TSTP Solution File: ITP161^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:21 EDT 2024
% Result : Theorem 33.88s 7.95s
% Output : Refutation 34.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 500
% Syntax : Number of formulae : 859 ( 290 unt; 143 typ; 0 def)
% Number of atoms : 2000 ( 526 equ; 20 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 6231 ( 216 ~; 1 |; 58 &;4872 @)
% ( 0 <=>;1084 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 568 ( 568 >; 0 *; 0 +; 0 <<)
% Number of symbols : 121 ( 117 usr; 13 con; 0-4 aty)
% Number of variables : 2123 ( 82 ^2003 !; 38 ?;2123 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1587512412nres_b_type,type,
produc1587512412nres_b: $tType ).
thf(produc1609974940nres_a_type,type,
produc1609974940nres_a: $tType ).
thf(set_Pr451126599t_unit_type,type,
set_Pr451126599t_unit: $tType ).
thf(refine2031285398od_b_b_type,type,
refine2031285398od_b_b: $tType ).
thf(refine891721109od_b_a_type,type,
refine891721109od_b_a: $tType ).
thf(refine1811374551od_a_b_type,type,
refine1811374551od_a_b: $tType ).
thf(refine671810262od_a_a_type,type,
refine671810262od_a_a: $tType ).
thf(refine787176636t_unit_type,type,
refine787176636t_unit: $tType ).
thf(set_Pr1707992533t_unit_type,type,
set_Pr1707992533t_unit: $tType ).
thf(set_Pr1628433942t_unit_type,type,
set_Pr1628433942t_unit: $tType ).
thf(refine432681134nres_b_type,type,
refine432681134nres_b: $tType ).
thf(refine424419629nres_a_type,type,
refine424419629nres_a: $tType ).
thf(set_Product_prod_b_b_type,type,
set_Product_prod_b_b: $tType ).
thf(set_Product_prod_b_a_type,type,
set_Product_prod_b_a: $tType ).
thf(set_Product_prod_a_b_type,type,
set_Product_prod_a_b: $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_b_b_type,type,
product_prod_b_b: $tType ).
thf(product_prod_b_a_type,type,
product_prod_b_a: $tType ).
thf(product_prod_a_b_type,type,
product_prod_a_b: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(set_b_type,type,
set_b: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(if_o_R1705037948nres_a_type,type,
if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
thf(if_o_R697118589nres_b_type,type,
if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
thf(if_Ref1369692790t_unit_type,type,
if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(if_Ref1724547303nres_a_type,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(if_Ref1732808808nres_b_type,type,
if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(if_set_a_type,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(if_set_b_type,type,
if_set_b: $o > set_b > set_b > set_b ).
thf(ord_le516598614nres_a_type,type,
ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
thf(ord_le1656162903nres_b_type,type,
ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
thf(ord_le915866422od_a_a_type,type,
ord_le915866422od_a_a: refine671810262od_a_a > refine671810262od_a_a > $o ).
thf(ord_le2055430711od_a_b_type,type,
ord_le2055430711od_a_b: refine1811374551od_a_b > refine1811374551od_a_b > $o ).
thf(ord_le1135777269od_b_a_type,type,
ord_le1135777269od_b_a: refine891721109od_b_a > refine891721109od_b_a > $o ).
thf(ord_le127857910od_b_b_type,type,
ord_le127857910od_b_b: refine2031285398od_b_b > refine2031285398od_b_b > $o ).
thf(ord_le1051254044t_unit_type,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(ord_le519537037nres_a_type,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(ord_le527798542nres_b_type,type,
ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ord_less_eq_set_b_type,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(order_1714329108nres_a_type,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(order_1722590613nres_b_type,type,
order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
thf(top_top_a_o_type,type,
top_top_a_o: a > $o ).
thf(top_to177290092t_unit_type,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(top_to231829469nres_a_type,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(top_to240090974nres_b_type,type,
top_to240090974nres_b: refine432681134nres_b ).
thf(top_top_set_a_type,type,
top_top_set_a: set_a ).
thf(top_top_set_b_type,type,
top_top_set_b: set_b ).
thf(partia1658438072t_unit_type,type,
partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
thf(partia906949161nres_a_type,type,
partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
thf(partia915210666nres_b_type,type,
partia915210666nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b > $o ).
thf(produc1136923598nres_a_type,type,
produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
thf(produc2130641934nres_b_type,type,
produc2130641934nres_b: refine432681134nres_b > refine432681134nres_b > produc1587512412nres_b ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(product_Pair_a_b_type,type,
product_Pair_a_b: a > b > product_prod_a_b ).
thf(product_Pair_b_a_type,type,
product_Pair_b_a: b > a > product_prod_b_a ).
thf(product_Pair_b_b_type,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(refine2039610767ASSERT_type,type,
refine2039610767ASSERT: $o > refine787176636t_unit ).
thf(refine1420258419t_unit_type,type,
refine1420258419t_unit: product_unit > refine787176636t_unit ).
thf(refine2063221604TURN_a_type,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine2063221605TURN_b_type,type,
refine2063221605TURN_b: b > refine432681134nres_b ).
thf(refine838861686t_unit_type,type,
refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(refine341651653t_unit_type,type,
refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit ).
thf(refine1136779702un_a_a_type,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine1136779703un_a_b_type,type,
refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
thf(refine460904452t_unit_type,type,
refine460904452t_unit: set_Pr1707992533t_unit > refine432681134nres_b > refine787176636t_unit ).
thf(refine1964549109un_b_a_type,type,
refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
thf(refine1964549110un_b_b_type,type,
refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(refine988994910_a_a_b_type,type,
refine988994910_a_a_b: refine671810262od_a_a > ( product_prod_a_a > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine681446406t_unit_type,type,
refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(refine119808503unit_a_type,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine119808504unit_b_type,type,
refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine96995669t_unit_type,type,
refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
thf(refine436832838nd_a_a_type,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine436832839nd_a_b_type,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine216248468t_unit_type,type,
refine216248468t_unit: refine432681134nres_b > ( b > refine787176636t_unit ) > refine787176636t_unit ).
thf(refine1264602245nd_b_a_type,type,
refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine1264602246nd_b_b_type,type,
refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine944483349t_unit_type,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(refine2021053540t_unit_type,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(refine1441824853un_a_a_type,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine1441824854un_a_b_type,type,
refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
thf(refine2140306339t_unit_type,type,
refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
thf(refine122110612un_b_a_type,type,
refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
thf(refine122110613un_b_b_type,type,
refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(refine558004794t_unit_type,type,
refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
thf(refine1001002027nres_a_type,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(refine1001002028nres_b_type,type,
refine1001002028nres_b: refine432681134nres_b > b > $o ).
thf(refine378960780od_a_a_type,type,
refine378960780od_a_a: refine671810262od_a_a > product_prod_a_a > $o ).
thf(refine387222285od_a_b_type,type,
refine387222285od_a_b: refine1811374551od_a_b > product_prod_a_b > $o ).
thf(refine1206730187od_b_a_type,type,
refine1206730187od_b_a: refine891721109od_b_a > product_prod_b_a > $o ).
thf(refine1214991692od_b_b_type,type,
refine1214991692od_b_b: refine2031285398od_b_b > product_prod_b_b > $o ).
thf(refine983493746t_unit_type,type,
refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
thf(refine1312857699nres_a_type,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(refine1312857700nres_b_type,type,
refine1312857700nres_b: refine432681134nres_b > b > $o ).
thf(refine579265252t_unit_type,type,
refine579265252t_unit: refine787176636t_unit > $o ).
thf(refine412683989fail_a_type,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(refine412683990fail_b_type,type,
refine412683990fail_b: refine432681134nres_b > $o ).
thf(refine1607584204t_unit_type,type,
refine1607584204t_unit: refine787176636t_unit ).
thf(refine464223677AILi_a_type,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(refine464223678AILi_b_type,type,
refine464223678AILi_b: refine432681134nres_b ).
thf(refine622451633od_a_a_type,type,
refine622451633od_a_a: set_Product_prod_a_a > refine671810262od_a_a ).
thf(refine630713138od_a_b_type,type,
refine630713138od_a_b: set_Product_prod_a_b > refine1811374551od_a_b ).
thf(refine1450221040od_b_a_type,type,
refine1450221040od_b_a: set_Product_prod_b_a > refine891721109od_b_a ).
thf(refine1458482545od_b_b_type,type,
refine1458482545od_b_b: set_Product_prod_b_b > refine2031285398od_b_b ).
thf(refine1777164439t_unit_type,type,
refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
thf(refine1198353288_RES_a_type,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(refine1198353289_RES_b_type,type,
refine1198353289_RES_b: set_b > refine432681134nres_b ).
thf(refine1208325748t_unit_type,type,
refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
thf(refine1822134885_RES_a_type,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(refine1822134886_RES_b_type,type,
refine1822134886_RES_b: refine432681134nres_b > set_b ).
thf(domain799550107t_unit_type,type,
domain799550107t_unit: set_Pr1628433942t_unit > set_a ).
thf(domain_a_a_type,type,
domain_a_a: set_Product_prod_a_a > set_a ).
thf(domain_a_b_type,type,
domain_a_b: set_Product_prod_a_b > set_a ).
thf(domain918802906t_unit_type,type,
domain918802906t_unit: set_Pr1707992533t_unit > set_b ).
thf(domain_b_a_type,type,
domain_b_a: set_Product_prod_b_a > set_b ).
thf(domain_b_b_type,type,
domain_b_b: set_Product_prod_b_b > set_b ).
thf(image_a_a_type,type,
image_a_a: set_Product_prod_a_a > set_a > set_a ).
thf(image_a_b_type,type,
image_a_b: set_Product_prod_a_b > set_a > set_b ).
thf(image_b_a_type,type,
image_b_a: set_Product_prod_b_a > set_b > set_a ).
thf(image_b_b_type,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(collec645855634od_a_a_type,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collec654117139od_a_b_type,type,
collec654117139od_a_b: ( product_prod_a_b > $o ) > set_Product_prod_a_b ).
thf(collec1473625041od_b_a_type,type,
collec1473625041od_b_a: ( product_prod_b_a > $o ) > set_Product_prod_b_a ).
thf(collec1481886546od_b_b_type,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(collect_Product_unit_type,type,
collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(collect_b_type,type,
collect_b: ( b > $o ) > set_b ).
thf(member449909584od_a_a_type,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member458171089od_a_b_type,type,
member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
thf(member1277678991od_b_a_type,type,
member1277678991od_b_a: product_prod_b_a > set_Product_prod_b_a > $o ).
thf(member1285940496od_b_b_type,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(member_Product_unit_type,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(member_b_type,type,
member_b: b > set_b > $o ).
thf(phi_type,type,
phi: a > $o ).
thf(f_type,type,
f: a > refine432681134nres_b ).
thf(m_type,type,
m: refine432681134nres_b ).
thf(x_type,type,
x: a ).
thf(286,axiom,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_nres_Oinject) ).
thf(1322,plain,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(291,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ord__le__eq__subst) ).
thf(1337,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(301,axiom,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_nres__order__simps_I21_J) ).
thf(1411,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)],[301]) ).
thf(250,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_SPEC__rule) ).
thf(1190,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(262,axiom,
! [A: set_b,B: b > $o] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_RES__rule) ).
thf(1237,plain,
! [A: set_b,B: b > $o] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(171,axiom,
! [A: set_b] :
( ( refine1822134886_RES_b @ ( refine1198353289_RES_b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_the__RES_Osimps) ).
thf(909,plain,
! [A: set_b] :
( ( refine1822134886_RES_b @ ( refine1198353289_RES_b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(165,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( refine378960780od_a_a @ ( refine622451633od_a_a @ A ) @ B )
= ( member449909584od_a_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nf__inres__RES) ).
thf(893,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( refine378960780od_a_a @ ( refine622451633od_a_a @ A ) @ B )
= ( member449909584od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(284,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: a,E: refine424419629nres_a,F: set_Product_prod_a_b,G: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( refine1001002027nres_a @ A @ D )
=> ( ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ H ) @ B )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( G @ H ) ) ) )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_rhs__step__bind) ).
thf(1315,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: a,E: refine424419629nres_a,F: set_Product_prod_a_b,G: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( refine1001002027nres_a @ A @ D )
=> ( ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ H ) @ B )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( G @ H ) ) ) )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(39,axiom,
! [A: set_b] :
( ( refine1001002028nres_b @ ( refine1198353289_RES_b @ A ) )
= ( ^ [B: b] : ( member_b @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_inres__simps_I2_J) ).
