: set_Pr1720557880unit_a] :
( ( refine364464487unit_a @ A @ bot_bo658782032t_unit )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_abs__fun__strict) ).
thf(1538,plain,
! [A: set_Pr1720557880unit_a] :
( ( refine364464487unit_a @ A @ bot_bo658782032t_unit )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(4,axiom,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_order__subst1) ).
thf(359,plain,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(325,axiom,
! [A: refine787176636t_unit,B: product_unit > refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine119808503unit_a @ A @ B ) )
= ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine412683989fail_a @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_pw__bind__nofail) ).
thf(1579,plain,
! [A: refine787176636t_unit,B: product_unit > refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine119808503unit_a @ A @ B ) )
= ( ( refine579265252t_unit @ A )
& ! [C: product_unit] :
( ( refine558004794t_unit @ A @ C )
=> ( refine412683989fail_a @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(239,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine838861686t_unit @ A @ B ) )
= ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( member_Product_unit @ C @ ( domain2090798924t_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_pw__abs__nofail) ).
thf(1285,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( refine579265252t_unit @ ( refine838861686t_unit @ A @ B ) )
= ( ( refine579265252t_unit @ B )
& ! [C: product_unit] :
( ( refine558004794t_unit @ B @ C )
=> ( member_Product_unit @ C @ ( domain2090798924t_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(222,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine436832838nd_a_a @ A @ C )
= ( refine436832838nd_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_bind__cong) ).
thf(1220,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine436832838nd_a_a @ A @ C )
= ( refine436832838nd_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(46,axiom,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst) ).
thf(544,plain,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(255,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ ( refine1136779702un_a_a @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_abs__trans) ).
thf(1336,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ A @ B ) @ C )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ C ) @ E )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ D @ ( refine1136779702un_a_a @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(69,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_le__nofailI) ).
thf(643,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(101,axiom,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ ( refine944483349t_unit @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_conc__trans) ).
thf(744,plain,
! [A: refine787176636t_unit,B: set_Pr451126599t_unit,C: refine787176636t_unit,D: set_Pr451126599t_unit,E: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ B @ ( refine944483349t_unit @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(90,axiom,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: a] :
( ( refine1001002027nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
= ( ( refine412683989fail_a @ ( refine364464487unit_a @ A @ B ) )
=> ? [D: product_unit] :
( ( refine558004794t_unit @ B @ D )
& ( member1211819009unit_a @ ( produc1799512520unit_a @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_pw__abs__inres) ).
thf(703,plain,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: a] :
( ( refine1001002027nres_a @ ( refine364464487unit_a @ A @ B ) @ C )
= ( ( refine412683989fail_a @ ( refine364464487unit_a @ A @ B ) )
=> ? [D: product_unit] :
( ( refine558004794t_unit @ B @ D )
& ( member1211819009unit_a @ ( produc1799512520unit_a @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(304,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_bot_Oextremum__unique) ).
thf(1506,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(97,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia906949161nres_a @ top_to231829469nres_a @ ( C @ E ) @ ( D @ E ) )
=> ( partia906949161nres_a @ top_to231829469nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(727,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia906949161nres_a @ top_to231829469nres_a @ ( C @ E ) @ ( D @ E ) )
=> ( partia906949161nres_a @ top_to231829469nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(170,axiom,
! [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit] :
( ! [C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ C @ ( A @ D ) )
= ( ord_le1051254044t_unit @ ( B @ C ) @ D ) )
=> ( refine230495195t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_galois__connection_Ointro) ).
thf(1008,plain,
! [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit] :
( ! [C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ C @ ( A @ D ) )
= ( ord_le1051254044t_unit @ ( B @ C ) @ D ) )
=> ( refine230495195t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(27,axiom,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_antisym__conv) ).
thf(446,plain,
! [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
=> ( ( ord_le2070001880unit_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(226,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_eq__iff) ).
thf(1240,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(276,axiom,
! [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a] :
( ! [C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ C @ ( A @ D ) )
= ( ord_le519537037nres_a @ ( B @ C ) @ D ) )
=> ( refine2004812827nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_galois__connection_Ointro) ).
thf(1404,plain,
! [A: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a] :
( ! [C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ C @ ( A @ D ) )
= ( ord_le519537037nres_a @ ( B @ C ) @ D ) )
=> ( refine2004812827nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(261,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_top__greatest) ).
thf(1358,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(327,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
=> ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_bot_Oextremum__uniqueI) ).
thf(1585,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
=> ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(195,axiom,
! [A: $o,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit,E: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ ( if_Ref1369692790t_unit @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Refine__Misc_Oif__mono) ).
