%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP159^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:59 AM UTC 2026
% Result : Theorem 20.30s 5.49s
% Output : Refutation 22.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 355
% Syntax : Number of formulae : 712 ( 295 unt; 0 typ; 0 def)
% Number of atoms : 1987 ( 562 equ; 46 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5233 ( 56 ~; 1 |; 66 &;4182 @)
% ( 0 <=>; 928 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 412 ( 412 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 12 con; 0-4 aty)
% Number of variables : 1877 ( 124 ^;1741 !; 12 ?;1877 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr451126599t_unit_type,type,
set_Pr451126599t_unit: $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(set_Pr712638521unit_b_type,type,
set_Pr712638521unit_b: $tType ).
thf(set_Pr1720557880unit_a_type,type,
set_Pr1720557880unit_a: $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(product_prod_b_b_type,type,
product_prod_b_b: $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_decl,type,
if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
thf(if_o_R697118589nres_b_decl,type,
if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
thf(if_Ref1724547303nres_a_decl,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(if_Ref1732808808nres_b_decl,type,
if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(if_set1550076877od_a_a_decl,type,
if_set1550076877od_a_a: $o > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(if_set_a_decl,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(if_set_b_decl,type,
if_set_b: $o > set_b > set_b > set_b ).
thf(sup_su2034729561nres_a_decl,type,
sup_su2034729561nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(sup_su2042991066nres_b_decl,type,
sup_su2042991066nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(ord_le516598614nres_a_decl,type,
ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
thf(ord_le1656162903nres_b_decl,type,
ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
thf(ord_le1051254044t_unit_decl,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(ord_le519537037nres_a_decl,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(ord_le527798542nres_b_decl,type,
ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
thf(ord_le1824328871od_a_a_decl,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_le816409512od_a_b_decl,type,
ord_le816409512od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o ).
thf(ord_le2044239718od_b_a_decl,type,
ord_le2044239718od_b_a: set_Product_prod_b_a > set_Product_prod_b_a > $o ).
thf(ord_le1036320359od_b_b_decl,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ord_less_eq_set_b_decl,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(order_1714329108nres_a_decl,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(order_1722590613nres_b_decl,type,
order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
thf(top_to2046902534nres_a_decl,type,
top_to2046902534nres_a: $o > refine424419629nres_a ).
thf(top_to177290092t_unit_decl,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(top_to231829469nres_a_decl,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(top_to240090974nres_b_decl,type,
top_to240090974nres_b: refine432681134nres_b ).
thf(top_to398455383od_a_a_decl,type,
top_to398455383od_a_a: set_Product_prod_a_a ).
thf(top_top_set_a_decl,type,
top_top_set_a: set_a ).
thf(product_Pair_a_a_decl,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(product_Pair_a_b_decl,type,
product_Pair_a_b: a > b > product_prod_a_b ).
thf(product_Pair_b_b_decl,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(refine2063221604TURN_a_decl,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine2063221605TURN_b_decl,type,
refine2063221605TURN_b: b > refine432681134nres_b ).
thf(refine1136779702un_a_a_decl,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine1136779703un_a_b_decl,type,
refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
thf(refine1964549109un_b_a_decl,type,
refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
thf(refine1964549110un_b_b_decl,type,
refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(refine119808503unit_a_decl,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine119808504unit_b_decl,type,
refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine436832838nd_a_a_decl,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine436832839nd_a_b_decl,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine1264602245nd_b_a_decl,type,
refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine1264602246nd_b_b_decl,type,
refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine944483349t_unit_decl,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(refine2043866374unit_a_decl,type,
refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
thf(refine2043866375unit_b_decl,type,
refine2043866375unit_b: set_Pr712638521unit_b > refine432681134nres_b > refine787176636t_unit ).
thf(refine2021053540t_unit_decl,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(refine1441824853un_a_a_decl,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(refine1441824854un_a_b_decl,type,
refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
thf(refine2140306339t_unit_decl,type,
refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
thf(refine122110612un_b_a_decl,type,
refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
thf(refine122110613un_b_b_decl,type,
refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(refine1001002027nres_a_decl,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(refine1001002028nres_b_decl,type,
refine1001002028nres_b: refine432681134nres_b > b > $o ).
thf(refine412683989fail_a_decl,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(refine412683990fail_b_decl,type,
refine412683990fail_b: refine432681134nres_b > $o ).
thf(refine1198353288_RES_a_decl,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(refine1198353289_RES_b_decl,type,
refine1198353289_RES_b: set_b > refine432681134nres_b ).
thf(id_a_decl,type,
id_a: set_Product_prod_a_a ).
thf(id_b_decl,type,
id_b: set_Product_prod_b_b ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(collect_b_decl,type,
collect_b: ( b > $o ) > set_b ).
thf(member449909584od_a_a_decl,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member458171089od_a_b_decl,type,
member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
thf(member1285940496od_b_b_decl,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(member_b_decl,type,
member_b: b > set_b > $o ).
thf(r_decl,type,
r: set_Product_prod_a_b ).
thf(x_decl,type,
x: refine424419629nres_a ).
thf(281,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/sandbox/benchmark/theBenchmark.p',fact_217_ord__eq__le__subst) ).
thf(1322,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)],[281]) ).
thf(331,axiom,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ C @ ( refine2063221604TURN_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_RETURN__refine) ).
thf(1501,plain,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824853un_a_a @ C @ ( refine2063221604TURN_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',fact_222_order__subst2) ).
thf(1469,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)],[325]) ).
thf(241,axiom,
( refine412683990fail_b
= ( ^ [A: refine432681134nres_b] : ( A != top_to240090974nres_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_nofail__def) ).
thf(1190,plain,
( refine412683990fail_b
= ( ^ [A: refine432681134nres_b] : ( A != top_to240090974nres_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(122,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nres__order__simps_I4_J) ).
thf(760,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(346,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_le__nofailI) ).