thf(479,plain,
! [A: set_b] :
( ( refine1001002028nres_b @ ( refine1198353289_RES_b @ A ) )
= ( ^ [B: b] : ( member_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(225,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > refine432681134nres_b,D: b > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ! [E: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ E ) @ A )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ A @ C ) @ ( refine1264602246nd_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1105,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > refine432681134nres_b,D: b > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ! [E: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ E ) @ A )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ A @ C ) @ ( refine1264602246nd_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(253,axiom,
! [A: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_the__RES__inv) ).
thf(1200,plain,
! [A: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(192,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_RETURN__rule) ).
thf(977,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(299,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_eq__iff) ).
thf(1406,plain,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',fact_102_order_Otrans) ).
thf(730,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)],[112]) ).
thf(326,axiom,
! [A: set_a,B: set_b,C: set_Product_prod_a_b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: b] :
( ( member_b @ E @ B )
& ( member458171089od_a_b @ ( product_Pair_a_b @ D @ E ) @ C ) ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1441824854un_a_b @ C @ ( refine1198353289_RES_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_RES__refine) ).
thf(1522,plain,
! [A: set_a,B: set_b,C: set_Product_prod_a_b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: b] :
( ( member_b @ E @ B )
& ( member458171089od_a_b @ ( product_Pair_a_b @ D @ E ) @ C ) ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1441824854un_a_b @ C @ ( refine1198353289_RES_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(198,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( C @ B ) @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_order__subst2) ).
thf(994,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( C @ B ) @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(30,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__class_Oorder_Oantisym) ).
thf(449,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)],[30]) ).
thf(281,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: refine432681134nres_b,D: product_prod_a_a > refine432681134nres_b] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine988994910_a_a_b @ ( refine622451633od_a_a @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_RES__bind__choose) ).
thf(1305,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: refine432681134nres_b,D: product_prod_a_a > refine432681134nres_b] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine988994910_a_a_b @ ( refine622451633od_a_a @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(207,axiom,
! [A: $o,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b,E: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ E ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ ( if_Ref1732808808nres_b @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Refine__Misc_Oif__mono) ).
thf(1041,plain,
! [A: $o,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b,E: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ E ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ ( if_Ref1732808808nres_b @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(68,axiom,
! [A: set_Product_prod_b_a,B: product_prod_b_a] :
( ( refine1206730187od_b_a @ ( refine1450221040od_b_a @ A ) @ B )
= ( member1277678991od_b_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nf__inres__RES) ).
thf(582,plain,
! [A: set_Product_prod_b_a,B: product_prod_b_a] :
( ( refine1206730187od_b_a @ ( refine1450221040od_b_a @ A ) @ B )
= ( member1277678991od_b_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: set_b,B: set_Product_prod_b_b] :
( ( ord_less_eq_set_b @ A @ ( domain_b_b @ B ) )
=> ( ( refine1964549110un_b_b @ B @ ( refine1198353289_RES_b @ A ) )
= ( refine1198353289_RES_b @ ( image_b_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_abs__fun__simps_I2_J) ).
thf(762,plain,
! [A: set_b,B: set_Product_prod_b_b] :
( ( ord_less_eq_set_b @ A @ ( domain_b_b @ B ) )
=> ( ( refine1964549110un_b_b @ B @ ( refine1198353289_RES_b @ A ) )
= ( refine1198353289_RES_b @ ( image_b_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(8,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__funE) ).
thf(379,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(272,axiom,
! [A: a > $o,B: a,C: refine432681134nres_b,D: set_Product_prod_b_b,E: a > refine432681134nres_b] :
( ( A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( E @ B ) ) )
=> ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rhs__step__bind__SPEC) ).
thf(1269,plain,
! [A: a > $o,B: a,C: refine432681134nres_b,D: set_Product_prod_b_b,E: a > refine432681134nres_b] :
( ( A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( E @ B ) ) )
=> ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(161,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( refine1214991692od_b_b @ ( refine1458482545od_b_b @ A ) @ B )
= ( member1285940496od_b_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nf__inres__RES) ).
thf(878,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( refine1214991692od_b_b @ ( refine1458482545od_b_b @ A ) @ B )
= ( member1285940496od_b_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(28,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_meta__le__everything__if__top) ).
thf(440,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(384,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)],[10]) ).
thf(236,axiom,
! [A: a,B: set_a,C: refine432681134nres_b,D: set_Product_prod_b_b,E: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( E @ A ) ) )
=> ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_rhs__step__bind__RES) ).
thf(1137,plain,
! [A: a,B: set_a,C: refine432681134nres_b,D: set_Product_prod_b_b,E: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( E @ A ) ) )
=> ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(53,axiom,
! [A: b] : ( member_b @ A @ top_top_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_UNIV__I) ).
thf(533,plain,
! [A: b] : ( member_b @ A @ top_top_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(108,axiom,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_ImageE) ).
thf(715,plain,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(36,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_UNIV__I) ).
thf(472,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(269,axiom,
! [A: refine424419629nres_a,B: set_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ B ) )
=> ( refine412683989fail_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_le__RES__nofailI) ).
thf(1260,plain,
! [A: refine424419629nres_a,B: set_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ B ) )
=> ( refine412683989fail_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(55,axiom,
! [A: set_b,B: b > $o] :
( ( ord_less_eq_set_b @ A @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_subset__Collect__conv) ).
thf(538,plain,
! [A: set_b,B: b > $o] :
( ( ord_less_eq_set_b @ A @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(177,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_top_Oextremum__uniqueI) ).
thf(930,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(242,axiom,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b] :
( ( A @ B )
=> ( ! [C: refine432681134nres_b] :
( ( A @ C )
=> ( ord_le527798542nres_b @ C @ B ) )
=> ( ( order_1722590613nres_b @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Greatest__equality) ).
thf(1164,plain,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b] :
( ( A @ B )
=> ( ! [C: refine432681134nres_b] :
( ( A @ C )
=> ( ord_le527798542nres_b @ C @ B ) )
=> ( ( order_1722590613nres_b @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',fact_170_pwD2) ).
thf(797,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)],[135]) ).
thf(167,axiom,
! [A: a,B: set_a,C: b,D: set_Product_prod_a_b] :
( ( member_a @ A @ B )
=> ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_a_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_rev__ImageI) ).
thf(898,plain,
! [A: a,B: set_a,C: b,D: set_Product_prod_a_b] :
( ( member_a @ A @ B )
=> ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_a_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(200,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ A )
=> ( ord_le527798542nres_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_dual__order_Otrans) ).
thf(1001,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ A )
=> ( ord_le527798542nres_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(264,axiom,
! [A: a,B: set_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( E @ A ) ) )
=> ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_rhs__step__bind__RES) ).
thf(1243,plain,
! [A: a,B: set_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( E @ A ) ) )
=> ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(106,axiom,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_nres_Oinject) ).
thf(709,plain,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(22,axiom,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_ibind__strict_I2_J) ).
thf(417,plain,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(163,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ( C = D )
=> ( ord_le519537037nres_a @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_ord__eq__le__eq__trans) ).
thf(885,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ( C = D )
=> ( ord_le519537037nres_a @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(351,axiom,
! [A: refine432681134nres_b,B: refine424419629nres_a,C: a > refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le527798542nres_b @ ( C @ D ) @ A ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_pw__bind__leI) ).
thf(1601,plain,
! [A: refine432681134nres_b,B: refine424419629nres_a,C: a > refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [D: a] :
( ( refine412683989fail_a @ B )
=> ( ( refine1001002027nres_a @ B @ D )
=> ( ord_le527798542nres_b @ ( C @ D ) @ A ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(267,axiom,
! [A: refine432681134nres_b,B: a,C: set_Product_prod_a_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824854un_a_b @ C @ A ) )
= ( ? [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ B @ D ) @ C )
& ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ret__le__down__conv) ).
thf(1254,plain,
! [A: refine432681134nres_b,B: a,C: set_Product_prod_a_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824854un_a_b @ C @ A ) )
= ( ? [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ B @ D ) @ C )
& ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(89,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_subsetI) ).
thf(651,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(146,axiom,
! [A: refine432681134nres_b] :
( ( refine412683990fail_b @ A )
=> ( ( refine1198353289_RES_b @ ( refine1822134886_RES_b @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_the__RES__inv) ).
thf(829,plain,
! [A: refine432681134nres_b] :
( ( refine412683990fail_b @ A )
=> ( ( refine1198353289_RES_b @ ( refine1822134886_RES_b @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(221,axiom,
( refine1001002028nres_b
= ( ^ [A: refine432681134nres_b,B: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inres__def) ).
thf(1095,plain,
( refine1001002028nres_b
= ( ^ [A: refine432681134nres_b,B: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(17,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T) ).
thf(404,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(110,axiom,
! [A: product_unit,B: set_Product_unit,C: refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine681446406t_unit @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_RES__bind__choose) ).
thf(724,plain,
! [A: product_unit,B: set_Product_unit,C: refine787176636t_unit,D: product_unit > refine787176636t_unit] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine681446406t_unit @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(46,axiom,
! [A: a,B: b,C: set_Product_prod_a_b,D: set_a] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ C )
=> ( ( member_a @ A @ D )
=> ( member_b @ B @ ( image_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_ImageI) ).
thf(504,plain,
! [A: a,B: b,C: set_Product_prod_a_b,D: set_a] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ C )
=> ( ( member_a @ A @ D )
=> ( member_b @ B @ ( image_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(324,axiom,
( ord_le1656162903nres_b
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_le527798542nres_b @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_le__rel__bool__arg__iff) ).
thf(1511,plain,
( ord_le1656162903nres_b
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_le527798542nres_b @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(137,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_antisym) ).
thf(802,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)],[137]) ).
thf(283,axiom,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] :
? [B: set_a] :
( A
= ( refine1198353288_RES_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_nofail__RES__conv) ).
thf(1313,plain,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] :
? [B: set_a] :
( A
= ( refine1198353288_RES_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(234,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_dual__order_Orefl) ).
thf(1132,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(32,axiom,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ B ) )
=> ( ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ refine464223678AILi_b ) )
=> ~ ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_less__nres_Ocases) ).
thf(460,plain,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ B ) )
=> ( ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ refine464223678AILi_b ) )
=> ~ ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(343,axiom,
! [A: b,B: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine2063221605TURN_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_nres__order__simps_I20_J) ).
thf(1577,plain,
! [A: b,B: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine2063221605TURN_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(311,axiom,
! [A: set_a] :
( refine464223677AILi_a
!= ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_nres_Odistinct_I1_J) ).
thf(1455,plain,
! [A: set_a] :
( refine464223677AILi_a
!= ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(332,axiom,
phi @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(1545,plain,
phi @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(142,axiom,
! [A: b,B: set_b,C: refine787176636t_unit,D: b > refine787176636t_unit] :
( ( member_b @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine216248468t_unit @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_RES__bind__choose) ).
thf(817,plain,
! [A: b,B: set_b,C: refine787176636t_unit,D: b > refine787176636t_unit] :
( ( member_b @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine216248468t_unit @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(62,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T) ).
thf(559,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(218,axiom,
! [A: set_a,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ A ) @ B )
= ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_nf__inres__RES) ).
thf(1087,plain,
! [A: set_a,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ A ) @ B )
= ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(352,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( B != refine464223678AILi_b )
=> ~ ! [C: set_b] :
( ( A
= ( refine1198353289_RES_b @ C ) )
=> ! [D: set_b] :
( ( B
= ( refine1198353289_RES_b @ D ) )
=> ~ ( ord_less_eq_set_b @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_less__eq__nres_Oelims_I2_J) ).
thf(1609,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( B != refine464223678AILi_b )
=> ~ ! [C: set_b] :
( ( A
= ( refine1198353289_RES_b @ C ) )
=> ! [D: set_b] :
( ( B
= ( refine1198353289_RES_b @ D ) )
=> ~ ( ord_less_eq_set_b @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(75,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(606,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',fact_31_SPEC__cons__rule) ).
thf(881,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)],[162]) ).
thf(319,axiom,
! [A: refine424419629nres_a,B: refine432681134nres_b > refine424419629nres_a,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order__subst1) ).
thf(1494,plain,
! [A: refine424419629nres_a,B: refine432681134nres_b > refine424419629nres_a,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(296,axiom,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: b > $o,D: a > refine432681134nres_b,E: b > $o] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le527798542nres_b @ ( B @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le527798542nres_b @ ( D @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bind__sim__select__rule) ).
thf(1362,plain,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: b > $o,D: a > refine432681134nres_b,E: b > $o] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le527798542nres_b @ ( B @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le527798542nres_b @ ( D @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(223,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( partia915210666nres_b @ top_to240090974nres_b @ A @ B )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_flat__ord__compat_I2_J) ).
thf(1100,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( partia915210666nres_b @ top_to240090974nres_b @ A @ B )
=> ( ord_le527798542nres_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(285,axiom,
! [A: set_a,B: a > refine432681134nres_b,C: b] :
( ( refine1001002028nres_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ A ) @ B ) @ C )
= ( ? [D: a] :
( ( member_a @ D @ A )
& ( refine1001002028nres_b @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_pw__RES__bind__choose_I2_J) ).