thf(1094,plain,
! [A: $o,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit,E: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ E ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ ( if_Ref1369692790t_unit @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(164,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_order__trans) ).
thf(978,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(208,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( A = B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ord__eq__le__trans) ).
thf(1140,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( A = B )
=> ( ( ord_le1051254044t_unit @ B @ C )
=> ( ord_le1051254044t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(281,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_top_Oextremum__unique) ).
thf(1421,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(150,axiom,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
& ( ord_le1051254044t_unit @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_eq__iff) ).
thf(931,plain,
( ( (=) @ refine787176636t_unit )
= ( ^ [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
& ( ord_le1051254044t_unit @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(84,axiom,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_inres__def) ).
thf(688,plain,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(203,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_top_Oextremum__uniqueI) ).
thf(1126,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(350,axiom,
( bot_bo658782032t_unit
= ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_bot__nres__def) ).
thf(1646,plain,
( bot_bo658782032t_unit
= ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(296,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_nres__order__simps_I5_J) ).
thf(1476,plain,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(185,axiom,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_conc__fun__FAIL) ).
thf(1062,plain,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(72,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_conc__fun__FAIL) ).
thf(652,plain,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_order__class_Oorder_Oeq__iff) ).
thf(390,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(344,axiom,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ top_to177290092t_unit @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_bind__FAIL) ).
thf(1629,plain,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ top_to177290092t_unit @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(308,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ! [E: product_unit] : ( partia906949161nres_a @ top_to231829469nres_a @ ( C @ E ) @ ( D @ E ) )
=> ( partia906949161nres_a @ top_to231829469nres_a @ ( refine119808503unit_a @ A @ C ) @ ( refine119808503unit_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(1523,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ! [E: product_unit] : ( partia906949161nres_a @ top_to231829469nres_a @ ( C @ E ) @ ( D @ E ) )
=> ( partia906949161nres_a @ top_to231829469nres_a @ ( refine119808503unit_a @ A @ C ) @ ( refine119808503unit_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(19,axiom,
( ( (=) @ set_Pr1720557880unit_a )
= ( ^ [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
& ( ord_le2070001880unit_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_eq__iff) ).
thf(418,plain,
( ( (=) @ set_Pr1720557880unit_a )
= ( ^ [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
& ( ord_le2070001880unit_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(318,axiom,
! [A: product_unit,B: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ ( refine1420258419t_unit @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nres__monad1) ).
thf(1558,plain,
! [A: product_unit,B: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ ( refine1420258419t_unit @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(236,axiom,
! [A: set_Pr451126599t_unit] :
( ( single330234563t_unit @ A )
=> ( refine230495195t_unit @ ( refine838861686t_unit @ A ) @ ( refine944483349t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_ac__galois) ).
thf(1276,plain,
! [A: set_Pr451126599t_unit] :
( ( single330234563t_unit @ A )
=> ( refine230495195t_unit @ ( refine838861686t_unit @ A ) @ ( refine944483349t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(329,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_flat__ord__compat_I1_J) ).
thf(1590,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(161,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( A = B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine681446406t_unit @ A @ C )
= ( refine681446406t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_bind__cong) ).
thf(961,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( A = B )
=> ( ! [E: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine681446406t_unit @ A @ C )
= ( refine681446406t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(270,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_eq__refl) ).
thf(1385,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(299,axiom,
! [A: set_Product_unit,B: set_Pr451126599t_unit] :
( ~ ( ord_le1023748749t_unit @ A @ ( domain2090798924t_unit @ B ) )
=> ( ( refine838861686t_unit @ B @ ( refine1777164439t_unit @ A ) )
= top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_abs__fun__simps_I3_J) ).
thf(1491,plain,
! [A: set_Product_unit,B: set_Pr451126599t_unit] :
( ~ ( ord_le1023748749t_unit @ A @ ( domain2090798924t_unit @ B ) )
=> ( ( refine838861686t_unit @ B @ ( refine1777164439t_unit @ A ) )
= top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(242,axiom,
! [A: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_nofail__simps_I3_J) ).
thf(1294,plain,
! [A: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(190,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( C @ E ) @ ( D @ E ) )
=> ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine96995669t_unit @ A @ C ) @ ( refine96995669t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(1077,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine787176636t_unit,D: a > refine787176636t_unit] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( C @ E ) @ ( D @ E ) )
=> ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine96995669t_unit @ A @ C ) @ ( refine96995669t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(335,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_conc__fun__strict) ).
thf(1607,plain,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(125,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord__eq__le__subst) ).
thf(832,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(245,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_abs__fun__simps_I1_J) ).
thf(1309,plain,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(286,axiom,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_inres__simps_I2_J) ).