thf(1559,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)],[346]) ).
thf(195,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( ( refine944483349t_unit @ A @ B )
= top_to177290092t_unit )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_conc__fun__fail__iff_I1_J) ).
thf(1031,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)],[195]) ).
thf(237,axiom,
! [A: refine432681134nres_b] :
( ( A != top_to240090974nres_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_nres__cases) ).
thf(1179,plain,
! [A: refine432681134nres_b] :
( ( A != top_to240090974nres_b )
=> ~ ! [B: set_b] :
( A
!= ( refine1198353289_RES_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(57,axiom,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( ( refine2021053540t_unit @ A @ B )
= top_to231829469nres_a )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_conc__fun__fail__iff_I1_J) ).
thf(555,plain,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( ( refine2021053540t_unit @ A @ B )
= top_to231829469nres_a )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(189,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_order__class_Oorder_Oantisym) ).
thf(1005,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(100,axiom,
! [A: set_b,B: set_b] :
( ( if_set_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_Itf__b_J_T) ).
thf(683,plain,
! [A: set_b,B: set_b] :
( ( if_set_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(113,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_order__class_Oorder_Oeq__iff) ).
thf(730,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)],[113]) ).
thf(207,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_antisym) ).
thf(1068,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(185,axiom,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine122110613un_b_b @ A @ B ) )
= ( refine412683990fail_b @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_pw__conc__nofail) ).
thf(994,plain,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( refine412683990fail_b @ ( refine122110613un_b_b @ A @ B ) )
= ( refine412683990fail_b @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(305,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_conc__trans__additional_I2_J) ).
thf(1401,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(349,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_conc__trans__additional_I5_J) ).
thf(1569,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(117,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_ord__eq__le__trans) ).
thf(741,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(246,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order__subst1) ).
thf(1205,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)],[246]) ).
thf(315,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_eq__refl) ).
thf(1437,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(78,axiom,
! [A: $o,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a,E: $o > refine424419629nres_a] :
( ( A
=> ( ord_le516598614nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le516598614nres_a @ D @ E ) )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ A @ B @ D ) @ ( if_o_R1705037948nres_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Refine__Misc_Oif__mono) ).
thf(614,plain,
! [A: $o,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a,E: $o > refine424419629nres_a] :
( ( A
=> ( ord_le516598614nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le516598614nres_a @ D @ E ) )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ A @ B @ D ) @ ( if_o_R1705037948nres_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(98,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_dual__order_Otrans) ).
thf(677,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(277,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nres__order__simps_I4_J) ).
thf(1310,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(43,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( A = B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_ord__eq__le__trans) ).
thf(500,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( A = B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(34,axiom,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
& ( ord_less_eq_set_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_order__class_Oorder_Oeq__iff) ).
thf(472,plain,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
& ( ord_less_eq_set_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(263,axiom,
! [A: set_Product_prod_b_a] :
( ( refine122110612un_b_a @ A @ top_to231829469nres_a )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_conc__fun__FAIL) ).
thf(1260,plain,
! [A: set_Product_prod_b_a] :
( ( refine122110612un_b_a @ A @ top_to231829469nres_a )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(285,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_abs__trans__additional_I2_J) ).
thf(1342,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_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)],[285]) ).
thf(173,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_eq__refl) ).
thf(945,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(289,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_conc__trans) ).
thf(1354,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(322,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__trans) ).
thf(1458,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)],[322]) ).
thf(224,axiom,
! [A: set_Product_prod_a_b] :
( ( refine1136779703un_a_b @ A @ top_to231829469nres_a )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_abs__fun__simps_I1_J) ).
thf(1127,plain,
! [A: set_Product_prod_a_b] :
( ( refine1136779703un_a_b @ A @ top_to231829469nres_a )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(316,axiom,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( ( refine1441824854un_a_b @ A @ B )
= top_to231829469nres_a )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_conc__fun__fail__iff_I1_J) ).
thf(1441,plain,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( ( refine1441824854un_a_b @ A @ B )
= top_to231829469nres_a )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(142,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
=> ( A = top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_top_Oextremum__uniqueI) ).
thf(841,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
=> ( A = top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_96_Refine__Misc_Oif__mono) ).
thf(436,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)],[24]) ).
thf(10,axiom,
! [A: set_b,B: set_b] :
( ( A = B )
=> ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_eq__refl) ).
thf(389,plain,
! [A: set_b,B: set_b] :
( ( A = B )
=> ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(273,axiom,
! [A: refine424419629nres_a,B: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Id__SPEC__refine) ).
thf(1298,plain,
! [A: refine424419629nres_a,B: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_223_order__subst2) ).
thf(719,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)],[110]) ).
thf(278,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_conc__trans) ).
thf(1313,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824853un_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(321,axiom,
! [A: product_unit > refine432681134nres_b] :
( ( refine119808504unit_b @ top_to177290092t_unit @ A )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_ibind__strict_I2_J) ).
thf(1455,plain,
! [A: product_unit > refine432681134nres_b] :
( ( refine119808504unit_b @ top_to177290092t_unit @ A )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1,conjecture,
ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(357,plain,
~ ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(174,axiom,
! [A: set_a,B: set_a] :
( ( if_set_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_Itf__a_J_T) ).
thf(949,plain,
! [A: set_a,B: set_a] :
( ( if_set_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(111,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_dual__order_Otrans) ).
thf(724,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(203,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_order__class_Oorder_Oantisym) ).
thf(1055,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',fact_343_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1409,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)],[308]) ).
thf(334,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1511,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)],[334]) ).
thf(165,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( refine412683990fail_b @ B )
=> ( refine412683990fail_b @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_pwD1) ).
thf(917,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)],[165]) ).
thf(343,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_top__greatest) ).
thf(1545,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(83,axiom,
! [A: refine424419629nres_a] :
( ( top_to231829469nres_a != A )
= ( refine412683989fail_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_intro__nofail_I2_J) ).