thf(1319,plain,
! [A: set_a,B: a > refine432681134nres_b,C: b] :
( ( refine1001002028nres_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ A ) @ B ) @ C )
= ( ? [D: a] :
( ( member_a @ D @ A )
& ( refine1001002028nres_b @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(158,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_nres__order__simps_I3_J) ).
thf(870,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(132,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ refine464223677AILi_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_less__eq__nres_Osimps_I1_J) ).
thf(789,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ refine464223677AILi_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(226,axiom,
( ord_le527798542nres_b
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( refine412683990fail_b @ B )
=> ( ( refine412683990fail_b @ A )
& ! [C: b] :
( ( refine1001002028nres_b @ A @ C )
=> ( refine1001002028nres_b @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_pw__le__iff) ).
thf(1109,plain,
( ord_le527798542nres_b
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( refine412683990fail_b @ B )
=> ( ( refine412683990fail_b @ A )
& ! [C: b] :
( ( refine1001002028nres_b @ A @ C )
=> ( refine1001002028nres_b @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(7,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__funD) ).
thf(376,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(80,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_subset__eq) ).
thf(623,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(204,axiom,
! [A: a] :
( ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ A ) ) )
= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_SPEC__eq__is__RETURN_I1_J) ).
thf(1020,plain,
! [A: a] :
( ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ A ) ) )
= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(248,axiom,
! [A: refine432681134nres_b,B: a,C: set_Product_prod_a_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824854un_a_b @ C @ A ) )
=> ~ ! [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ B @ D ) @ C )
=> ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_return__refine__prop__return) ).
thf(1183,plain,
! [A: refine432681134nres_b,B: a,C: set_Product_prod_a_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824854un_a_b @ C @ A ) )
=> ~ ! [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ B @ D ) @ C )
=> ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(290,axiom,
! [A: b,B: set_Product_prod_b_a,C: a > $o] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110612un_b_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ~ ! [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_RETURN__ref__SPECD) ).
thf(1334,plain,
! [A: b,B: set_Product_prod_b_a,C: a > $o] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110612un_b_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ~ ! [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(87,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(646,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(41,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_top__greatest) ).
thf(485,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(148,axiom,
! [A: set_b] :
( ! [B: b] : ( member_b @ B @ A )
=> ( top_top_set_b = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_UNIV__eq__I) ).
thf(834,plain,
! [A: set_b] :
( ! [B: b] : ( member_b @ B @ A )
=> ( top_top_set_b = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(73,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_dual__order_Oeq__iff) ).
thf(602,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)],[73]) ).
thf(258,axiom,
! [A: refine424419629nres_a,B: refine432681134nres_b > refine424419629nres_a,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_ord__eq__le__subst) ).
thf(1215,plain,
! [A: refine424419629nres_a,B: refine432681134nres_b > refine424419629nres_a,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(156,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_pwD1) ).
thf(866,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)],[156]) ).
thf(199,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__eq__nres_Oinduct) ).
thf(998,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(47,axiom,
( ( refine2039610767ASSERT @ $false )
= top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_ASSERT__simps_I2_J) ).
thf(507,plain,
( ( refine2039610767ASSERT @ $false )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(339,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_le__funD) ).
thf(1564,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(243,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 ) )
= ( refine1198353288_RES_a @ ( image_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_abs__fun__simps_I2_J) ).
thf(1169,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 ) )
= ( refine1198353288_RES_a @ ( image_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(14,axiom,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit] : ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_FAIL__refine) ).
thf(397,plain,
! [A: refine424419629nres_a,B: set_Pr1628433942t_unit] : ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ B @ top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(230,axiom,
! [A: refine432681134nres_b,B: b,C: set_Product_prod_b_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110613un_b_b @ C @ A ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ C )
=> ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_return__refine__prop__return) ).
thf(1119,plain,
! [A: refine432681134nres_b,B: b,C: set_Product_prod_b_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110613un_b_b @ C @ A ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ C )
=> ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(355,axiom,
! [A: refine424419629nres_a,B: a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ B ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine2063221604TURN_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_RETURN__to__SPEC__rule) ).
thf(1622,plain,
! [A: refine424419629nres_a,B: a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ B ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine2063221604TURN_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(20,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_subsetD) ).
thf(411,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(292,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ refine464223677AILi_a @ D )
=> ( ! [D: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_less__nres_Oinduct) ).
thf(1345,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ refine464223677AILi_a @ D )
=> ( ! [D: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(196,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_ref__two__step) ).
thf(988,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(215,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Collect__mono) ).
thf(1074,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(49,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T) ).
thf(512,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(92,axiom,
! [A: set_b] :
( top_to240090974nres_b
!= ( refine1198353289_RES_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_nres__inequalities_I1_J) ).
thf(661,plain,
! [A: set_b] :
( top_to240090974nres_b
!= ( refine1198353289_RES_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(175,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_order__mono__setup_Orefl) ).
thf(925,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(140,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_top_Oextremum__unique) ).
thf(810,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(5,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ! [C: $o] : ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) )
=> ( ord_le516598614nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__funI) ).
thf(366,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ! [C: $o] : ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) )
=> ( ord_le516598614nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(255,axiom,
! [A: set_a,B: a > $o] :
( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_subset__Collect__conv) ).
thf(1206,plain,
! [A: set_a,B: a > $o] :
( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(31,axiom,
! [A: $o,B: set_b,C: set_b,D: set_b] :
( ( A
=> ( ord_less_eq_set_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_b @ D @ C ) )
=> ( ord_less_eq_set_b @ ( if_set_b @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lhs__step__If) ).
thf(452,plain,
! [A: $o,B: set_b,C: set_b,D: set_b] :
( ( A
=> ( ord_less_eq_set_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_b @ D @ C ) )
=> ( ord_less_eq_set_b @ ( if_set_b @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(259,axiom,
! [A: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ top_to231829469nres_a @ A )
= top_to240090974nres_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_bind__FAIL) ).
thf(1223,plain,
! [A: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ top_to231829469nres_a @ A )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(128,axiom,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_nres__order__simps_I20_J) ).
thf(778,plain,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(344,axiom,
! [A: set_a,B: a > $o] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_RES__rule) ).
thf(1580,plain,
! [A: set_a,B: a > $o] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(231,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_sup__nres_Oinduct) ).
thf(1123,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(341,axiom,
! [A: set_a,B: refine424419629nres_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_lhs__step__RES) ).
thf(1570,plain,
! [A: set_a,B: refine424419629nres_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(354,axiom,
! [A: set_a] :
~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_less__eq__nres_Osimps_I3_J) ).
thf(1619,plain,
! [A: set_a] :
~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(321,axiom,
! [A: set_a,B: a > refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ A ) @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( refine412683990fail_b @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_pw__RES__bind__choose_I1_J) ).
thf(1502,plain,
! [A: set_a,B: a > refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ A ) @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( refine412683990fail_b @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(143,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le127857910od_b_b @ ( refine1458482545od_b_b @ A ) @ ( refine1458482545od_b_b @ ( collec1481886546od_b_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_RES__rule) ).
thf(820,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le127857910od_b_b @ ( refine1458482545od_b_b @ A ) @ ( refine1458482545od_b_b @ ( collec1481886546od_b_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(12,axiom,
! [A: b,B: set_Product_prod_a_b,C: set_a] :
( ( member_b @ A @ ( image_a_b @ B @ C ) )
=> ~ ! [D: a] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ D @ A ) @ B )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ImageE) ).
thf(392,plain,
! [A: b,B: set_Product_prod_a_b,C: set_a] :
( ( member_b @ A @ ( image_a_b @ B @ C ) )
=> ~ ! [D: a] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ D @ A ) @ B )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(317,axiom,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ B ) )
=> ( ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ refine464223677AILi_a ) )
=> ~ ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_less__nres_Ocases) ).
thf(1487,plain,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ B ) )
=> ( ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ refine464223677AILi_a ) )
=> ~ ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(18,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ImageI) ).
thf(407,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(82,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_antisym__conv) ).
thf(630,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)],[82]) ).
thf(34,axiom,
! [A: set_a] :
( ( A = top_top_set_a )
= ( ! [B: a] : ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_eq__UNIV__iff) ).
thf(467,plain,
! [A: set_a] :
( ( A = top_top_set_a )
= ( ! [B: a] : ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(153,axiom,
! [A: $o,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b] :
( ( A
=> ( ord_le1656162903nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1656162903nres_b @ D @ C ) )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_lhs__step__If) ).
thf(847,plain,
! [A: $o,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b] :
( ( A
=> ( ord_le1656162903nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1656162903nres_b @ D @ C ) )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_96_ord__eq__le__trans) ).
thf(625,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)],[81]) ).
thf(246,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_top_Oextremum__unique) ).
thf(1178,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(93,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T) ).
thf(665,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(356,axiom,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ C )
= ( ( ( refine412683990fail_b @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le527798542nres_b @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_pw__bind__le__iff) ).
thf(1624,plain,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ C )
= ( ( ( refine412683990fail_b @ C )
=> ( refine412683989fail_a @ A ) )
& ! [D: a] :
( ( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ D ) )
=> ( ord_le527798542nres_b @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_70_Refine__Misc_Oif__mono) ).
thf(522,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)],[51]) ).
thf(206,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ~ ( ord_le527798542nres_b @ A @ B )
=> ( ! [C: set_b] :
( ( A
= ( refine1198353289_RES_b @ C ) )
=> ! [D: set_b] :
( ( B
= ( refine1198353289_RES_b @ D ) )
=> ( ord_less_eq_set_b @ C @ D ) ) )
=> ~ ( ( A = refine464223678AILi_b )
=> ! [C: set_b] :
( B
!= ( refine1198353289_RES_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__eq__nres_Oelims_I3_J) ).
thf(1027,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ~ ( ord_le527798542nres_b @ A @ B )
=> ( ! [C: set_b] :
( ( A
= ( refine1198353289_RES_b @ C ) )
=> ! [D: set_b] :
( ( B
= ( refine1198353289_RES_b @ D ) )
=> ( ord_less_eq_set_b @ C @ D ) ) )
=> ~ ( ( A = refine464223678AILi_b )
=> ! [C: set_b] :
( B
!= ( refine1198353289_RES_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(98,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_top_Oextremum__unique) ).
thf(682,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
top_to177290092t_unit = refine1607584204t_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_top__nres__def) ).
thf(551,plain,
top_to177290092t_unit = refine1607584204t_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(202,axiom,
! [A: refine424419629nres_a] :
( ( A != top_to231829469nres_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_nres__cases) ).
thf(1012,plain,
! [A: refine424419629nres_a] :
( ( A != top_to231829469nres_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(342,axiom,
! [A: set_a] :
( top_to231829469nres_a
!= ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_nres__inequalities_I1_J) ).
thf(1573,plain,
! [A: set_a] :
( top_to231829469nres_a
!= ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(191,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_nres__order__simps_I4_J) ).
thf(974,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(295,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_nres__order__simps_I3_J) ).
thf(1360,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(348,axiom,
! [A: set_b,B: set_b,C: set_Product_prod_b_b] :
( ! [D: b] :
( ( member_b @ D @ A )
=> ? [E: b] :
( ( member_b @ E @ B )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine122110613un_b_b @ C @ ( refine1198353289_RES_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_RES__refine) ).
thf(1592,plain,
! [A: set_b,B: set_b,C: set_Product_prod_b_b] :
( ! [D: b] :
( ( member_b @ D @ A )
=> ? [E: b] :
( ( member_b @ E @ B )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine122110613un_b_b @ C @ ( refine1198353289_RES_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(261,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_antisym__conv) ).
thf(1234,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(183,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_in__mono) ).
thf(948,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(212,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_RETURN__rule) ).
thf(1064,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(227,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
=> ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_top_Oextremum__uniqueI) ).
thf(1111,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
=> ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(304,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b,E: $o] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ E @ A @ C ) @ ( if_Ref1732808808nres_b @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_order__mono__setup_Omono__if) ).
thf(1425,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b,E: $o] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ E @ A @ C ) @ ( if_Ref1732808808nres_b @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(70,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T) ).
thf(593,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(44,axiom,
( ord_le516598614nres_a
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_le519537037nres_a @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__rel__bool__arg__iff) ).
thf(499,plain,
( ord_le516598614nres_a
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_le519537037nres_a @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(320,axiom,
! [A: refine424419629nres_a,B: b,C: set_Product_prod_b_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110612un_b_a @ C @ A ) )
= ( ? [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ B @ D ) @ C )
& ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_ret__le__down__conv) ).