thf(1442,plain,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(181,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le519537037nres_a @ ( C @ D ) @ A ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_pw__bind__leI) ).
thf(1045,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le519537037nres_a @ ( C @ D ) @ A ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(210,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = B )
=> ( ord_le1051254044t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_eq__refl) ).
thf(1161,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = B )
=> ( ord_le1051254044t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(117,axiom,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_conc__fun__FAIL) ).
thf(800,plain,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(61,axiom,
( ( (=) @ set_Pr1720557880unit_a )
= ( ^ [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
& ( ord_le2070001880unit_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_order__class_Oorder_Oeq__iff) ).
thf(620,plain,
( ( (=) @ set_Pr1720557880unit_a )
= ( ^ [A: set_Pr1720557880unit_a,B: set_Pr1720557880unit_a] :
( ( ord_le2070001880unit_a @ A @ B )
& ( ord_le2070001880unit_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(157,axiom,
! [A: set_Product_prod_a_a] :
( ( single_valued_a_a @ A )
=> ( refine2004812827nres_a @ ( refine1136779702un_a_a @ A ) @ ( refine1441824853un_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_ac__galois) ).
thf(950,plain,
! [A: set_Product_prod_a_a] :
( ( single_valued_a_a @ A )
=> ( refine2004812827nres_a @ ( refine1136779702un_a_a @ A ) @ ( refine1441824853un_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(223,axiom,
! [A: refine787176636t_unit,B: product_unit > refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ A @ B ) @ C )
= ( ( ( refine579265252t_unit @ C )
=> ( refine579265252t_unit @ A ) )
& ! [D: product_unit] :
( ( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ D ) )
=> ( ord_le1051254044t_unit @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_pw__bind__le__iff) ).
thf(1229,plain,
! [A: refine787176636t_unit,B: product_unit > refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ A @ B ) @ C )
= ( ( ( refine579265252t_unit @ C )
=> ( refine579265252t_unit @ A ) )
& ! [D: product_unit] :
( ( ( refine579265252t_unit @ A )
& ( refine558004794t_unit @ A @ D ) )
=> ( ord_le1051254044t_unit @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(314,axiom,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ bot_bo658782032t_unit @ A )
= bot_bo658782032t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_bind__SUCCEED) ).
thf(1546,plain,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ bot_bo658782032t_unit @ A )
= bot_bo658782032t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(273,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine2021053540t_unit @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_conc__trans) ).
thf(1395,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Pr1628433942t_unit,E: refine787176636t_unit] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine2021053540t_unit @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(121,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_abs__fun__simps_I1_J) ).
thf(818,plain,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(269,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_ord__le__eq__trans) ).
thf(1380,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(319,axiom,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ bot_bo658782032t_unit @ A )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_bind__SUCCEED) ).
thf(1561,plain,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ bot_bo658782032t_unit @ A )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(278,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( ord_le1051254044t_unit @ B @ A ) )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_le__nofailI) ).
thf(1410,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( ( refine579265252t_unit @ A )
=> ( ord_le1051254044t_unit @ B @ A ) )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(186,axiom,
! [A: set_Product_unit,B: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1420258419t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ ( insert_Product_unit @ B @ bot_bo1087887705t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_nres__order__simps_I22_J) ).
thf(1065,plain,
! [A: set_Product_unit,B: product_unit] :
( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1420258419t_unit @ B ) )
= ( ord_le1023748749t_unit @ A @ ( insert_Product_unit @ B @ bot_bo1087887705t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(87,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(696,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(336,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
=> ( A = bot_bo658782032t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_bot_Oextremum__uniqueI) ).
thf(1610,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
=> ( A = bot_bo658782032t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(263,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( refine1441824853un_a_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_conc__fun__fail__iff_I2_J) ).
thf(1363,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( refine1441824853un_a_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(247,axiom,
! [A: a,B: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nres__monad1) ).
thf(1314,plain,
! [A: a,B: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(177,axiom,
( refine327276970t_unit
= ( ^ [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a] :
! [C: refine424419629nres_a,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_galois__connection__def) ).
thf(1033,plain,
( refine327276970t_unit
= ( ^ [A: refine424419629nres_a > refine787176636t_unit,B: refine787176636t_unit > refine424419629nres_a] :
! [C: refine424419629nres_a,D: refine787176636t_unit] :
( ( ord_le519537037nres_a @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(240,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C )
= ( ( ( refine412683989fail_a @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_pw__bind__le__iff) ).
thf(1288,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C )
= ( ( ( refine412683989fail_a @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(217,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( ( refine944483349t_unit @ A @ B )
= top_to177290092t_unit )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_conc__fun__fail__iff_I1_J) ).