thf(638,plain,
! [A: refine424419629nres_a] :
( ( top_to231829469nres_a != A )
= ( refine412683989fail_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(213,axiom,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] : ( A != top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_nofail__def) ).
thf(1087,plain,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] : ( A != top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_282_abs__trans__additional_I1_J) ).
thf(1247,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)],[258]) ).
thf(280,axiom,
! [A: set_Product_prod_b_b] :
( ( refine122110613un_b_b @ A @ top_to240090974nres_b )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_conc__fun__FAIL) ).
thf(1319,plain,
! [A: set_Product_prod_b_b] :
( ( refine122110613un_b_b @ A @ top_to240090974nres_b )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(304,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_SPEC__trans) ).
thf(1398,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)],[304]) ).
thf(252,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_dual__order_Orefl) ).
thf(1232,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(181,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_order__class_Oorder_Oantisym) ).
thf(969,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)],[181]) ).
thf(350,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order_Otrans) ).
thf(1572,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)],[350]) ).
thf(70,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_abs__trans__additional_I4_J) ).
thf(591,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(198,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(1040,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(86,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( if_set1550076877od_a_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T) ).
thf(646,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( if_set1550076877od_a_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_274_SPEC__trans) ).
thf(514,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)],[46]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',fact_295_RETURN__to__SPEC__rule) ).
thf(1383,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)],[298]) ).
thf(180,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_abs__trans__additional_I5_J) ).
thf(966,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(37,axiom,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__class_Oorder_Oantisym) ).
thf(480,plain,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
& ( ord_le1656162903nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_eq__iff) ).
thf(485,plain,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
& ( ord_le1656162903nres_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_165_ord__eq__le__trans) ).
thf(834,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)],[140]) ).
thf(238,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_dual__order_Oeq__iff) ).
thf(1183,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)],[238]) ).
thf(270,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_abs__trans__additional_I1_J) ).
thf(1283,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)],[270]) ).
thf(74,axiom,
! [A: set_Product_prod_b_a,B: set_Product_prod_b_a,C: refine424419629nres_a] :
( ( ord_le2044239718od_b_a @ A @ B )
=> ( ord_le527798542nres_b @ ( refine122110612un_b_a @ A @ C ) @ ( refine122110612un_b_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_conc__fun__R__mono) ).
thf(602,plain,
! [A: set_Product_prod_b_a,B: set_Product_prod_b_a,C: refine424419629nres_a] :
( ( ord_le2044239718od_b_a @ A @ B )
=> ( ord_le527798542nres_b @ ( refine122110612un_b_a @ A @ C ) @ ( refine122110612un_b_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(296,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_less__eq__nres_Osimps_I2_J) ).
thf(1377,plain,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(248,axiom,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( refine412683989fail_a @ ( refine1441824854un_a_b @ A @ B ) )
= ( refine412683990fail_b @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_pw__conc__nofail) ).
thf(1215,plain,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( refine412683989fail_a @ ( refine1441824854un_a_b @ A @ B ) )
= ( refine412683990fail_b @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(153,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1441824853un_a_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_pw__conc__nofail) ).
thf(877,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( refine1441824853un_a_a @ A @ B ) )
= ( refine412683989fail_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(318,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nres__order__simps_I3_J) ).
thf(1447,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(151,axiom,
( ( refine1001002027nres_a @ top_to231829469nres_a )
= ( ^ [A: a] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_inres__simps_I1_J) ).
thf(866,plain,
( ( refine1001002027nres_a @ top_to231829469nres_a )
= ( ^ [A: a] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(91,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
& ( ord_le527798542nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_eq__iff) ).
thf(660,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)],[91]) ).
thf(286,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ B ) @ D )
=> ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_abs__trans__additional_I2_J) ).
thf(1345,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_a,D: refine424419629nres_a] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_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)],[286]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_229_Greatest__equality) ).
thf(527,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)],[50]) ).
thf(234,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_abs__trans__additional_I4_J) ).
thf(1169,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(13,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order__mono__setup_Orefl) ).
thf(397,plain,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_36_conc__trans__additional_I1_J) ).
thf(1242,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)],[256]) ).
thf(145,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__trans) ).
thf(849,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(209,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a,E: $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ E @ A @ C ) @ ( if_set1550076877od_a_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__mono__setup_Omono__if) ).
thf(1074,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a,E: $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ E @ A @ C ) @ ( if_set1550076877od_a_a @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(28,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_order_Otrans) ).
thf(452,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_conc__trans__additional_I5_J) ).
thf(546,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(229,axiom,
! [A: set_Product_prod_b_b] :
( ( refine1964549110un_b_b @ A @ top_to240090974nres_b )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_abs__fun__simps_I1_J) ).
thf(1153,plain,
! [A: set_Product_prod_b_b] :
( ( refine1964549110un_b_b @ A @ top_to240090974nres_b )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(5,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > $o > refine432681134nres_b,D: $o > refine432681134nres_b] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_le1656162903nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1656162903nres_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_ord__le__eq__subst) ).
thf(366,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > $o > refine432681134nres_b,D: $o > refine432681134nres_b] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_le1656162903nres_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1656162903nres_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(267,axiom,
! [A: set_Pr1707992533t_unit,B: refine787176636t_unit] :
( ( top_to240090974nres_b
= ( refine2140306339t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_conc__fun__fail__iff_I2_J) ).
thf(1274,plain,
! [A: set_Pr1707992533t_unit,B: refine787176636t_unit] :
( ( top_to240090974nres_b
= ( refine2140306339t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(137,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: set_Product_prod_b_b,E: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ ( refine122110613un_b_b @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_conc__trans) ).
thf(825,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: set_Product_prod_b_b,E: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ ( refine122110613un_b_b @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(175,axiom,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A )
= ( A = top_to398455383od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_top_Oextremum__unique) ).
thf(952,plain,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A )
= ( A = top_to398455383od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(352,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_ord__le__eq__trans) ).