thf(1498,plain,
! [A: refine424419629nres_a,B: b,C: set_Product_prod_b_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110612un_b_a @ C @ A ) )
= ( ? [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ B @ D ) @ C )
& ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(346,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ refine464223678AILi_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_less__eq__nres_Osimps_I1_J) ).
thf(1587,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ refine464223678AILi_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',fact_248_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(783,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)],[130]) ).
thf(23,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( ( refine944483349t_unit @ A @ B )
= top_to177290092t_unit )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_conc__fun__fail__iff_I1_J) ).
thf(420,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)],[23]) ).
thf(340,axiom,
! [A: product_unit,B: set_Product_unit,C: refine432681134nres_b,D: product_unit > refine432681134nres_b] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine119808504unit_b @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_RES__bind__choose) ).
thf(1567,plain,
! [A: product_unit,B: set_Product_unit,C: refine432681134nres_b,D: product_unit > refine432681134nres_b] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine119808504unit_b @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(288,axiom,
! [A: refine432681134nres_b,B: set_Pr1707992533t_unit] : ( ord_le527798542nres_b @ A @ ( refine2140306339t_unit @ B @ top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_FAIL__refine) ).
thf(1329,plain,
! [A: refine432681134nres_b,B: set_Pr1707992533t_unit] : ( ord_le527798542nres_b @ A @ ( refine2140306339t_unit @ B @ top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(120,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_eq__iff) ).
thf(753,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)],[120]) ).
thf(302,axiom,
! [A: a > $o,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nf__inres__SPEC) ).
thf(1414,plain,
! [A: a > $o,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(84,axiom,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_mem__Collect__eq) ).
thf(637,plain,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(203,axiom,
! [A: refine432681134nres_b,B: b,C: set_Product_prod_b_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110613un_b_b @ C @ A ) )
= ( ? [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ C )
& ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_ret__le__down__conv) ).
thf(1016,plain,
! [A: refine432681134nres_b,B: b,C: set_Product_prod_b_b] :
( ( refine412683990fail_b @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110613un_b_b @ C @ A ) )
= ( ? [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ C )
& ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(97,axiom,
! [A: a,B: set_Product_prod_a_a,C: set_a] :
( ( member_a @ A @ ( image_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ B )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_ImageE) ).
thf(679,plain,
! [A: a,B: set_Product_prod_a_a,C: set_a] :
( ( member_a @ A @ ( image_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ B )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(58,axiom,
! [A: refine424419629nres_a,B: a,C: set_Product_prod_a_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824853un_a_a @ C @ A ) )
= ( ? [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C )
& ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_ret__le__down__conv) ).
thf(547,plain,
! [A: refine424419629nres_a,B: a,C: set_Product_prod_a_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824853un_a_a @ C @ A ) )
= ( ? [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C )
& ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_264_abs__trans__additional_I1_J) ).
thf(706,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)],[105]) ).
thf(277,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord__eq__le__trans) ).
thf(1292,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(178,axiom,
( refine579265252t_unit
= ( ^ [A: refine787176636t_unit] : ( A != top_to177290092t_unit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_nofail__def) ).
thf(933,plain,
( refine579265252t_unit
= ( ^ [A: refine787176636t_unit] : ( A != top_to177290092t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(168,axiom,
? [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_UNIV__witness) ).
thf(901,plain,
? [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(38,axiom,
! [A: b,B: set_b,C: a,D: set_Product_prod_b_a] :
( ( member_b @ A @ B )
=> ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ C ) @ D )
=> ( member_a @ C @ ( image_b_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_rev__ImageI) ).
thf(476,plain,
! [A: b,B: set_b,C: a,D: set_Product_prod_b_a] :
( ( member_b @ A @ B )
=> ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ C ) @ D )
=> ( member_a @ C @ ( image_b_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(149,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T) ).
thf(837,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(228,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_abs__trans__additional_I1_J) ).
thf(1114,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(270,axiom,
! [A: refine432681134nres_b,B: set_b] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ B ) )
=> ( refine412683990fail_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__RES__nofailI) ).
thf(1263,plain,
! [A: refine432681134nres_b,B: set_b] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ B ) )
=> ( refine412683990fail_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(103,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(701,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( if_Ref1369692790t_unit @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(278,axiom,
! [A: set_b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__eq__nres_Osimps_I2_J) ).
thf(1297,plain,
! [A: set_b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(271,axiom,
! [A: a,B: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_nres__monad1) ).
thf(1266,plain,
! [A: a,B: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(90,axiom,
! [A: refine424419629nres_a,B: a,C: set_Product_prod_a_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824853un_a_a @ C @ A ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C )
=> ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_return__refine__prop__return) ).
thf(654,plain,
! [A: refine424419629nres_a,B: a,C: set_Product_prod_a_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1441824853un_a_a @ C @ A ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C )
=> ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(265,axiom,
! [A: refine432681134nres_b,B: b > $o,C: b > $o] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) )
=> ( ! [D: b] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_SPEC__cons__rule) ).
thf(1246,plain,
! [A: refine432681134nres_b,B: b > $o,C: b > $o] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) )
=> ( ! [D: b] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_132_GreatestI2__order) ).
thf(515,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)],[50]) ).
thf(239,axiom,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ B @ refine464223677AILi_a ) )
=> ( ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) )
=> ~ ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_less__eq__nres_Ocases) ).
thf(1150,plain,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ B @ refine464223677AILi_a ) )
=> ( ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) )
=> ~ ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(357,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: $o] :
( ( ( ord_le527798542nres_b @ A @ B )
= C )
=> ( ( ( B = refine464223678AILi_b )
=> ~ C )
=> ( ! [D: set_b] :
( ( A
= ( refine1198353289_RES_b @ D ) )
=> ! [E: set_b] :
( ( B
= ( refine1198353289_RES_b @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_b @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223678AILi_b )
=> ( ? [D: set_b] :
( B
= ( refine1198353289_RES_b @ D ) )
=> C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_less__eq__nres_Oelims_I1_J) ).
thf(1627,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: $o] :
( ( ( ord_le527798542nres_b @ A @ B )
= C )
=> ( ( ( B = refine464223678AILi_b )
=> ~ C )
=> ( ! [D: set_b] :
( ( A
= ( refine1198353289_RES_b @ D ) )
=> ! [E: set_b] :
( ( B
= ( refine1198353289_RES_b @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_b @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223678AILi_b )
=> ( ? [D: set_b] :
( B
= ( refine1198353289_RES_b @ D ) )
=> C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',fact_23_SPEC__trans) ).
thf(1525,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)],[327]) ).
thf(138,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( partia1658438072t_unit @ top_to177290092t_unit @ A @ B )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_flat__ord__compat_I2_J) ).
thf(805,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)],[138]) ).
thf(56,axiom,
! [A: set_Product_unit,B: product_unit] :
( ( refine983493746t_unit @ ( refine1777164439t_unit @ A ) @ B )
= ( member_Product_unit @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nf__inres__RES) ).
thf(541,plain,
! [A: set_Product_unit,B: product_unit] :
( ( refine983493746t_unit @ ( refine1777164439t_unit @ A ) @ B )
= ( member_Product_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(124,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_nres__order__simps_I4_J) ).
thf(765,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(249,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_dual__order_Oantisym) ).
thf(1187,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(353,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_antisym) ).
thf(1616,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(52,axiom,
! [A: set_b,B: set_b] :
( ( if_set_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_Itf__b_J_T) ).
thf(530,plain,
! [A: set_b,B: set_b] :
( ( if_set_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(134,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le915866422od_a_a @ ( refine622451633od_a_a @ A ) @ ( refine622451633od_a_a @ ( collec645855634od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_RES__rule) ).
thf(794,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le915866422od_a_a @ ( refine622451633od_a_a @ A ) @ ( refine622451633od_a_a @ ( collec645855634od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(109,axiom,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b] :
( ( A @ refine464223678AILi_b )
=> ( ! [C: set_b] : ( A @ ( refine1198353289_RES_b @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_nres_Oinduct) ).
thf(718,plain,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b] :
( ( A @ refine464223678AILi_b )
=> ( ! [C: set_b] : ( A @ ( refine1198353289_RES_b @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(83,axiom,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ B @ refine464223678AILi_b ) )
=> ( ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) )
=> ~ ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_less__eq__nres_Ocases) ).
thf(633,plain,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ B @ refine464223678AILi_b ) )
=> ( ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) )
=> ~ ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',fact_324_pw__flat__ge__iff) ).
thf(360,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)],[3]) ).
thf(170,axiom,
! [A: a,B: set_Product_prod_a_b,C: b > $o] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ~ ! [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_RETURN__ref__SPECD) ).
thf(906,plain,
! [A: a,B: set_Product_prod_a_b,C: b > $o] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ~ ! [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(275,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o,D: a > refine432681134nres_b,E: b > $o] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le519537037nres_a @ ( B @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le527798542nres_b @ ( D @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_bind__sim__select__rule) ).
thf(1278,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o,D: a > refine432681134nres_b,E: b > $o] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le519537037nres_a @ ( B @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le527798542nres_b @ ( D @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(117,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_top_Oextremum__uniqueI) ).
thf(745,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(349,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__trans) ).
thf(1595,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(113,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( top_to177290092t_unit
= ( refine944483349t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_conc__fun__fail__iff_I2_J) ).
thf(733,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)],[113]) ).
thf(188,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_abs__fun__simps_I1_J) ).
thf(965,plain,
! [A: set_Pr451126599t_unit] :
( ( refine838861686t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_80_order__mono__setup_Omono__if) ).
thf(750,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)],[119]) ).
thf(240,axiom,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b > $o] :
( ( A @ B )
=> ( ! [D: refine432681134nres_b] :
( ( A @ D )
=> ( ord_le527798542nres_b @ D @ B ) )
=> ( ! [D: refine432681134nres_b] :
( ( A @ D )
=> ( ! [E: refine432681134nres_b] :
( ( A @ E )
=> ( ord_le527798542nres_b @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1722590613nres_b @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_GreatestI2__order) ).
thf(1154,plain,
! [A: refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b > $o] :
( ( A @ B )
=> ( ! [D: refine432681134nres_b] :
( ( A @ D )
=> ( ord_le527798542nres_b @ D @ B ) )
=> ( ! [D: refine432681134nres_b] :
( ( A @ D )
=> ( ! [E: refine432681134nres_b] :
( ( A @ E )
=> ( ord_le527798542nres_b @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1722590613nres_b @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(63,axiom,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_top__empty__eq) ).
thf(562,plain,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_118_ord__le__eq__subst) ).
thf(423,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)],[24]) ).
thf(151,axiom,
( ( refine558004794t_unit @ top_to177290092t_unit )
= ( ^ [A: product_unit] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_inres__simps_I1_J) ).
thf(843,plain,
( ( refine558004794t_unit @ top_to177290092t_unit )
= ( ^ [A: product_unit] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(116,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__mono__setup_Orefl) ).
thf(743,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_90_order__trans) ).
thf(579,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)],[67]) ).
thf(330,axiom,
! [A: b,B: set_Product_prod_b_a,C: a > $o] :
( ? [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110612un_b_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_RETURN__SPEC__refine) ).
thf(1535,plain,
! [A: b,B: set_Product_prod_b_a,C: a > $o] :
( ? [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110612un_b_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(186,axiom,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ refine464223678AILi_b @ D )
=> ( ! [D: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ refine464223678AILi_b )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_less__nres_Oinduct) ).
thf(958,plain,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ refine464223678AILi_b @ D )
=> ( ! [D: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ refine464223678AILi_b )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(260,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord__le__eq__subst) ).
thf(1226,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(160,axiom,
! [A: a,B: set_Product_prod_b_a,C: set_b] :
( ( member_a @ A @ ( image_b_a @ B @ C ) )
=> ~ ! [D: b] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_ImageE) ).
thf(875,plain,
! [A: a,B: set_Product_prod_b_a,C: set_b] :
( ( member_a @ A @ ( image_b_a @ B @ C ) )
=> ~ ! [D: b] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(145,axiom,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ D @ refine464223678AILi_b )
=> ( ! [D: set_b] : ( A @ refine464223678AILi_b @ ( refine1198353289_RES_b @ D ) )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_sup__nres_Oinduct) ).
thf(826,plain,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ D @ refine464223678AILi_b )
=> ( ! [D: set_b] : ( A @ refine464223678AILi_b @ ( refine1198353289_RES_b @ D ) )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_177_pw__le__iff) ).
thf(577,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)],[66]) ).
thf(305,axiom,
! [A: $o,B: refine432681134nres_b,C: b > $o,D: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_if__rule) ).
thf(1428,plain,
! [A: $o,B: refine432681134nres_b,C: b > $o,D: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_74_order__subst1) ).
thf(445,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)],[29]) ).
thf(9,axiom,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__mono__setup_Orefl) ).
thf(382,plain,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_130_Greatest__equality) ).