thf(1197,plain,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( ( refine944483349t_unit @ A @ B )
= top_to177290092t_unit )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(66,axiom,
( ( refine1001002027nres_a @ top_to231829469nres_a )
= ( ^ [A: a] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_inres__simps_I1_J) ).
thf(635,plain,
( ( refine1001002027nres_a @ top_to231829469nres_a )
= ( ^ [A: a] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(295,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ! [E: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( C @ E ) @ ( D @ E ) )
=> ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ A @ C ) @ ( refine681446406t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(1473,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: product_unit > refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ! [E: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( C @ E ) @ ( D @ E ) )
=> ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ A @ C ) @ ( refine681446406t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(95,axiom,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a] :
( ( single249782708unit_a @ A )
=> ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ A @ C ) )
= ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_conc__abs__swap) ).
thf(720,plain,
! [A: set_Pr1720557880unit_a,B: refine787176636t_unit,C: refine424419629nres_a] :
( ( single249782708unit_a @ A )
=> ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ A @ C ) )
= ( ord_le519537037nres_a @ ( refine364464487unit_a @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(211,axiom,
! [A: a,B: a] :
( ( ( refine2063221604TURN_a @ A )
= ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nres__more__simps_I6_J) ).
thf(1165,plain,
! [A: a,B: a] :
( ( ( refine2063221604TURN_a @ A )
= ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(139,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_SPEC__trans) ).
thf(886,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(149,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ A )
=> ( ord_le1051254044t_unit @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_dual__order_Otrans) ).
thf(928,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ A )
=> ( ord_le1051254044t_unit @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(18,axiom,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit,C: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ C )
=> ( ord_le1977877942t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order_Otrans) ).
thf(415,plain,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit,C: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ C )
=> ( ord_le1977877942t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_antisym) ).
thf(464,plain,
! [A: set_Pr1628433942t_unit,B: set_Pr1628433942t_unit] :
( ( ord_le1977877942t_unit @ A @ B )
=> ( ( ord_le1977877942t_unit @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(204,axiom,
! [A: set_a,B: set_Pr1628433942t_unit] :
( ~ ( ord_less_eq_set_a @ A @ ( domain799550107t_unit @ B ) )
=> ( ( refine341651653t_unit @ B @ ( refine1198353288_RES_a @ A ) )
= top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_abs__fun__simps_I3_J) ).
thf(1129,plain,
! [A: set_a,B: set_Pr1628433942t_unit] :
( ~ ( ord_less_eq_set_a @ A @ ( domain799550107t_unit @ B ) )
=> ( ( refine341651653t_unit @ B @ ( refine1198353288_RES_a @ A ) )
= top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(232,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_antisym) ).
thf(1261,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(311,axiom,
refine412683989fail_a @ bot_bo529555393nres_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nofail__simps_I4_J) ).
thf(1537,plain,
refine412683989fail_a @ bot_bo529555393nres_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(326,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
= ( A = bot_bo658782032t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nres__order__simps_I2_J) ).
thf(1582,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
= ( A = bot_bo658782032t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(31,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le2035129575t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le2035129575t_unit @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__subst2) ).
thf(459,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_Pr451126599t_unit,D: set_Pr451126599t_unit] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le2035129575t_unit @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le2035129575t_unit @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le2035129575t_unit @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(302,axiom,
( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_bot__nres__def) ).
thf(1500,plain,
( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(127,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_dual__order_Orefl) ).
thf(850,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(341,axiom,
! [A: set_Product_unit] :
( ( bot_bo658782032t_unit
= ( refine1777164439t_unit @ A ) )
= ( A = bot_bo1087887705t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_nres__more__simps_I1_J) ).
thf(1621,plain,
! [A: set_Product_unit] :
( ( bot_bo658782032t_unit
= ( refine1777164439t_unit @ A ) )
= ( A = bot_bo1087887705t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(201,axiom,
! [A: refine787176636t_unit,B: product_unit] :
( ~ ( refine579265252t_unit @ A )
=> ( refine558004794t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_not__nofail__inres) ).
thf(1120,plain,
! [A: refine787176636t_unit,B: product_unit] :
( ~ ( refine579265252t_unit @ A )
=> ( refine558004794t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(253,axiom,
! [A: set_Pr1720557880unit_a] :
( ( refine364464487unit_a @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_abs__fun__simps_I1_J) ).
thf(1331,plain,
! [A: set_Pr1720557880unit_a] :
( ( refine364464487unit_a @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(118,axiom,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ E ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( if_Ref1724547303nres_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Refine__Misc_Oif__mono) ).