thf(1580,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)],[352]) ).
thf(261,axiom,
( ord_le516598614nres_a
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
! [C: $o] : ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_le__fun__def) ).
thf(1255,plain,
( ord_le516598614nres_a
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
! [C: $o] : ( ord_le519537037nres_a @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_318_RES__refine) ).
thf(598,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)],[73]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_296_RETURN__to__SPEC__rule) ).
thf(820,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)],[135]) ).
thf(19,axiom,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_antisym__conv) ).
thf(424,plain,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ! [C: $o] : ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) )
=> ( ord_le1656162903nres_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__funI) ).
thf(429,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ! [C: $o] : ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) )
=> ( ord_le1656162903nres_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(294,axiom,
~ ( refine412683990fail_b @ top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_nofail__simps_I1_J) ).
thf(1370,plain,
~ ( refine412683990fail_b @ top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(134,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_ord__eq__le__trans) ).
thf(815,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(300,axiom,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_nres__order__simps_I21_J) ).
thf(1387,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)],[300]) ).
thf(163,axiom,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_dual__order_Orefl) ).
thf(910,plain,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(177,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__trans) ).
thf(957,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(158,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( ( refine1441824853un_a_a @ A @ B )
= top_to231829469nres_a )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_conc__fun__fail__iff_I1_J) ).
thf(894,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( ( refine1441824853un_a_a @ A @ B )
= top_to231829469nres_a )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(118,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( A = B )
=> ( ord_le516598614nres_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_eq__refl) ).
thf(746,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( A = B )
=> ( ord_le516598614nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(215,axiom,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ top_to177290092t_unit @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_ibind__strict_I2_J) ).
thf(1091,plain,
! [A: product_unit > refine424419629nres_a] :
( ( refine119808503unit_a @ top_to177290092t_unit @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(15,axiom,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_antisym) ).
thf(407,plain,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,axiom,
! [A: b,B: set_b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine1198353289_RES_b @ B ) )
= ( member_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_nres__order__simps_I21_J) ).
thf(630,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)],[81]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_227_order__subst1) ).
thf(625,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)],[80]) ).
thf(146,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T) ).
thf(852,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)],[146]) ).
thf(93,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_abs__trans__additional_I6_J) ).
thf(665,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(247,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ord__eq__le__trans) ).
thf(1210,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)],[247]) ).
thf(121,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_abs__fun__simps_I1_J) ).
thf(757,plain,
! [A: set_Product_prod_a_a] :
( ( refine1136779702un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_144_order__trans) ).
thf(710,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)],[107]) ).
thf(218,axiom,
! [A: refine432681134nres_b,B: b > $o] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Id__SPEC__refine) ).
thf(1106,plain,
! [A: refine432681134nres_b,B: b > $o] :
( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ ( refine1198353289_RES_b @ ( collect_b @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(144,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nres__order__simps_I3_J) ).
thf(847,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_186_order_Otrans) ).
thf(566,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)],[61]) ).
thf(67,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ C @ ( refine2063221605TURN_b @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_RETURN__refine) ).
thf(583,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine122110613un_b_b @ C @ ( refine2063221605TURN_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_order__class_Oorder_Oeq__iff) ).
thf(522,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(231,axiom,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( top_to231829469nres_a
= ( refine1441824854un_a_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_conc__fun__fail__iff_I2_J) ).
thf(1159,plain,
! [A: set_Product_prod_a_b,B: refine432681134nres_b] :
( ( top_to231829469nres_a
= ( refine1441824854un_a_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(31,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_ord__eq__le__trans) ).
thf(461,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( A = B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(243,axiom,
! [A: set_Pr1707992533t_unit,B: refine787176636t_unit] :
( ( ( refine2140306339t_unit @ A @ B )
= top_to240090974nres_b )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_conc__fun__fail__iff_I1_J) ).
thf(1195,plain,
! [A: set_Pr1707992533t_unit,B: refine787176636t_unit] :
( ( ( refine2140306339t_unit @ A @ B )
= top_to240090974nres_b )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',fact_88_le__funI) ).
thf(1407,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)],[307]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',fact_319_RES__refine) ).
thf(1360,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)],[291]) ).
thf(65,axiom,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_conc__fun__FAIL) ).
thf(578,plain,
! [A: set_Product_prod_a_a] :
( ( refine1441824853un_a_a @ A @ top_to231829469nres_a )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(228,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( refine412683989fail_a @ B ) )
=> ( ! [C: a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_pw__leI_H) ).
thf(1143,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)],[228]) ).
thf(250,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_eq__iff) ).
thf(1227,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)],[250]) ).
thf(311,axiom,
! [A: set_Product_prod_b_a,B: refine424419629nres_a] :
( ( ( refine122110612un_b_a @ A @ B )
= top_to240090974nres_b )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_conc__fun__fail__iff_I1_J) ).
thf(1425,plain,
! [A: set_Product_prod_b_a,B: refine424419629nres_a] :
( ( ( refine122110612un_b_a @ A @ B )
= top_to240090974nres_b )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',fact_342_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1138,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)],[227]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_268_if__rule) ).
thf(783,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)],[126]) ).
thf(103,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T) ).
thf(697,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)],[103]) ).
thf(214,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_order__class_Oorder_Oeq__iff) ).
thf(1089,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(253,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nres__order__simps_I3_J) ).
thf(1234,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(339,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Id__refine) ).
thf(1534,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(191,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order__mono__setup_Orefl) ).
thf(1017,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(120,axiom,
! [A: set_a] :
( top_to231829469nres_a
!= ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_nres__inequalities_I1_J) ).
thf(753,plain,
! [A: set_a] :
( top_to231829469nres_a
!= ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(323,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_dual__order_Oantisym) ).
thf(1461,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)],[323]) ).
thf(309,axiom,
! [A: a,B: b,C: set_Product_prod_a_b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ C @ ( refine2063221605TURN_b @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_RETURN__refine) ).