thf(572,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)],[65]) ).
thf(131,axiom,
! [A: a,B: set_Product_prod_a_b,C: b > $o] :
( ? [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_RETURN__SPEC__refine) ).
thf(787,plain,
! [A: a,B: set_Product_prod_a_b,C: b > $o] :
( ? [D: b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(210,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Collect__cong) ).
thf(1058,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)],[210]) ).
thf(220,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_order__class_Oorder_Oantisym) ).
thf(1092,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(219,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( refine412683990fail_b @ B )
=> ( refine412683990fail_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_pwD1) ).
thf(1090,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( refine412683990fail_b @ B )
=> ( refine412683990fail_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(268,axiom,
! [A: b,B: set_Product_prod_b_b,C: b > $o] :
( ? [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_RETURN__SPEC__refine) ).
thf(1258,plain,
! [A: b,B: set_Product_prod_b_b,C: b > $o] :
( ? [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(104,axiom,
! [A: set_b] : ( refine412683990fail_b @ ( refine1198353289_RES_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_nofail__simps_I2_J) ).
thf(704,plain,
! [A: set_b] : ( refine412683990fail_b @ ( refine1198353289_RES_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',fact_75_less__eq__nres_Osimps_I2_J) ).
thf(1209,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)],[256]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',fact_77_nres__order__simps_I5_J) ).
thf(1408,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)],[300]) ).
thf(229,axiom,
! [A: refine432681134nres_b,B: b] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ ( (=) @ b @ B ) ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine2063221605TURN_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_RETURN__to__SPEC__rule) ).
thf(1117,plain,
! [A: refine432681134nres_b,B: b] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ ( (=) @ b @ B ) ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine2063221605TURN_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(114,axiom,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ B @ refine464223678AILi_b ) )
=> ( ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ B ) ) )
=> ~ ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_sup__nres_Ocases) ).
thf(736,plain,
! [A: produc1587512412nres_b] :
( ! [B: refine432681134nres_b] :
( A
!= ( produc2130641934nres_b @ B @ refine464223678AILi_b ) )
=> ( ! [B: set_b] :
( A
!= ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ B ) ) )
=> ~ ! [B: set_b,C: set_b] :
( A
!= ( produc2130641934nres_b @ ( refine1198353289_RES_b @ B ) @ ( refine1198353289_RES_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(347,axiom,
! [A: a,B: set_a,C: refine432681134nres_b,D: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_RES__bind__choose) ).
thf(1589,plain,
! [A: a,B: set_a,C: refine432681134nres_b,D: a > refine432681134nres_b] :
( ( member_a @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(238,axiom,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: b > $o,D: a > refine424419629nres_a,E: a > $o] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le527798542nres_b @ ( B @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le519537037nres_a @ ( D @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ E ) ) ) ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_bind__sim__select__rule) ).
thf(1144,plain,
! [A: refine424419629nres_a,B: a > refine432681134nres_b,C: b > $o,D: a > refine424419629nres_a,E: a > $o] :
( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ! [F: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ A @ F )
=> ( ( ord_le527798542nres_b @ ( B @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le519537037nres_a @ ( D @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ E ) ) ) ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',fact_126_order__subst2) ).
thf(616,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)],[78]) ).
thf(245,axiom,
! [A: set_b,B: set_Product_prod_b_a] :
( ( ord_less_eq_set_b @ A @ ( domain_b_a @ B ) )
=> ( ( refine1964549109un_b_a @ B @ ( refine1198353289_RES_b @ A ) )
= ( refine1198353288_RES_a @ ( image_b_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_abs__fun__simps_I2_J) ).
thf(1175,plain,
! [A: set_b,B: set_Product_prod_b_a] :
( ( ord_less_eq_set_b @ A @ ( domain_b_a @ B ) )
=> ( ( refine1964549109un_b_a @ B @ ( refine1198353289_RES_b @ A ) )
= ( refine1198353288_RES_a @ ( image_b_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(193,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_SPEC__rule) ).
thf(979,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(74,axiom,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inres__def) ).
thf(604,plain,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [A: b,B: a,C: set_Product_prod_b_a,D: set_b] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_a @ B @ ( image_b_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ImageI) ).
thf(509,plain,
! [A: b,B: a,C: set_Product_prod_b_a,D: set_b] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_a @ B @ ( image_b_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(88,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_subset__eq) ).
thf(649,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(26,axiom,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_bind__FAIL) ).
thf(434,plain,
! [A: product_unit > refine787176636t_unit] :
( ( refine681446406t_unit @ top_to177290092t_unit @ A )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(72,axiom,
! [A: refine787176636t_unit] :
( ( top_to177290092t_unit != A )
= ( refine579265252t_unit @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_intro__nofail_I2_J) ).
thf(599,plain,
! [A: refine787176636t_unit] :
( ( top_to177290092t_unit != A )
= ( refine579265252t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(307,axiom,
! [A: set_a,B: set_Product_prod_a_b] :
( ( ord_less_eq_set_a @ A @ ( domain_a_b @ B ) )
=> ( ( refine1136779703un_a_b @ B @ ( refine1198353288_RES_a @ A ) )
= ( refine1198353289_RES_b @ ( image_a_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_abs__fun__simps_I2_J) ).
thf(1439,plain,
! [A: set_a,B: set_Product_prod_a_b] :
( ( ord_less_eq_set_a @ A @ ( domain_a_b @ B ) )
=> ( ( refine1136779703un_a_b @ B @ ( refine1198353288_RES_a @ A ) )
= ( refine1198353289_RES_b @ ( image_a_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(164,axiom,
! [A: b > $o,B: b] :
( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nf__inres__SPEC) ).
thf(890,plain,
! [A: b > $o,B: b] :
( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(11,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_meta__le__everything__if__top) ).
thf(387,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(315,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ~ ( ord_le519537037nres_a @ A @ B )
=> ( ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( ord_less_eq_set_a @ C @ D ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ! [C: set_a] :
( B
!= ( refine1198353288_RES_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__eq__nres_Oelims_I3_J) ).
thf(1471,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ~ ( ord_le519537037nres_a @ A @ B )
=> ( ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( ord_less_eq_set_a @ C @ D ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ! [C: set_a] :
( B
!= ( refine1198353288_RES_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(217,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B != refine464223677AILi_a )
=> ~ ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ~ ( ord_less_eq_set_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__eq__nres_Oelims_I2_J) ).
thf(1080,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B != refine464223677AILi_a )
=> ~ ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ~ ( ord_less_eq_set_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(122,axiom,
! [A: refine432681134nres_b] :
( ( A != top_to240090974nres_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_nres__cases) ).
thf(758,plain,
! [A: refine432681134nres_b] :
( ( A != top_to240090974nres_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(155,axiom,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ C ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_lhs__step__If) ).
thf(858,plain,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ C ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(54,axiom,
! [A: set_Product_unit] :
( ( refine1208325748t_unit @ ( refine1777164439t_unit @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_the__RES_Osimps) ).
thf(535,plain,
! [A: set_Product_unit] :
( ( refine1208325748t_unit @ ( refine1777164439t_unit @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(76,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(609,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',fact_32_SPEC__cons__rule) ).
thf(1325,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)],[287]) ).
thf(336,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_top__greatest) ).
thf(1556,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(181,axiom,
! [A: set_b,B: set_Pr1707992533t_unit] :
( ~ ( ord_less_eq_set_b @ A @ ( domain918802906t_unit @ B ) )
=> ( ( refine460904452t_unit @ B @ ( refine1198353289_RES_b @ A ) )
= top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_abs__fun__simps_I3_J) ).
thf(943,plain,
! [A: set_b,B: set_Pr1707992533t_unit] :
( ~ ( ord_less_eq_set_b @ A @ ( domain918802906t_unit @ B ) )
=> ( ( refine460904452t_unit @ B @ ( refine1198353289_RES_b @ A ) )
= top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(94,axiom,
! [A: set_b,B: set_b] :
( ( if_set_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_Itf__b_J_T) ).
thf(668,plain,
! [A: set_b,B: set_b] :
( ( if_set_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(211,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__funE) ).
thf(1061,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(15,axiom,
? [A: b] : ( member_b @ A @ top_top_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_UNIV__witness) ).
thf(399,plain,
? [A: b] : ( member_b @ A @ top_top_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(125,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_dual__order_Oantisym) ).
thf(768,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)],[125]) ).
thf(195,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__mono__setup_Orefl) ).
thf(986,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(266,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: a,E: refine432681134nres_b,F: set_Product_prod_b_b,G: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( refine1001002027nres_a @ A @ D )
=> ( ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ H ) @ B )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( G @ H ) ) ) )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_rhs__step__bind) ).
thf(1250,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: a,E: refine432681134nres_b,F: set_Product_prod_b_b,G: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( refine1001002027nres_a @ A @ D )
=> ( ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ H ) @ B )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( G @ H ) ) ) )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(224,axiom,
! [A: b,B: set_b,C: refine432681134nres_b,D: b > refine432681134nres_b] :
( ( member_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine1264602246nd_b_b @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_RES__bind__choose) ).
thf(1102,plain,
! [A: b,B: set_b,C: refine432681134nres_b,D: b > refine432681134nres_b] :
( ( member_b @ A @ B )
=> ( ( ord_le527798542nres_b @ C @ ( D @ A ) )
=> ( ord_le527798542nres_b @ C @ ( refine1264602246nd_b_b @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(25,axiom,
! [A: set_a,B: set_a] :
( ( if_set_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_Itf__a_J_T) ).
thf(431,plain,
! [A: set_a,B: set_a] :
( ( if_set_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(174,axiom,
! [A: refine787176636t_unit] :
( ( ~ ( refine579265252t_unit @ A ) )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_not__nofail__iff) ).
thf(922,plain,
! [A: refine787176636t_unit] :
( ( ~ ( refine579265252t_unit @ A ) )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_21_SPEC__trans) ).
thf(658,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)],[91]) ).
thf(172,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__mono__setup_Orefl) ).
thf(912,plain,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(99,axiom,
! [A: set_b,B: set_b] :
( ( ( refine1198353289_RES_b @ A )
= ( refine1198353289_RES_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nres__more__simps_I4_J) ).
thf(685,plain,
! [A: set_b,B: set_b] :
( ( ( refine1198353289_RES_b @ A )
= ( refine1198353289_RES_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(213,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le527798542nres_b @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_order__subst2) ).
thf(1066,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le527798542nres_b @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le527798542nres_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(157,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_dual__order_Orefl) ).
thf(868,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(309,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_ord__le__eq__subst) ).
thf(1445,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(328,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Collect__mem__eq) ).
thf(1528,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(254,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_ref__two__step) ).
thf(1203,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(176,axiom,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ D @ refine464223678AILi_b )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( ! [D: set_b] : ( A @ refine464223678AILi_b @ ( refine1198353289_RES_b @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_less__eq__nres_Oinduct) ).
thf(927,plain,
! [A: refine432681134nres_b > refine432681134nres_b > $o,B: refine432681134nres_b,C: refine432681134nres_b] :
( ! [D: refine432681134nres_b] : ( A @ D @ refine464223678AILi_b )
=> ( ! [D: set_b,E: set_b] : ( A @ ( refine1198353289_RES_b @ D ) @ ( refine1198353289_RES_b @ E ) )
=> ( ! [D: set_b] : ( A @ refine464223678AILi_b @ ( refine1198353289_RES_b @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_173_pw__leI) ).
thf(939,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)],[180]) ).
thf(60,axiom,
! [A: set_b] :
( ( A = top_top_set_b )
= ( ! [B: b] : ( member_b @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_eq__UNIV__iff) ).
thf(553,plain,
! [A: set_b] :
( ( A = top_top_set_b )
= ( ! [B: b] : ( member_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(208,axiom,
! [A: set_a] :
( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_the__RES_Osimps) ).
thf(1049,plain,
! [A: set_a] :
( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_175_pw__leI_H) ).
thf(490,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)],[43]) ).
thf(345,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: b,E: refine432681134nres_b,F: set_Product_prod_b_b,G: a > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( refine1001002028nres_b @ A @ D )
=> ( ! [H: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ H ) @ B )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( G @ H ) ) ) )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_rhs__step__bind) ).
thf(1583,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: b,E: refine432681134nres_b,F: set_Product_prod_b_b,G: a > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( refine1001002028nres_b @ A @ D )
=> ( ! [H: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ H ) @ B )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( G @ H ) ) ) )
=> ( ord_le527798542nres_b @ E @ ( refine122110613un_b_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(235,axiom,
! [A: b,B: set_Product_prod_b_b,C: b > $o] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_RETURN__ref__SPECD) ).
thf(1134,plain,
! [A: b,B: set_Product_prod_b_b,C: b > $o] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(42,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Collect__mono) ).
thf(487,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(189,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( refine1001002028nres_b @ A @ C )
=> ( refine1001002028nres_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_pwD2) ).