thf(803,plain,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ E ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( if_Ref1724547303nres_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(3,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_order__subst1) ).
thf(354,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(292,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_order__subst1) ).
thf(1463,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ A @ ( B @ C ) )
=> ( ( ord_le1051254044t_unit @ C @ D )
=> ( ! [E: refine787176636t_unit,F: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ E @ F )
=> ( ord_le1051254044t_unit @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1051254044t_unit @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(289,axiom,
! [A: set_a,B: a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_nres__order__simps_I22_J) ).
thf(1449,plain,
! [A: set_a,B: a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(293,axiom,
( ( refine558004794t_unit @ top_to177290092t_unit )
= ( ^ [A: product_unit] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_inres__simps_I1_J) ).
thf(1468,plain,
( ( refine558004794t_unit @ top_to177290092t_unit )
= ( ^ [A: product_unit] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(5,axiom,
! [A: product_unit > $o,B: product_unit > $o] :
( ! [C: product_unit] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_Product_unit @ A )
= ( collect_Product_unit @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Collect__cong) ).
thf(364,plain,
! [A: product_unit > $o,B: product_unit > $o] :
( ! [C: product_unit] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_Product_unit @ A )
= ( collect_Product_unit @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(172,axiom,
( refine230495195t_unit
= ( ^ [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit] :
! [C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_galois__connection__def) ).
thf(1014,plain,
( refine230495195t_unit
= ( ^ [A: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit > refine787176636t_unit] :
! [C: refine787176636t_unit,D: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ C @ ( B @ D ) )
= ( ord_le1051254044t_unit @ ( A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(179,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1037,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(108,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_order__class_Oorder_Oeq__iff) ).
thf(775,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(104,axiom,
! [A: refine787176636t_unit > $o,B: refine787176636t_unit] :
( ( A @ B )
=> ( ! [C: refine787176636t_unit] :
( ( A @ C )
=> ( ord_le1051254044t_unit @ C @ B ) )
=> ( ( order_453013155t_unit @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_Greatest__equality) ).
thf(755,plain,
! [A: refine787176636t_unit > $o,B: refine787176636t_unit] :
( ( A @ B )
=> ( ! [C: refine787176636t_unit] :
( ( A @ C )
=> ( ord_le1051254044t_unit @ C @ B ) )
=> ( ( order_453013155t_unit @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(80,axiom,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( top_to231829469nres_a
= ( refine2021053540t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_conc__fun__fail__iff_I2_J) ).
thf(676,plain,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( top_to231829469nres_a
= ( refine2021053540t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1683,plain,
$false,
inference(e,[status(thm)],[892,1322,1168,518,1083,777,666,1549,352,628,1031,1200,1211,1005,730,1068,1618,1401,741,449,1269,597,523,582,878,655,1497,1426,384,797,472,814,945,670,1342,747,913,829,898,1576,782,841,973,1613,1601,1366,1518,1482,1254,724,570,785,1264,1059,1132,1319,1479,1115,1641,1494,1232,606,1347,1398,881,789,1373,1632,1334,821,480,981,397,1447,866,1526,660,428,1242,507,1564,1206,925,1306,1470,714,1057,1074,1604,942,439,910,1091,1355,1123,1570,1502,392,693,1042,952,1619,1370,625,1178,1296,1624,889,1281,1392,1291,456,1573,916,467,852,1555,682,1407,1592,1328,1375,1111,1138,869,420,1360,1350,697,1541,1567,884,1028,933,1461,901,1424,637,489,1644,706,1419,1414,526,1016,590,679,970,622,647,1588,1552,371,1086,1054,1035,1616,794,558,1071,1278,750,430,1273,1595,444,375,1135,1648,412,1251,618,423,1389,772,579,1520,1256,875,826,711,936,1312,498,1635,1107,1258,947,1638,540,764,406,1011,990,1439,451,567,509,649,863,1175,477,1080,631,1339,609,594,700,1325,895,769,811,387,858,367,959,780,394,1435,1102,658,685,1171,1445,1528,1113,563,1626,1203,531,663,1509,939,1145,553,1181,1003,855,640,1025,872,954,739,1368,409,993,690,1598,673,1452,791,441,585,717,1235,1317,1538,359,1579,1285,1220,544,1336,643,744,703,1506,727,1008,446,1240,1404,1358,1585,1094,978,1140,1421,931,688,1126,1646,1476,1062,652,390,1629,1523,418,1558,1276,1590,961,1385,1491,1294,1077,1607,832,1309,1442,1045,1161,800,620,950,1229,1546,1395,818,1380,1561,1410,1065,696,1610,1363,1314,1033,1288,1197,635,1473,720,1165,886,928,415,464,1129,1261,1537,1582,459,1500,850,1621,1120,1331,803,354,1463,1449,1468,364,1014,1037,775,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP164^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n016.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:09:20 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.38/1.25 % [INFO] Parsing done (443ms).