thf(1414,plain,
! [A: a,B: b,C: set_Product_prod_a_b] :
( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1441824854un_a_b @ C @ ( refine2063221605TURN_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(194,axiom,
! [A: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A )
= ( A = top_to2046902534nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_top_Oextremum__unique) ).
thf(1028,plain,
! [A: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A )
= ( A = top_to2046902534nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(211,axiom,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
& ( ord_le516598614nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_order__class_Oorder_Oeq__iff) ).
thf(1082,plain,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
& ( ord_le516598614nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(160,axiom,
! [A: refine424419629nres_a] :
( ( ~ ( refine412683989fail_a @ A ) )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_not__nofail__iff) ).
thf(901,plain,
! [A: refine424419629nres_a] :
( ( ~ ( refine412683989fail_a @ A ) )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_215_ord__le__eq__subst) ).
thf(686,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)],[101]) ).
thf(79,axiom,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( refine1441824853un_a_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_conc__fun__fail__iff_I2_J) ).
thf(622,plain,
! [A: set_Product_prod_a_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( refine1441824853un_a_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(116,axiom,
! [A: set_b,B: set_b] :
( ( if_set_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_Itf__b_J_T) ).
thf(738,plain,
! [A: set_b,B: set_b] :
( ( if_set_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_34_conc__trans__additional_I1_J) ).
thf(654,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)],[89]) ).
thf(242,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_antisym) ).
thf(1192,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)],[242]) ).
thf(188,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ C @ A )
=> ( ord_le516598614nres_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_dual__order_Otrans) ).
thf(1002,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ C @ A )
=> ( ord_le516598614nres_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_272_SPEC__rule) ).
thf(569,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)],[62]) ).
thf(11,axiom,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_order__mono__setup_Orefl) ).
thf(393,plain,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_267_if__rule) ).
thf(1114,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)],[221]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',fact_221_order__subst2) ).
thf(1263,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)],[264]) ).
thf(186,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_dual__order_Orefl) ).
thf(997,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',fact_269_RES__rule) ).
thf(1530,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)],[338]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',fact_85_le__funD) ).
thf(1539,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)],[341]) ).
thf(205,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ord__le__eq__trans) ).
thf(1060,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_276_SPEC__cons__rule) ).
thf(1050,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)],[202]) ).
thf(75,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_antisym) ).
thf(605,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)],[75]) ).
thf(302,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_order__class_Oorder_Oeq__iff) ).
thf(1393,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)],[302]) ).
thf(314,axiom,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( top_to240090974nres_b
= ( refine122110613un_b_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_conc__fun__fail__iff_I2_J) ).
thf(1434,plain,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( top_to240090974nres_b
= ( refine122110613un_b_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(170,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_top__greatest) ).
thf(938,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_235_ord__eq__le__eq__trans) ).
thf(633,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)],[82]) ).
thf(53,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = top_to398455383od_a_a )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_meta__le__everything__if__top) ).
thf(541,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = top_to398455383od_a_a )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(124,axiom,
! [A: $o,B: set_a,C: set_a,D: set_a,E: set_a] :
( ( A
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_a @ D @ E ) )
=> ( ord_less_eq_set_a @ ( if_set_a @ A @ B @ D ) @ ( if_set_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Refine__Misc_Oif__mono) ).
thf(765,plain,
! [A: $o,B: set_a,C: set_a,D: set_a,E: set_a] :
( ( A
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_a @ D @ E ) )
=> ( ord_less_eq_set_a @ ( if_set_a @ A @ B @ D ) @ ( if_set_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(271,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_conc__trans__additional_I4_J) ).
thf(1286,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(233,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_pwD1) ).
thf(1167,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)],[233]) ).
thf(239,axiom,
! [A: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ top_to231829469nres_a @ A )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_bind__FAIL) ).
thf(1185,plain,
! [A: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ top_to231829469nres_a @ A )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_330_pw__leI_H) ).
thf(773,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)],[125]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_326_pwD2) ).
thf(662,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)],[92]) ).
thf(168,axiom,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_conc__fun__FAIL) ).
thf(926,plain,
! [A: set_Pr451126599t_unit] :
( ( refine944483349t_unit @ A @ top_to177290092t_unit )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(347,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_antisym__conv) ).
thf(1563,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)],[347]) ).
thf(90,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T) ).
thf(657,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(58,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_top__greatest) ).
thf(558,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ top_to398455383od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(208,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
= ( A = top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_top_Oextremum__unique) ).
thf(1071,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
= ( A = top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(119,axiom,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_bind__FAIL) ).
thf(750,plain,
! [A: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(329,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_order__mono__setup_Orefl) ).
thf(1483,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(63,axiom,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( ( refine2043866374unit_a @ A @ B )
= top_to177290092t_unit )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_conc__fun__fail__iff_I1_J) ).
thf(573,plain,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( ( refine2043866374unit_a @ A @ B )
= top_to177290092t_unit )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(25,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b,E: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ C @ D )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ E @ A @ C ) @ ( if_o_R697118589nres_b @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_order__mono__setup_Omono__if) ).
thf(444,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b,E: $o] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ C @ D )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ E @ A @ C ) @ ( if_o_R697118589nres_b @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__trans) ).
thf(375,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(161,axiom,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( top_to177290092t_unit
= ( refine2043866374unit_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conc__fun__fail__iff_I2_J) ).
thf(904,plain,
! [A: set_Pr1720557880unit_a,B: refine424419629nres_a] :
( ( top_to177290092t_unit
= ( refine2043866374unit_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_130_dual__order_Otrans) ).
thf(732,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)],[114]) ).
thf(223,axiom,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( ( refine122110613un_b_b @ A @ B )
= top_to240090974nres_b )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_conc__fun__fail__iff_I1_J) ).
thf(1124,plain,
! [A: set_Product_prod_b_b,B: refine432681134nres_b] :
( ( ( refine122110613un_b_b @ A @ B )
= top_to240090974nres_b )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(17,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > set_b,D: set_b] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_less_eq_set_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_ord__le__eq__subst) ).