thf(968,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( refine1001002028nres_b @ A @ C )
=> ( refine1001002028nres_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(247,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__class_Oorder_Oeq__iff) ).
thf(1181,plain,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(144,axiom,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Collect__mem__eq) ).
thf(823,plain,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(107,axiom,
! [A: set_a,B: set_a] :
( ( if_set_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_Itf__a_J_T) ).
thf(712,plain,
! [A: set_a,B: set_a] :
( ( if_set_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(154,axiom,
! [A: set_Product_prod_b_a,B: product_prod_b_a > $o] :
( ! [C: product_prod_b_a] :
( ( member1277678991od_b_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le1135777269od_b_a @ ( refine1450221040od_b_a @ A ) @ ( refine1450221040od_b_a @ ( collec1473625041od_b_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_RES__rule) ).
thf(855,plain,
! [A: set_Product_prod_b_a,B: product_prod_b_a > $o] :
( ! [C: product_prod_b_a] :
( ( member1277678991od_b_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le1135777269od_b_a @ ( refine1450221040od_b_a @ A ) @ ( refine1450221040od_b_a @ ( collec1473625041od_b_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(350,axiom,
! [A: a,B: set_a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_RES__bind__choose) ).
thf(1598,plain,
! [A: a,B: set_a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(85,axiom,
! [A: set_Product_prod_a_b,B: product_prod_a_b] :
( ( refine387222285od_a_b @ ( refine630713138od_a_b @ A ) @ B )
= ( member458171089od_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nf__inres__RES) ).
thf(640,plain,
! [A: set_Product_prod_a_b,B: product_prod_a_b] :
( ( refine387222285od_a_b @ ( refine630713138od_a_b @ A ) @ B )
= ( member458171089od_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(297,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_order__subst2) ).
thf(1368,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(329,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_order__subst1) ).
thf(1531,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(214,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > refine424419629nres_a,D: b > refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ! [E: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ A @ C ) @ ( refine1264602245nd_b_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1070,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > refine424419629nres_a,D: b > refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ! [E: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ A @ C ) @ ( refine1264602245nd_b_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_150_ref__two__step) ).
thf(872,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)],[159]) ).
thf(21,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_in__mono) ).
thf(414,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(190,axiom,
! [A: set_a,B: set_a,C: set_Product_prod_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ C ) ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1441824853un_a_a @ C @ ( refine1198353288_RES_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_RES__refine) ).
thf(971,plain,
! [A: set_a,B: set_a,C: set_Product_prod_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ C ) ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1441824853un_a_a @ C @ ( refine1198353288_RES_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(279,axiom,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nres__more__simps_I4_J) ).
thf(1300,plain,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(133,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_nres__order__simps_I4_J) ).
thf(791,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(69,axiom,
! [A: $o,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ C ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_lhs__step__If) ).
thf(585,plain,
! [A: $o,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ C ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(150,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_subsetD) ).
thf(840,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(35,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_subset__iff) ).
thf(470,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(184,axiom,
! [A: product_unit] :
( top_to177290092t_unit
!= ( refine1420258419t_unit @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_nres__inequalities_I3_J) ).
thf(951,plain,
! [A: product_unit] :
( top_to177290092t_unit
!= ( refine1420258419t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1,conjecture,
ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(359,plain,
~ ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_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)],[86]) ).
thf(57,axiom,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_subsetI) ).
thf(544,plain,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(205,axiom,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ B @ refine464223677AILi_a ) )
=> ( ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ B ) ) )
=> ~ ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sup__nres_Ocases) ).
thf(1023,plain,
! [A: produc1609974940nres_a] :
( ! [B: refine424419629nres_a] :
( A
!= ( produc1136923598nres_a @ B @ refine464223677AILi_a ) )
=> ( ! [B: set_a] :
( A
!= ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ B ) ) )
=> ~ ! [B: set_a,C: set_a] :
( A
!= ( produc1136923598nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine1198353288_RES_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(276,axiom,
! [A: refine432681134nres_b,B: refine424419629nres_a > refine432681134nres_b,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_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_ord__eq__le__subst) ).
thf(1284,plain,
! [A: refine432681134nres_b,B: refine424419629nres_a > refine432681134nres_b,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_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(111,axiom,
! [A: b] :
( ( refine1198353289_RES_b @ ( collect_b @ ( (=) @ b @ A ) ) )
= ( refine2063221605TURN_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_SPEC__eq__is__RETURN_I1_J) ).
thf(727,plain,
! [A: b] :
( ( refine1198353289_RES_b @ ( collect_b @ ( (=) @ b @ A ) ) )
= ( refine2063221605TURN_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(237,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( ( refine412683990fail_b @ B )
& ! [C: b] :
( ( refine1001002028nres_b @ B @ C )
=> ( refine1001002028nres_b @ A @ C ) ) ) )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_pw__leI) ).
thf(1140,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( ( refine412683990fail_b @ B )
& ! [C: b] :
( ( refine1001002028nres_b @ B @ C )
=> ( refine1001002028nres_b @ A @ C ) ) ) )
=> ( ord_le527798542nres_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(298,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: $o] :
( ( ( ord_le519537037nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ~ C )
=> ( ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_a @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ( ? [D: set_a] :
( B
= ( refine1198353288_RES_a @ D ) )
=> C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__eq__nres_Oelims_I1_J) ).
thf(1372,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: $o] :
( ( ( ord_le519537037nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ~ C )
=> ( ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_a @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ( ? [D: set_a] :
( B
= ( refine1198353288_RES_a @ D ) )
=> C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(316,axiom,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ? [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_RETURN__SPEC__refine) ).
thf(1485,plain,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ? [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(209,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ refine464223677AILi_a )
=> ( ! [C: set_a] : ( A @ ( refine1198353288_RES_a @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_nres_Oinduct) ).
thf(1052,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ refine464223677AILi_a )
=> ( ! [C: set_a] : ( A @ ( refine1198353288_RES_a @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(323,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( B = C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_ord__le__eq__trans) ).
thf(1506,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( B = C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(273,axiom,
! [A: refine424419629nres_a] :
( ( A != refine464223677AILi_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_nres_Oexhaust) ).
thf(1272,plain,
! [A: refine424419629nres_a] :
( ( A != refine464223677AILi_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(77,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_eq__refl) ).
thf(612,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(263,axiom,
! [A: a,B: set_a,C: refine787176636t_unit,D: a > refine787176636t_unit] :
( ( member_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine96995669t_unit @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_RES__bind__choose) ).
thf(1240,plain,
! [A: a,B: set_a,C: refine787176636t_unit,D: a > refine787176636t_unit] :
( ( member_a @ A @ B )
=> ( ( ord_le1051254044t_unit @ C @ ( D @ A ) )
=> ( ord_le1051254044t_unit @ C @ ( refine96995669t_unit @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(197,axiom,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_inres__simps_I2_J) ).
thf(991,plain,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(152,axiom,
( refine412683990fail_b
= ( ^ [A: refine432681134nres_b] :
? [B: set_b] :
( A
= ( refine1198353289_RES_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_nofail__RES__conv) ).
thf(845,plain,
( refine412683990fail_b
= ( ^ [A: refine432681134nres_b] :
? [B: set_b] :
( A
= ( refine1198353289_RES_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(312,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = B )
=> ( ord_le527798542nres_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_eq__refl) ).
thf(1459,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = B )
=> ( ord_le527798542nres_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(335,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_order_Otrans) ).
thf(1553,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_86_dual__order_Otrans) ).
thf(482,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)],[40]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_94_ord__le__eq__trans) ).
thf(671,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)],[95]) ).
thf(232,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_abs__trans__additional_I1_J) ).
thf(1126,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(126,axiom,
! [A: refine432681134nres_b] :
( ( A != refine464223678AILi_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_nres_Oexhaust) ).
thf(771,plain,
! [A: refine432681134nres_b] :
( ( A != refine464223678AILi_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(4,axiom,
! [A: product_unit > $o,B: product_unit] :
( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nf__inres__SPEC) ).
thf(363,plain,
! [A: product_unit > $o,B: product_unit] :
( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ A ) ) @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,axiom,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nres__more__simps_I4_J) ).
thf(556,plain,
! [A: set_Product_unit,B: set_Product_unit] :
( ( ( refine1777164439t_unit @ A )
= ( refine1777164439t_unit @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(100,axiom,
! [A: $o,B: refine787176636t_unit,C: product_unit > $o,D: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_if__rule) ).
thf(688,plain,
! [A: $o,B: refine787176636t_unit,C: product_unit > $o,D: refine787176636t_unit] :
( ( A
=> ( ord_le1051254044t_unit @ B @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le1051254044t_unit @ D @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) )
=> ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ A @ B @ D ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(169,axiom,
! [A: set_b,B: set_b] :
( ( ( refine1198353289_RES_b @ A )
= ( refine1198353289_RES_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nres_Oinject) ).
thf(903,plain,
! [A: set_b,B: set_b] :
( ( ( refine1198353289_RES_b @ A )
= ( refine1198353289_RES_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(6,axiom,
! [A: $o,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
( ( A
=> ( ord_le516598614nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le516598614nres_a @ D @ C ) )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_lhs__step__If) ).
thf(368,plain,
! [A: $o,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
( ( A
=> ( ord_le516598614nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le516598614nres_a @ D @ C ) )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(310,axiom,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_nofail__simps_I2_J) ).
thf(1453,plain,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(274,axiom,
( top_top_set_a
= ( collect_a @ top_top_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_top__set__def) ).
thf(1276,plain,
( top_top_set_a
= ( collect_a @ top_top_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(102,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_flat__ord__compat_I2_J) ).
thf(699,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)],[102]) ).
thf(182,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_order__class_Oorder_Oeq__iff) ).
thf(946,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)],[182]) ).
thf(16,axiom,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Collect__mono__iff) ).
thf(401,plain,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(129,axiom,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_order__mono__setup_Orefl) ).
thf(781,plain,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(337,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_ref__two__step) ).
thf(1558,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(187,axiom,
! [A: refine787176636t_unit] :
( ( A != top_to177290092t_unit )
=> ~ ! [B: set_Product_unit] :
( A
!= ( refine1777164439t_unit @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_nres__cases) ).
thf(961,plain,
! [A: refine787176636t_unit] :
( ( A != top_to177290092t_unit )
=> ~ ! [B: set_Product_unit] :
( A
!= ( refine1777164439t_unit @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(141,axiom,
! [A: set_b] :
( refine464223678AILi_b
!= ( refine1198353289_RES_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_nres_Odistinct_I1_J) ).
thf(813,plain,
! [A: set_b] :
( refine464223678AILi_b
!= ( refine1198353289_RES_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(166,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_subset__iff) ).
thf(896,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(118,axiom,
refine1607584204t_unit = top_to177290092t_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_nres__simp__internals_I2_J) ).
thf(748,plain,
refine1607584204t_unit = top_to177290092t_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(318,axiom,
! [A: set_b,B: set_a,C: set_Product_prod_b_a] :
( ! [D: b] :
( ( member_b @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ E ) @ C ) ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine122110612un_b_a @ C @ ( refine1198353288_RES_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_RES__refine) ).
thf(1491,plain,
! [A: set_b,B: set_a,C: set_Product_prod_b_a] :
( ! [D: b] :
( ( member_b @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ E ) @ C ) ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine122110612un_b_a @ C @ ( refine1198353288_RES_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(173,axiom,
! [A: $o,B: set_a,C: set_a,D: set_a] :
( ( A
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_a @ D @ C ) )
=> ( ord_less_eq_set_a @ ( if_set_a @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lhs__step__If) ).
thf(914,plain,
! [A: $o,B: set_a,C: set_a,D: set_a] :
( ( A
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_a @ D @ C ) )
=> ( ord_less_eq_set_a @ ( if_set_a @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(282,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = top_to240090974nres_b )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_meta__le__everything__if__top) ).
thf(1308,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = top_to240090974nres_b )
=> ( ord_le527798542nres_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(251,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ C ) @ ( refine436832839nd_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1193,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le527798542nres_b @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ A @ C ) @ ( refine436832839nd_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(216,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( ord_le527798542nres_b @ B @ A ) )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_le__nofailI) ).
thf(1077,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( ord_le527798542nres_b @ B @ A ) )
=> ( ord_le527798542nres_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(257,axiom,
! [A: set_b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nres__order__simps_I5_J) ).
thf(1212,plain,
! [A: set_b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(325,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( refine412683990fail_b @ B ) )
=> ( ! [C: b] :
( ( refine412683990fail_b @ A )
=> ( ( refine1001002028nres_b @ B @ C )
=> ( refine1001002028nres_b @ A @ C ) ) )
=> ( ord_le527798542nres_b @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_pw__leI_H) ).