% 2.38/1.27 % [INFO] Running in sequential loop mode.
% 3.57/1.50 % [INFO] eprover registered as external prover.
% 3.57/1.51 % [INFO] Scanning for conjecture ...
% 3.93/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 357 axioms. Running axiom selection ...
% 4.32/1.71 % [INFO] Axiom selection finished. Selected 349 axioms (removed 8 axioms).
% 5.13/1.97 % [INFO] Problem is higher-order (TPTP THF).
% 5.13/2.00 % [INFO] Type checking passed.
% 5.13/2.00 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 22.59/6.41 % External prover 'e' found a proof!
% 22.59/6.41 % [INFO] Killing All external provers ...
% 22.59/6.41 % Time passed: 6049ms (effective reasoning time: 5141ms)
% 22.59/6.41 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 22.59/6.42 % Axioms used in derivation (349): fact_126_antisym, fact_341_SPEC__cons__rule, fact_240_not__nofail__inres, fact_345_nres__order__simps_I22_J, fact_206_abs__trans, fact_351_RETURN__def, fact_64_nres__order__simps_I3_J, fact_305_order__mono__setup_Omono__if, fact_24_nofail__simps_I4_J, fact_220_conc__trans, fact_12_abs__fun__strict, fact_157_Collect__cong, fact_241_not__nofail__inres, fact_318_nres__more__simps_I1_J, fact_149_mem__Collect__eq, fact_174_ord__le__eq__trans, fact_81_order__subst1, fact_2_bind__SUCCEED, fact_272_pw__abs__inres, fact_36_nofail__simps_I1_J, fact_161_antisym__conv, fact_306_ac__galois, fact_50_conc__fun__FAIL, fact_213_pw__le__iff, fact_86_order__subst2, fact_52_nres__order__simps_I20_J, fact_124_antisym, fact_0_bind__SUCCEED, fact_60_inres__simps_I3_J, fact_131_eq__refl, fact_180_dual__order_Orefl, fact_344_nres__order__simps_I22_J, fact_16_conc__fun__strict, fact_237_pw__conc__nofail, fact_73_conc__trans__additional_I1_J, fact_202_abs__trans, fact_207_abs__trans, fact_177_order__class_Oorder_Oantisym, fact_323_galois__connection__def, fact_102_ord__eq__le__subst, fact_319_nres__more__simps_I1_J, fact_40_conc__fun__fail__iff_I2_J, fact_231_top_Oextremum__uniqueI, fact_140_order_Otrans, fact_116_eq__iff, fact_232_pw__bind__le__iff, fact_4_nres__monad1, fact_217_conc__trans, fact_195_pw__eqI, fact_109_ord__le__eq__subst, fact_239_pw__conc__nofail, fact_78_order__subst1, fact_280_conc__abs__swap, fact_224_top_Oextremum__unique, fact_92_order__subst2, fact_7_nres__monad1, fact_311_abs__fun__simps_I3_J, fact_340_SPEC__cons__rule, fact_87_order__subst2, fact_32_nres__more__simps_I6_J, fact_328_galois__connection_Ointro, fact_248_pw__bind__nofail, fact_19_nres__inequalities_I5_J, fact_156_Collect__cong, fact_289_Greatest__equality, fact_91_order__subst2, fact_8_nres__monad2, fact_70_abs__trans__additional_I1_J, fact_281_conc__abs__swap, fact_3_bind__SUCCEED, fact_173_ord__eq__le__trans, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_39_inres__simps_I1_J, fact_267_nf__inres__def, fact_343_SPEC__trans, fact_22_nres__order__simps_I2_J, fact_80_order__subst1, fact_230_top_Oextremum__uniqueI, fact_260_nres__inequalities_I2_J, fact_295_flat__ord__compat_I2_J, fact_225_top_Oextremum__unique, fact_246_bot_Oextremum, fact_329_galois__connection_Ointro, fact_104_ord__eq__le__subst, fact_95_order__subst2, fact_127_antisym, fact_59_nofail__simps_I3_J, fact_65_nres__order__simps_I3_J, fact_160_antisym__conv, fact_181_dual__order_Orefl, fact_229_pw__bind__leI, fact_203_abs__trans, fact_252_bind__cong, fact_42_conc__fun__fail__iff_I2_J, fact_55_abs__fun__simps_I1_J, fact_249_pw__bind__nofail, fact_46_conc__fun__fail__iff_I1_J, fact_27_bind__FAIL, fact_186_pwD1, fact_155_Collect__mem__eq, fact_185_top__greatest, fact_66_nres__inequalities_I3_J, fact_154_Collect__mem__eq, fact_136_eq__refl, fact_107_ord__le__eq__subst, fact_283