thf(413,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > set_b,D: set_b] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_less_eq_set_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(332,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_conc__trans__additional_I1_J) ).
thf(1503,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)],[332]) ).
thf(266,axiom,
! [A: set_Product_prod_a_b,B: set_Product_prod_a_b,C: refine432681134nres_b] :
( ( ord_le816409512od_a_b @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824854un_a_b @ A @ C ) @ ( refine1441824854un_a_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_conc__fun__R__mono) ).
thf(1271,plain,
! [A: set_Product_prod_a_b,B: set_Product_prod_a_b,C: refine432681134nres_b] :
( ( ord_le816409512od_a_b @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824854un_a_b @ A @ C ) @ ( refine1441824854un_a_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(77,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_antisym) ).
thf(611,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(108,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__class_Oorder_Oantisym) ).
thf(713,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(204,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ ( refine1198353289_RES_b @ ( collect_b @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_RETURN__rule) ).
thf(1058,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)],[204]) ).
thf(255,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_abs__trans__additional_I6_J) ).
thf(1239,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(32,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_antisym__conv) ).
thf(466,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(166,axiom,
! [A: a] :
( top_to231829469nres_a
!= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_nres__inequalities_I3_J) ).
thf(919,plain,
! [A: a] :
( top_to231829469nres_a
!= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(324,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = top_to240090974nres_b )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_meta__le__everything__if__top) ).
thf(1464,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = top_to240090974nres_b )
=> ( ord_le527798542nres_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(84,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eq__iff) ).
thf(641,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',fact_33_conc__trans__additional_I1_J) ).
thf(1428,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)],[312]) ).
thf(139,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_dual__order_Oantisym) ).
thf(831,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(336,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nres__order__simps_I4_J) ).
thf(1524,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(201,axiom,
( ( (=) @ refine432681134nres_b )
= ( ^ [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ B @ A )
& ( ord_le527798542nres_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_dual__order_Oeq__iff) ).
thf(1048,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)],[201]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',fact_283_abs__trans__additional_I1_J) ).
thf(1603,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)],[355]) ).
thf(342,axiom,
! [A: set_Pr712638521unit_b,B: refine432681134nres_b] :
( ( ( refine2043866375unit_b @ A @ B )
= top_to177290092t_unit )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_conc__fun__fail__iff_I1_J) ).
thf(1542,plain,
! [A: set_Pr712638521unit_b,B: refine432681134nres_b] :
( ( ( refine2043866375unit_b @ A @ B )
= top_to177290092t_unit )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(222,axiom,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_inres__def) ).
thf(1122,plain,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(276,axiom,
! [A: refine432681134nres_b] :
( ( sup_su2042991066nres_b @ top_to240090974nres_b @ A )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_sup__top__left) ).
thf(1307,plain,
! [A: refine432681134nres_b] :
( ( sup_su2042991066nres_b @ top_to240090974nres_b @ A )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(150,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_antisym__conv) ).
thf(863,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(45,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( A = B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_ord__eq__le__trans) ).
thf(509,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( A = B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(154,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_order_Otrans) ).
thf(880,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(87,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_antisym__conv) ).
thf(649,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)],[87]) ).
thf(199,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_dual__order_Orefl) ).
thf(1043,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(23,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_dual__order_Orefl) ).
thf(434,plain,
! [A: set_b] : ( ord_less_eq_set_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_86_le__funE) ).
thf(477,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)],[36]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_233_le__rel__bool__arg__iff) ).
thf(811,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)],[132]) ).
thf(284,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: set_Product_prod_b_b,E: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ ( refine122110613un_b_b @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_conc__trans) ).
thf(1339,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: set_Product_prod_b_b,E: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ ( refine122110613un_b_b @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(71,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T) ).
thf(594,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(38,axiom,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ B @ A )
& ( ord_less_eq_set_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_dual__order_Oeq__iff) ).
thf(483,plain,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ B @ A )
& ( ord_less_eq_set_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(104,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_ord__le__eq__trans) ).
thf(700,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(345,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_order__class_Oorder_Oantisym) ).
thf(1556,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)],[345]) ).
thf(172,axiom,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
& ( ord_le516598614nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_eq__iff) ).
thf(943,plain,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
& ( ord_le516598614nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(94,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: set_Product_prod_b_a,E: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ ( refine122110612un_b_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_conc__trans) ).
thf(668,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_b,C: refine432681134nres_b,D: set_Product_prod_b_a,E: refine424419629nres_a] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ ( refine122110612un_b_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(220,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ B )
=> ( ( refine412683989fail_a @ A )
& ! [C: a] :
( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_pw__le__iff) ).
thf(1112,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)],[220]) ).
thf(148,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_order__mono__setup_Orefl) ).
thf(858,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(56,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( if_set1550076877od_a_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T) ).
thf(552,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( if_set1550076877od_a_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(129,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ( refine412683990fail_b @ A )
=> ( ord_le527798542nres_b @ B @ A ) )
=> ( ord_le527798542nres_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_le__nofailI) ).
thf(799,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)],[129]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_234_ord__eq__le__eq__trans) ).
thf(1162,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)],[232]) ).
thf(164,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( A = top_to2046902534nres_a )
=> ( ord_le516598614nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_meta__le__everything__if__top) ).
thf(912,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( A = top_to2046902534nres_a )
=> ( ord_le516598614nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',fact_226_order__subst1) ).
thf(1198,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)],[244]) ).
thf(14,axiom,
! [A: $o,B: set_b,C: set_b,D: set_b,E: set_b] :
( ( A
=> ( ord_less_eq_set_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_b @ D @ E ) )
=> ( ord_less_eq_set_b @ ( if_set_b @ A @ B @ D ) @ ( if_set_b @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Refine__Misc_Oif__mono) ).