thf(1513,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( refine412683990fail_b @ B ) )
=> ( ! [C: b] :
( ( refine412683990fail_b @ A )
=> ( ( refine1001002028nres_b @ B @ C )
=> ( refine1001002028nres_b @ A @ C ) ) )
=> ( ord_le527798542nres_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(358,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_abs__trans__additional_I1_J) ).
thf(1661,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(147,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_nres__order__simps_I3_J) ).
thf(832,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(308,axiom,
! [A: a > $o,B: a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: a > refine432681134nres_b] :
( ( A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( E @ B ) ) )
=> ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_rhs__step__bind__SPEC) ).
thf(1442,plain,
! [A: a > $o,B: a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: a > refine432681134nres_b] :
( ( A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( E @ B ) ) )
=> ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(241,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia915210666nres_b @ top_to240090974nres_b @ ( C @ E ) @ ( D @ E ) )
=> ( partia915210666nres_b @ top_to240090974nres_b @ ( refine436832839nd_a_b @ A @ C ) @ ( refine436832839nd_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J) ).
thf(1161,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( partia906949161nres_a @ top_to231829469nres_a @ A @ B )
=> ( ! [E: a] : ( partia915210666nres_b @ top_to240090974nres_b @ ( C @ E ) @ ( D @ E ) )
=> ( partia915210666nres_b @ top_to240090974nres_b @ ( refine436832839nd_a_b @ A @ C ) @ ( refine436832839nd_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(136,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_order__mono__setup_Orefl) ).
thf(800,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(293,axiom,
! [A: refine432681134nres_b,B: refine424419629nres_a > refine432681134nres_b,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__subst1) ).
thf(1348,plain,
! [A: refine432681134nres_b,B: refine424419629nres_a > refine432681134nres_b,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(79,axiom,
! [A: product_unit > $o,B: product_unit > $o] :
( ! [C: product_unit] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ A ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_SPEC__rule) ).
thf(620,plain,
! [A: product_unit > $o,B: product_unit > $o] :
( ! [C: product_unit] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ A ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(19,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T) ).
thf(410,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_265_abs__fun__simps_I3_J) ).
thf(1097,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)],[222]) ).
thf(333,axiom,
! [A: refine424419629nres_a,B: b,C: set_Product_prod_b_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110612un_b_a @ C @ A ) )
=> ~ ! [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ B @ D ) @ C )
=> ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_return__refine__prop__return) ).
thf(1546,plain,
! [A: refine424419629nres_a,B: b,C: set_Product_prod_b_a] :
( ( refine412683989fail_a @ A )
=> ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine122110612un_b_a @ C @ A ) )
=> ~ ! [D: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ B @ D ) @ C )
=> ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(280,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ B @ A )
& ( ord_le527798542nres_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_dual__order_Oeq__iff) ).
thf(1303,plain,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ B @ A )
& ( ord_le527798542nres_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_122_ord__eq__le__subst) ).
thf(564,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)],[64]) ).
thf(306,axiom,
! [A: refine424419629nres_a,B: a > refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine436832839nd_a_b @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine412683990fail_b @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_pw__bind__nofail) ).
thf(1436,plain,
! [A: refine424419629nres_a,B: a > refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine436832839nd_a_b @ A @ B ) )
= ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine412683990fail_b @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(139,axiom,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_rev__ImageI) ).
thf(807,plain,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(27,axiom,
! [A: a,B: set_a,C: a,D: set_Product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ D )
=> ( member_a @ C @ ( image_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_rev__ImageI) ).
thf(437,plain,
! [A: a,B: set_a,C: a,D: set_Product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ D )
=> ( member_a @ C @ ( image_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(338,axiom,
! [A: set_b] :
~ ( ord_le527798542nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__eq__nres_Osimps_I3_J) ).
thf(1561,plain,
! [A: set_b] :
~ ( ord_le527798542nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(252,axiom,
! [A: set_b,B: refine432681134nres_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ B ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_lhs__step__RES) ).
thf(1197,plain,
! [A: set_b,B: refine432681134nres_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ B ) )
=> ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(101,axiom,
! [A: set_Product_prod_a_b,B: product_prod_a_b > $o] :
( ! [C: product_prod_a_b] :
( ( member458171089od_a_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le2055430711od_a_b @ ( refine630713138od_a_b @ A ) @ ( refine630713138od_a_b @ ( collec654117139od_a_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_RES__rule) ).
thf(696,plain,
! [A: set_Product_prod_a_b,B: product_prod_a_b > $o] :
( ! [C: product_prod_a_b] :
( ( member458171089od_a_b @ C @ A )
=> ( B @ C ) )
=> ( ord_le2055430711od_a_b @ ( refine630713138od_a_b @ A ) @ ( refine630713138od_a_b @ ( collec654117139od_a_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(185,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( member_a @ A @ D )
=> ( member_a @ B @ ( image_a_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_ImageI) ).
thf(955,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( member_a @ A @ D )
=> ( member_a @ B @ ( image_a_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(244,axiom,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_RETURN__ref__SPECD) ).
thf(1172,plain,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ~ ! [D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ B )
=> ~ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(37,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_top__greatest) ).
thf(474,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
~ ( refine579265252t_unit @ top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_nofail__simps_I1_J) ).
thf(395,plain,
~ ( refine579265252t_unit @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(115,axiom,
! [A: b,B: set_b,C: refine424419629nres_a,D: b > refine424419629nres_a] :
( ( member_b @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine1264602245nd_b_a @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_RES__bind__choose) ).
thf(740,plain,
! [A: b,B: set_b,C: refine424419629nres_a,D: b > refine424419629nres_a] :
( ( member_b @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine1264602245nd_b_a @ ( refine1198353289_RES_b @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(233,axiom,
! [A: b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( member_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_nres__order__simps_I21_J) ).
thf(1129,plain,
! [A: b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( member_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(331,axiom,
! [A: $o,B: refine424419629nres_a,C: a > $o,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_if__rule) ).
thf(1537,plain,
! [A: $o,B: refine424419629nres_a,C: a > $o,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(71,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_conc__fun__FAIL) ).
thf(596,plain,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(334,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > $o] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_SPEC__trans) ).
thf(1550,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: b > $o] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(322,axiom,
ord_le527798542nres_b @ m @ ( f @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(1505,plain,
ord_le527798542nres_b @ m @ ( f @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(45,axiom,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_UNIV__eq__I) ).
thf(501,plain,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(294,axiom,
! [A: $o,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ C ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_lhs__step__If) ).
thf(1352,plain,
! [A: $o,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
=> ( ord_le527798542nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le527798542nres_b @ D @ C ) )
=> ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(33,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_b @ A )
= ( collect_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Collect__cong) ).
thf(464,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_b @ A )
= ( collect_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(194,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: b,E: refine424419629nres_a,F: set_Product_prod_a_b,G: a > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( refine1001002028nres_b @ A @ D )
=> ( ! [H: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ H ) @ B )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( G @ H ) ) ) )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_rhs__step__bind) ).
thf(982,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: b,E: refine424419629nres_a,F: set_Product_prod_a_b,G: a > refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( refine1001002028nres_b @ A @ D )
=> ( ! [H: a] :
( ( member1277678991od_b_a @ ( product_Pair_b_a @ D @ H ) @ B )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( G @ H ) ) ) )
=> ( ord_le519537037nres_a @ E @ ( refine1441824854un_a_b @ F @ ( refine436832839nd_a_b @ C @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(201,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_ord__eq__le__subst) ).
thf(1004,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ D )
=> ( ! [E: refine432681134nres_b,F: refine432681134nres_b] :
( ( ord_le527798542nres_b @ E @ F )
=> ( ord_le527798542nres_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le527798542nres_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(289,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mem__Collect__eq) ).
thf(1331,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(179,axiom,
! [A: set_Product_unit] :
( top_to177290092t_unit
!= ( refine1777164439t_unit @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_nres__inequalities_I1_J) ).
thf(935,plain,
! [A: set_Product_unit] :
( top_to177290092t_unit
!= ( refine1777164439t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(313,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ( C = D )
=> ( ord_le527798542nres_b @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ord__eq__le__eq__trans) ).
thf(1463,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ( C = D )
=> ( ord_le527798542nres_b @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(127,axiom,
! [A: set_b,B: b] :
( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ A ) @ B )
= ( member_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nf__inres__RES) ).
thf(775,plain,
! [A: set_b,B: b] :
( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ A ) @ B )
= ( member_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(314,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Collect__mono__iff) ).
thf(1468,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(303,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine436832839nd_a_b @ A @ C )
= ( refine436832839nd_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_bind__cong) ).
thf(1417,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine432681134nres_b,D: a > refine432681134nres_b] :
( ( A = B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine436832839nd_a_b @ A @ C )
= ( refine436832839nd_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(121,axiom,
! [A: set_Product_unit,B: product_unit > $o] :
( ! [C: product_unit] :
( ( member_Product_unit @ C @ A )
=> ( B @ C ) )
=> ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_RES__rule) ).
thf(755,plain,
! [A: set_Product_unit,B: product_unit > $o] :
( ! [C: product_unit] :
( ( member_Product_unit @ C @ A )
=> ( B @ C ) )
=> ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(96,axiom,
! [A: product_unit,B: set_Product_unit,C: refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine119808503unit_a @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_RES__bind__choose) ).
thf(676,plain,
! [A: product_unit,B: set_Product_unit,C: refine424419629nres_a,D: product_unit > refine424419629nres_a] :
( ( member_Product_unit @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine119808503unit_a @ ( refine1777164439t_unit @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(2553,plain,
$false,
inference(e,[status(thm)],[1322,1337,1411,1190,1237,909,893,1315,479,1105,1200,977,1406,730,1522,994,449,1305,1041,582,762,379,1269,878,440,384,1137,533,715,472,1260,538,930,1164,797,898,1001,1243,709,417,885,1601,1254,651,829,1095,404,724,504,1511,802,1313,1132,460,1577,1455,1545,817,559,1087,1609,606,881,1494,1362,1100,1319,870,789,1109,376,623,1020,1183,1334,646,485,834,602,1215,866,998,507,1564,1169,397,1119,1622,411,1345,988,1074,512,661,925,810,366,1206,452,1223,778,1580,1123,1570,1619,1502,820,392,1487,407,630,467,847,625,1178,665,1624,522,1027,682,551,1012,1573,974,1360,1592,1234,948,1064,1111,1425,593,499,1498,1587,783,420,1567,1329,753,1414,637,1016,679,547,706,1292,933,901,476,837,1114,1263,701,1297,1266,654,1246,515,1150,1627,1525,805,541,765,1187,1616,530,794,718,633,360,906,1278,745,1595,733,965,750,1154,562,423,843,743,579,1535,958,1226,875,826,577,1428,445,382,572,787,1058,1092,1090,1258,704,1209,1408,1117,736,1589,1144,616,1175,979,604,509,649,434,599,1439,890,387,1471,1080,758,858,535,609,1325,1556,943,668,1061,399,768,986,1250,1102,431,922,658,912,685,1066,868,1445,1528,1203,927,939,553,1049,490,1583,1134,487,968,1181,823,712,855,1598,640,1368,1531,1070,872,414,971,1300,791,585,840,470,951,359,643,544,1023,1284,727,1140,1372,1485,1052,1506,1272,612,1240,991,845,1459,1553,482,671,1126,771,363,556,688,903,368,1453,1276,699,946,401,781,1558,961,813,896,748,1491,914,1308,1193,1077,1212,1513,1661,832,1442,1161,800,1348,620,410,1097,1546,1303,564,1436,807,437,1561,1197,696,955,1172,474,395,740,1129,1537,596,1550,1505,501,1352,464,982,1004,1331,935,1463,775,1468,1417,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:27:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.12 % [INFO] Parsing done (258ms).
% 2.01/1.14 % [INFO] Running in sequential loop mode.
% 2.82/1.36 % [INFO] eprover registered as external prover.
% 2.82/1.36 % [INFO] cvc4 registered as external prover.
% 2.82/1.37 % [INFO] Scanning for conjecture ...
% 3.02/1.47 % [INFO] Found a conjecture and 358 axioms. Running axiom selection ...
% 3.51/1.58 % [INFO] Axiom selection finished. Selected 356 axioms (removed 2 axioms).
% 4.17/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 4.17/1.81 % [INFO] Type checking passed.
% 4.17/1.82 % [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 ...
% 33.88/7.94 % External prover 'e' found a proof!
% 33.88/7.94 % [INFO] Killing All external provers ...