_conc__abs__swap, fact_141_order_Otrans, fact_166_order__class_Oorder_Oeq__iff, fact_300_conc__fun__R__mono, fact_325_galois__connection__def, fact_205_abs__trans, fact_5_nres__monad1, fact_183_dual__order_Otrans, fact_194_pw__eqI, fact_349_nres__more__simps_I5_J, fact_10_abs__fun__strict, fact_44_conc__fun__fail__iff_I1_J, fact_94_order__subst2, fact_216_conc__trans, fact_170_order__class_Oorder_Oeq__iff, fact_47_conc__fun__fail__iff_I1_J, fact_268_meta__le__everything__if__top, fact_189_pwD2, fact_291_Refine__Misc_Oif__mono, fact_228_pw__bind__leI, fact_29_bind__FAIL, fact_322_galois__connection__def, fact_133_eq__refl, fact_292_flat__ord__compat_I1_J, fact_43_conc__fun__fail__iff_I2_J, fact_307_ac__galois, fact_234_pw__bind__le__iff, fact_93_order__subst2, fact_51_conc__fun__FAIL, fact_282_conc__abs__swap, fact_258_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_274_pw__abs__inres, fact_89_order__subst2, fact_304_order__mono__setup_Omono__if, fact_196_pw__leI, fact_184_top__greatest, fact_76_order__subst1, fact_88_order__subst2, fact_167_order__class_Oorder_Oeq__iff, fact_256_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_135_eq__refl, fact_204_abs__trans, fact_334_nres__order__simps_I5_J, fact_321_nres__order__simps_I21_J, fact_245_bot_Oextremum__unique, fact_1_bind__SUCCEED, fact_100_ord__eq__le__subst, fact_56_abs__fun__simps_I1_J, fact_243_bot_Oextremum__uniqueI, fact_11_abs__fun__strict, fact_261_nres__inequalities_I2_J, fact_279_pw__abs__nofail, fact_290_Refine__Misc_Oif__mono, fact_253_bind__cong, fact_235_pw__bind__le__iff, fact_132_eq__refl, fact_276_pw__abs__nofail, fact_326_galois__connection_Ointro, fact_293_flat__ord__compat_I1_J, fact_301_conc__fun__R__mono, fact_138_order_Otrans, fact_187_pwD1, fact_332_galois__connection_Ogalois, fact_26_bind__FAIL, fact_262_nres__inequalities_I4_J, fact_273_pw__abs__inres, fact_169_order__class_Oorder_Oeq__iff, fact_176_order__class_Oorder_Oantisym, fact_190_dual__order_Oeq__iff, fact_337_less__eq__nres_Osimps_I2_J, fact_302_conc__fun__R__mono, fact_25_nofail__simps_I4_J, fact_327_galois__connection_Ointro, fact_275_pw__abs__inres, fact_313_abs__fun__simps_I3_J, fact_314_inres__simps_I2_J, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_182_dual__order_Otrans, fact_58_nofail__simps_I3_J, fact_348_nres__more__simps_I5_J, fact_53_nres__order__simps_I20_J, fact_96_ord__eq__le__subst, fact_191_dual__order_Oeq__iff, fact_75_conc__trans__additional_I1_J, fact_312_abs__fun__simps_I3_J, fact_84_order__subst1, fact_244_bot_Oextremum__unique, fact_31_nres__order__simps_I1_J, fact_115_ord__le__eq__subst, fact_129_antisym, fact_163_antisym__conv, fact_6_nres__monad1, fact_98_ord__eq__le__subst, fact_139_order_Otrans, fact_254_bind__cong, fact_34_nres__order__simps_I4_J, fact_336_less__eq__nres_Osimps_I2_J, fact_350_RETURN__def, fact_238_pw__conc__nofail, fact_342_SPEC__trans, fact_310_abs__fun__simps_I3_J, fact_222_le__nofailI, fact_315_inres__simps_I2_J, fact_294_flat__ord__compat_I2_J, fact_74_conc__trans__additional_I1_J, fact_214_conc__trans, fact_114_ord__le__eq__subst, fact_227_pw__bind__leI, fact_121_eq__iff, fact_62_intro__nofail_I2_J, fact_320_nres__order__simps_I21_J, fact_33_nres__more__simps_I6_J, fact_316_nres__more__simps_I2_J, fact_117_eq__iff, fact_67_nres__inequalities_I3_J, fact_288_Greatest__equality, fact_20_inres__simps_I4_J, fact_17_conc__fun__strict, fact_303_conc__fun__R__mono, fact_270_pw__flat__le__iff, fact_120_eq__iff, fact_287_GreatestI2__order, fact_106_ord__le__eq__subst, fact_333_galois__connection_Ogalois, fact_15_conc__fun__strict, fact_209_inres__def, fact_317_nres__more__simps_I2_J, fact_298