thf(399,plain,
! [A: $o,B: set_b,C: set_b,D: set_b,E: set_b] :
( ( A
=> ( ord_less_eq_set_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_set_b @ D @ E ) )
=> ( ord_less_eq_set_b @ ( if_set_b @ A @ B @ D ) @ ( if_set_b @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(326,axiom,
! [A: set_Product_prod_a_b] :
( ( refine1441824854un_a_b @ A @ top_to240090974nres_b )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_conc__fun__FAIL) ).
thf(1474,plain,
! [A: set_Product_prod_a_b] :
( ( refine1441824854un_a_b @ A @ top_to240090974nres_b )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(354,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_ord__eq__le__subst) ).
thf(1594,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)],[354]) ).
thf(152,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > set_a,D: set_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_ord__le__eq__subst) ).
thf(868,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > set_a,D: set_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(60,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_antisym) ).
thf(563,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(327,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_nres__order__simps_I5_J) ).
thf(1477,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)],[327]) ).
thf(217,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_eq__refl) ).
thf(1102,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(44,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( A = B )
=> ( ord_le1656162903nres_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_eq__refl) ).
thf(505,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( A = B )
=> ( ord_le1656162903nres_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(22,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_dual__order_Oantisym) ).
thf(431,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(102,axiom,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_top__greatest) ).
thf(695,plain,
! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(257,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_top__greatest) ).
thf(1245,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(29,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_antisym) ).
thf(455,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(155,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_order_Otrans) ).
thf(883,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(236,axiom,
! [A: refine432681134nres_b] :
( ( ~ ( refine412683990fail_b @ A ) )
= ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_not__nofail__iff) ).
thf(1176,plain,
! [A: refine432681134nres_b] :
( ( ~ ( refine412683990fail_b @ A ) )
= ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(76,axiom,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A )
=> ( A = top_to398455383od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_top_Oextremum__uniqueI) ).
thf(608,plain,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A )
=> ( A = top_to398455383od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(292,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ E @ A @ C ) @ ( if_Ref1724547303nres_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__mono__setup_Omono__if) ).
thf(1364,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)],[292]) ).
thf(259,axiom,
! [A: set_Pr712638521unit_b,B: refine432681134nres_b] :
( ( top_to177290092t_unit
= ( refine2043866375unit_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_conc__fun__fail__iff_I2_J) ).
thf(1250,plain,
! [A: set_Pr712638521unit_b,B: refine432681134nres_b] :
( ( top_to177290092t_unit
= ( refine2043866375unit_b @ A @ B ) )
= ( B = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(196,axiom,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_conc__fun__FAIL) ).
thf(1034,plain,
! [A: set_Pr1628433942t_unit] :
( ( refine2021053540t_unit @ A @ top_to177290092t_unit )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(97,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_dual__order_Oeq__iff) ).
thf(675,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_299_RETURN__SPEC__refine) ).
thf(1203,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)],[245]) ).
thf(99,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_conc__trans__additional_I4_J) ).
thf(680,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(268,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_top_Oextremum__unique) ).
thf(1277,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(40,axiom,
! [A: $o,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b,E: $o > refine432681134nres_b] :
( ( A
=> ( ord_le1656162903nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1656162903nres_b @ D @ E ) )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ A @ B @ D ) @ ( if_o_R697118589nres_b @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Refine__Misc_Oif__mono) ).
thf(487,plain,
! [A: $o,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b,D: $o > refine432681134nres_b,E: $o > refine432681134nres_b] :
( ( A
=> ( ord_le1656162903nres_b @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1656162903nres_b @ D @ E ) )
=> ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ A @ B @ D ) @ ( if_o_R697118589nres_b @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(30,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_order_Otrans) ).
thf(458,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(344,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ B )
=> ( ! [C: refine424419629nres_a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ C @ B ) )
=> ( ( order_1714329108nres_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Greatest__equality) ).
thf(1547,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)],[344]) ).
thf(147,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a,E: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ C @ D )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ E @ A @ C ) @ ( if_o_R1705037948nres_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__mono__setup_Omono__if) ).
thf(855,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a,E: $o] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ C @ D )
=> ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ E @ A @ C ) @ ( if_o_R1705037948nres_a @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(335,axiom,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ E ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( if_Ref1724547303nres_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Refine__Misc_Oif__mono) ).
thf(1516,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)],[335]) ).
thf(348,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 @ ( refine1441824853un_a_a @ id_a @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_conc__trans__additional_I3_J) ).
thf(1566,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 @ ( refine1441824853un_a_a @ id_a @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(105,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_conc__trans__additional_I6_J) ).
thf(705,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
=> ( ord_le527798542nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(230,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824854un_a_b @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_conc__trans) ).
thf(1156,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ B @ ( refine1441824854un_a_b @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(96,axiom,
~ ( refine412683989fail_a @ top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_nofail__simps_I1_J) ).
thf(673,plain,
~ ( refine412683989fail_a @ top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_328_pw__leI) ).
thf(791,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)],[127]) ).
thf(240,axiom,
( ( refine1001002028nres_b @ top_to240090974nres_b )
= ( ^ [A: b] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_inres__simps_I1_J) ).
thf(1188,plain,
( ( refine1001002028nres_b @ top_to240090974nres_b )
= ( ^ [A: b] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(68,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_antisym__conv) ).
thf(585,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_order__mono__setup_Orefl) ).
thf(576,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(131,axiom,
! [A: set_Pr451126599t_unit,B: refine787176636t_unit] :
( ( top_to177290092t_unit
= ( refine944483349t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conc__fun__fail__iff_I2_J) ).
thf(808,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)],[131]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',fact_87_le__funE) ).
thf(1130,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)],[225]) ).
thf(249,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ord__le__eq__subst) ).
thf(1218,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)],[249]) ).
thf(162,axiom,
! [A: set_a,B: set_a] :
( ( if_set_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_Itf__a_J_T) ).