% 33.88/7.95 % Time passed: 7415ms (effective reasoning time: 6805ms)
% 33.88/7.95 % 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)>
% 33.88/7.95 % Axioms used in derivation (356): fact_106_antisym, fact_332_eq__UNIV__iff, fact_243_lhs__step__RES, fact_81_dual__order_Oantisym, fact_79_order__mono__setup_Omono__if, fact_312_nres__inequalities_I1_J, fact_76_less__eq__nres_Osimps_I2_J, fact_241_RETURN__rule, fact_240_RETURN__rule, fact_264_abs__trans__additional_I1_J, fact_54_nf__inres__RES, fact_15_RES__rule, fact_294_ImageE, fact_180_pw__bind__leI, fact_192_rhs__step__bind, fact_194_RES__refine, fact_98_order__class_Oorder_Oeq__iff, fact_51_the__RES_Osimps, fact_111_Collect__cong, fact_268_abs__fun__simps_I2_J, fact_181_Collect__mono__iff, fact_80_order__mono__setup_Omono__if, fact_24_lhs__step__If, fact_198_less__eq__nres_Oelims_I1_J, fact_328_flat__ord__compat_I2_J, fact_303_top_Oextremum__unique, fact_171_pw__RES__bind__choose_I2_J, fact_72_order__subst1, fact_104_eq__refl, fact_299_top__greatest, fact_295_ImageE, fact_222_less__eq__nres_Osimps_I3_J, fact_131_GreatestI2__order, fact_130_Greatest__equality, fact_340_top__empty__eq, fact_216_sup__nres_Oinduct, fact_153_pw__RES__bind__choose_I1_J, fact_162_bind__sim__select__rule, fact_252_inres__def, fact_314_nres__cases, fact_220_less__eq__nres_Oinduct, fact_71_order__subst1, fact_257_RETURN__SPEC__refine, fact_122_ord__eq__le__subst, fact_318_nofail__def, fact_27_lhs__step__If, fact_103_eq__refl, fact_175_pw__leI_H, fact_276_nres__order__simps_I4_J, fact_331_UNIV__I, fact_301_top__greatest, fact_224_less__eq__nres_Oelims_I3_J, fact_108_mem__Collect__eq, fact_17_RES__rule, help_If_2_1_If_001t__Set__Oset_Itf__a_J_T, fact_149_ref__two__step, fact_14_RES__rule, fact_296_ImageE, fact_136_ord__eq__le__eq__trans, fact_154_rhs__step__bind__RES, fact_125_order__subst2, fact_208_less__eq__nres_Osimps_I1_J, fact_218_less__nres_Oinduct, fact_142_pwD1, fact_290_rev__ImageI, fact_124_order__subst2, fact_113_eq__iff, fact_2_nres__more__simps_I4_J, help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_39_RES__bind__choose, fact_60_nf__inres__RES, fact_47_order__mono__setup_Orefl, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_186_subset__iff, fact_150_ref__two__step, fact_97_order__class_Oorder_Oeq__iff, fact_233_nres__order__simps_I20_J, fact_143_le__nofailI, fact_25_lhs__step__If, fact_101_order_Otrans, fact_68_le__funI, fact_258_RETURN__SPEC__refine, fact_204_less__nres_Ocases, fact_100_antisym__conv, fact_43_RES__bind__choose, fact_13_RES__rule, fact_273_ImageI, fact_59_nf__inres__RES, fact_205_sup__nres_Ocases, fact_132_GreatestI2__order, fact_44_order__mono__setup_Orefl, fact_36_RES__bind__choose, fact_6_nres_Oinject, fact_215_sup__nres_Oinduct, fact_266_abs__fun__simps_I3_J, fact_128_the__RES__inv, fact_160_bind__sim__select__rule, fact_338_UNIV__eq__I, fact_42_RES__bind__choose, fact_88_dual__order_Orefl, fact_251_inres__def, fact_189_rhs__step__bind, fact_242_lhs__step__RES, fact_191_rhs__step__bind, fact_119_ord__eq__le__subst, fact_22_SPEC__trans, fact_85_dual__order_Otrans, fact_274_ImageI, fact_336_top__set__def, fact_70_Refine__Misc_Oif__mono, fact_330_UNIV__I, fact_176_pw__le__iff, fact_282_bind__FAIL, fact_183_Collect__mono, fact_300_top__greatest, fact_55_nf__inres__RES, fact_230_ret__le__down__conv, help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_163_in__mono, fact_92_order__class_Oorder_Oantisym, fact_200_less__eq__nres_Oelims_I2_J, fact_210_nres_Odistinct_I1_J, fact_262_abs__trans__additional_I1_J, fact_280_conc__fun__fail__iff_I2_J, fact_206_sup__nres_Ocases, fact_172_pw__leI, fact_306_top_Oextremum__uniqueI, fact_313_nres__inequalities_I1_J, fact_284_inres__simps_I1_J, fact_91_order__class_Oorder_Oantisym, fact_95_ord__eq__le__trans, fact_61_nf__inres__SPEC, fact_281_bind__FAIL, fact_237_nres__order__simps_I21_J, fact_89_order__trans, fact_20_SPEC__rule, fact_178_pw__bind__nofail, fact_173_pw__leI, fact_302_top_Oextremum__unique, fact_227_return__refine__prop__return, fact_169_pwD2, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T, fact_45_order__mono__setup_Orefl, fact_146_nofail__RES__conv, fact_232_ret__le__down__conv, fact_65_le__funD, fact_179_pw__bind__le__iff, fact_248_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_129_Greatest__equality, fact_69_Refine__Misc_Oif__mono, fact_246_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_285_nres__simp__internals_I2_J, fact_261_abs__trans__additional_I1_J, fact_148_ref__two__step, fact_226_return__refine__prop__return, fact_37_RES__bind__choose, help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T, fact_96_ord__eq__le__trans, fact_152_le__RES__nofailI, fact_67_le__funE, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T, fact_316_nres__cases, fact_107_mem__Collect__eq, fact_112_Collect__cong, fact_322_meta__le__everything__if__top, fact_217_less__nres_Oinduct, fact_8_if__rule, fact_5_nres_Oinject, fact_342_ASSERT__simps_I2_J, fact_155_rhs__step__bind__RES, fact_195_RES__refine, fact_145_nofail__RES__conv, fact_48_order__mono__setup_Orefl, fact_58_nf__inres__RES, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_30_lhs__step__If, fact_151_le__RES__nofailI, fact_315_nres__cases, fact_49_order__mono__setup_Orefl, fact_7_nres_Oinject, fact_235_nres__monad1, help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T, fact_53_the__RES_Osimps, fact_50_order__mono__setup_Orefl, help_If_2_1_If_001t__Set__Oset_Itf__b_J_T, fact_197_less__eq__nres_Oelims_I1_J, fact_319_intro__nofail_I2_J, fact_157_rhs__step__bind__SPEC, fact_278_conc__fun__FAIL, fact_33_SPEC__cons__rule, fact_133_le__rel__bool__arg__iff, fact_62_nf__inres__SPEC, fact_187_subset__eq, fact_126_order__subst2, fact_75_less__eq__nres_Osimps_I2_J, fact_279_conc__fun__fail__iff_I1_J, fact_185_subset__iff, fact_73_order__subst1, fact_327_flat__ord__compat_I2_J, fact_117_ord__le__eq__subst, fact_120_ord__eq__le__subst, fact_115_ord__le__eq__subst, fact_1_assms_I2_J, fact_135_ord__eq__le__eq__trans, fact_309_nres__order__simps_I3_J, fact_12_RES__rule, fact_221_less__eq__nres_Osimps_I3_J, fact_244_RETURN__to__SPEC__rule, fact_78_nres__order__simps_I5_J, fact_188_subset__eq, fact_19_SPEC__rule, fact_211_nres_Oinduct, fact_193_RES__refine, fact_21_SPEC__trans, fact_83_dual__order_Oeq__iff, fact_292_rev__ImageI, fact_184_Collect__mono, fact_311_nres__inequalities_I1_J, fact_234_nres__order__simps_I20_J, fact_269_abs__fun__simps_I2_J, fact_255_RETURN__ref__SPECD, fact_167_inres__simps_I2_J, fact_38_RES__bind__choose, fact_304_top_Oextremum__unique, fact_105_antisym, fact_74_order__subst1, fact_114_eq__iff, fact_297_nres__inequalities_I3_J, fact_165_subsetD, fact_236_nres__order__simps_I21_J, fact_156_rhs__step__bind__SPEC, fact_228_return__refine__prop__return, fact_177_pw__le__iff, fact_41_RES__bind__choose, fact_249_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_64_le__funD, fact_271_ImageI, fact_16_RES__rule, fact_229_ret__le__down__conv, fact_77_nres__order__simps_I5_J, fact_23_SPEC__trans, fact_118_ord__le__eq__subst, fact_286_abs__fun__simps_I1_J, fact_164_in__mono, fact_84_dual__order_Oeq__iff, fact_166_subsetD, fact_209_nres_Odistinct_I1_J, fact_333_eq__UNIV__iff, fact_219_less__eq__nres_Oinduct, fact_239_SPEC__eq__is__RETURN_I1_J, fact_247_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_231_ret__le__down__conv, fact_267_abs__fun__simps_I2_J, fact_334_UNIV__witness, fact_9_if__rule, fact_109_Collect__mem__eq, fact_339_UNIV__eq__I, fact_32_SPEC__cons__rule, fact_275_nres__order__simps_I4_J, fact_320_ibind__strict_I2_J, fact_123_order__subst2, fact_127_the__RES__inv, fact_253_RETURN__ref__SPECD, fact_90_order__trans, fact_298_top__nres__def, fact_161_bind__sim__select__rule, fact_28_lhs__step__If, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_307_top_Oextremum__uniqueI, fact_291_rev__ImageI, fact_225_return__refine__prop__return, fact_4_nres__more__simps_I4_J, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_137_nofail__simps_I2_J, fact_245_RETURN__to__SPEC__rule, fact_57_nf__inres__RES, fact_201_less__eq__nres_Ocases, fact_259_RETURN__SPEC__refine, fact_196_RES__refine, fact_199_less__eq__nres_Oelims_I2_J, fact_293_ImageE, fact_270_abs__fun__simps_I2_J, fact_26_lhs__step__If, fact_323_meta__le__everything__if__top, fact_310_nres__order__simps_I3_J, fact_56_nf__inres__RES, fact_147_ref__two__step, fact_35_RES__bind__choose, fact_3_nres__more__simps_I4_J, fact_40_RES__bind__choose, fact_29_lhs__step__If, fact_144_le__nofailI, fact_223_less__eq__nres_Oelims_I3_J, fact_212_nres_Oinduct, fact_159_subsetI, fact_94_ord__le__eq__trans, fact_182_Collect__mono__iff, fact_31_SPEC__cons__rule, fact_289_rev__ImageI, fact_207_less__eq__nres_Osimps_I1_J, fact_99_antisym__conv, help_If_1_1_If_001t__Set__Oset_Itf__a_J_T, fact_170_pwD2, fact_66_le__funE, fact_260_RETURN__SPEC__refine, fact_174_pw__leI_H, fact_203_less__nres_Ocases, fact_158_subsetI, fact_87_dual__order_Orefl, fact_335_UNIV__witness, fact_110_Collect__mem__eq, help_If_1_1_If_001t__Set__Oset_Itf__b_J_T, fact_214_nres_Oexhaust, fact_256_RETURN__ref__SPECD, fact_0_assms_I1_J, fact_190_rhs__step__bind, fact_121_ord__eq__le__subst, fact_46_order__mono__setup_Orefl, fact_140_subset__Collect__conv, fact_18_SPEC__rule, fact_63_nf__inres__SPEC, fact_134_le__rel__bool__arg__iff, fact_139_subset__Collect__conv, fact_34_RES__bind__choose, fact_10_if__rule, help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_287_FAIL__refine, fact_11_RES__rule, fact_288_FAIL__refine, fact_265_abs__fun__simps_I3_J, fact_263_abs__trans__additional_I1_J, fact_202_less__eq__nres_Ocases, fact_86_dual__order_Otrans, fact_305_top_Oextremum__uniqueI, fact_329_flat__ord__compat_I2_J, fact_141_pwD1, fact_308_nres__order__simps_I3_J, fact_82_dual__order_Oantisym, fact_283_nofail__simps_I1_J, fact_250_bind__cong, fact_277_nres__order__simps_I4_J, fact_238_SPEC__eq__is__RETURN_I1_J, fact_52_the__RES_Osimps, fact_321_meta__le__everything__if__top, fact_168_inres__simps_I2_J, fact_317_not__nofail__iff, fact_138_nofail__simps_I2_J, fact_213_nres_Oexhaust, fact_326_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J, fact_324_pw__flat__ge__iff, fact_272_ImageI, fact_254_RETURN__ref__SPECD, fact_116_ord__le__eq__subst, fact_93_ord__le__eq__trans, fact_102_order_Otrans
% 33.88/7.95 % No. of inferences in proof: 716
% 33.88/7.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7415 ms resp. 6805 ms w/o parsing
% 34.47/8.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.47/8.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------