_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_111_ord__le__eq__subst, fact_251_pw__bind__nofail, fact_199_pw__leI_H, fact_330_galois__connection_Ogalois, fact_250_pw__bind__nofail, fact_130_eq__refl, fact_271_pw__flat__le__iff, fact_210_pw__eq__iff, fact_339_bot__nres__def, fact_269_meta__le__everything__if__top, fact_233_pw__bind__le__iff, fact_122_eq__iff, fact_23_nres__order__simps_I2_J, fact_201_abs__trans, fact_77_order__subst1, fact_178_order__trans, fact_212_pw__le__iff, fact_263_nres__inequalities_I4_J, fact_346_nres__more__simps_I3_J, fact_192_dual__order_Oantisym, fact_226_pw__bind__leI, fact_30_nres__order__simps_I1_J, fact_90_order__subst2, fact_264_order__mono__setup_Orefl, fact_219_conc__trans, fact_247_bot_Oextremum, fact_118_eq__iff, fact_113_ord__le__eq__subst, fact_331_galois__connection_Ogalois, fact_211_pw__eq__iff, fact_68_abs__trans__additional_I1_J, fact_165_order__class_Oorder_Oeq__iff, fact_143_order_Otrans, fact_221_conc__trans, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_134_eq__refl, fact_108_ord__le__eq__subst, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_101_ord__eq__le__subst, fact_35_nres__order__simps_I4_J, fact_9_nres__monad2, fact_97_ord__eq__le__subst, fact_286_GreatestI2__order, fact_159_antisym__conv, fact_63_intro__nofail_I2_J, fact_99_ord__eq__le__subst, fact_193_dual__order_Oantisym, fact_200_abs__trans, fact_299_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_309_ac__galois, fact_28_bind__FAIL, fact_335_nres__order__simps_I5_J, fact_296_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_175_ord__le__eq__trans, fact_284_pw__flat__ge__iff, fact_257_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_71_abs__trans__additional_I1_J, fact_103_ord__eq__le__subst, fact_242_bot_Oextremum__uniqueI, fact_347_nres__more__simps_I3_J, fact_218_conc__trans, fact_297_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_223_le__nofailI, fact_54_abs__fun__simps_I1_J, fact_278_pw__abs__nofail, fact_41_conc__fun__fail__iff_I2_J, fact_112_ord__le__eq__subst, fact_266_nf__inres__def, fact_142_order_Otrans, fact_48_conc__fun__FAIL, fact_57_abs__fun__simps_I1_J, fact_79_order__subst1, fact_198_pw__leI_H, fact_179_order__trans, fact_324_galois__connection__def, fact_69_abs__trans__additional_I1_J, fact_13_abs__fun__strict, fact_158_antisym__conv, fact_45_conc__fun__fail__iff_I1_J, fact_148_mem__Collect__eq, fact_215_conc__trans, fact_188_pwD2, fact_285_pw__flat__ge__iff, fact_82_order__subst1, fact_338_bot__nres__def, fact_38_inres__simps_I1_J, fact_197_pw__leI, help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_21_inres__simps_I4_J, fact_168_order__class_Oorder_Oeq__iff, fact_123_antisym, fact_208_inres__def, fact_37_nofail__simps_I1_J, fact_85_order__subst1, fact_164_antisym__conv, fact_119_eq__iff, fact_49_conc__fun__FAIL, fact_18_nres__inequalities_I5_J, fact_172_ord__eq__le__trans, fact_105_ord__eq__le__subst, fact_110_ord__le__eq__subst, fact_308_ac__galois, fact_236_pw__conc__nofail, fact_125_antisym, fact_61_inres__simps_I3_J, fact_72_conc__trans__additional_I1_J, fact_255_bind__cong, fact_128_antisym, fact_259_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_14_conc__fun__strict, fact_277_pw__abs__nofail, fact_162_antisym__conv, fact_171_order__class_Oorder_Oeq__iff, fact_83_order__subst1, fact_265_order__mono__setup_Orefl, fact_137_order_Otrans
% 22.59/6.42 % No. of inferences in proof: 702
% 22.59/6.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6049 ms resp. 5141 ms w/o parsing
% 24.04/6.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.04/6.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------