thf(907,plain,
! [A: set_a,B: set_a] :
( ( if_set_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(274,axiom,
! [A: b > refine424419629nres_a] :
( ( refine1264602245nd_b_a @ top_to240090974nres_b @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_bind__FAIL) ).
thf(1300,plain,
! [A: b > refine424419629nres_a] :
( ( refine1264602245nd_b_a @ top_to240090974nres_b @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(320,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine1001002027nres_a @ A @ C )
=> ( refine1001002027nres_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_pwD2) ).
thf(1452,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)],[320]) ).
thf(283,axiom,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: set_Product_prod_b_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ ( refine122110612un_b_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_conc__trans) ).
thf(1336,plain,
! [A: refine424419629nres_a,B: set_Product_prod_a_b,C: refine432681134nres_b,D: set_Product_prod_b_a,E: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ C ) )
=> ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ D @ E ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ ( refine122110612un_b_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(85,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_dual__order_Oantisym) ).
thf(643,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(306,axiom,
! [A: set_Product_prod_b_a] :
( ( refine1964549109un_b_a @ A @ top_to240090974nres_b )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_abs__fun__simps_I1_J) ).
thf(1404,plain,
! [A: set_Product_prod_b_a] :
( ( refine1964549109un_b_a @ A @ top_to240090974nres_b )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(262,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: refine424419629nres_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ A @ C ) @ ( refine1441824853un_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_conc__fun__R__mono) ).
thf(1257,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: refine424419629nres_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ A @ C ) @ ( refine1441824853un_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(340,axiom,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ ( refine1441824854un_a_b @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_conc__trans) ).
thf(1536,plain,
! [A: refine432681134nres_b,B: set_Product_prod_b_a,C: refine424419629nres_a,D: set_Product_prod_a_b,E: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ D @ E ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ ( refine1441824854un_a_b @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',fact_344_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1023,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)],[193]) ).
thf(112,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_antisym__conv) ).
thf(727,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_219_ord__eq__le__subst) ).
thf(1008,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)],[190]) ).
thf(42,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ A )
=> ( ord_less_eq_set_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_dual__order_Otrans) ).
thf(497,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ A )
=> ( ord_less_eq_set_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(330,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a > $o] :
( ( A @ B )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ord_le519537037nres_a @ D @ B ) )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ! [E: refine424419629nres_a] :
( ( A @ E )
=> ( ord_le519537037nres_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1714329108nres_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_GreatestI2__order) ).
thf(1485,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)],[330]) ).
thf(333,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_order__subst2) ).
thf(1506,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)],[333]) ).
thf(353,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/sandbox/benchmark/theBenchmark.p',fact_218_ord__eq__le__subst) ).
thf(1585,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)],[353]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_84_le__funD) ).
thf(386,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)],[9]) ).
thf(216,axiom,
! [A: $o,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a,E: set_Product_prod_a_a] :
( ( A
=> ( ord_le1824328871od_a_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1824328871od_a_a @ D @ E ) )
=> ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ A @ B @ D ) @ ( if_set1550076877od_a_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Refine__Misc_Oif__mono) ).
thf(1094,plain,
! [A: $o,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a,E: set_Product_prod_a_a] :
( ( A
=> ( ord_le1824328871od_a_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le1824328871od_a_a @ D @ E ) )
=> ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ A @ B @ D ) @ ( if_set1550076877od_a_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',fact_231_GreatestI2__order) ).
thf(978,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)],[184]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',fact_225_order__subst1) ).
thf(1372,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)],[295]) ).
thf(72,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ C @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_conc__trans__additional_I2_J) ).
thf(595,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
=> ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ C @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',fact_109_order__mono__setup_Omono__if) ).
thf(363,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)],[4]) ).
thf(52,axiom,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ B @ A )
& ( ord_le516598614nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_dual__order_Oeq__iff) ).
thf(539,plain,
( ( (=) @ ( $o > refine424419629nres_a ) )
= ( ^ [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ B @ A )
& ( ord_le516598614nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(95,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( ord_le1824328871od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_dual__order_Oeq__iff) ).
thf(671,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( ord_le1824328871od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(183,axiom,
( refine1001002028nres_b
= ( ^ [A: refine432681134nres_b,B: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_inres__def) ).
thf(976,plain,
( refine1001002028nres_b
= ( ^ [A: refine432681134nres_b,B: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(41,axiom,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
& ( ord_le1656162903nres_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_order__class_Oorder_Oeq__iff) ).
thf(495,plain,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
& ( ord_le1656162903nres_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(157,axiom,
! [A: b,B: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine2063221605TURN_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_nres__order__simps_I20_J) ).
thf(891,plain,
! [A: b,B: b] :
( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A ) @ ( refine2063221605TURN_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_317_RES__refine) ).
thf(1108,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)],[219]) ).
thf(279,axiom,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_nres__order__simps_I20_J) ).
thf(1316,plain,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(27,axiom,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ B @ A )
& ( ord_le1656162903nres_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_dual__order_Oeq__iff) ).
thf(450,plain,
( ( (=) @ ( $o > refine432681134nres_b ) )
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ B @ A )
& ( ord_le1656162903nres_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(212,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 @ ( refine122110613un_b_b @ id_b @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_conc__trans__additional_I3_J) ).
thf(1084,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 @ ( refine122110613un_b_b @ id_b @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(49,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( if_o_R697118589nres_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T) ).
thf(524,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)],[49]) ).
thf(66,axiom,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_order__mono__setup_Orefl) ).
thf(581,plain,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(301,axiom,
! [A: set_Product_prod_b_a,B: refine424419629nres_a] :
( ( top_to240090974nres_b
= ( refine122110612un_b_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conc__fun__fail__iff_I2_J) ).
thf(1390,plain,
! [A: set_Product_prod_b_a,B: refine424419629nres_a] :
( ( top_to240090974nres_b
= ( refine122110612un_b_a @ A @ B ) )
= ( B = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(351,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [D: a] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_SPEC__cons__rule) ).
thf(1575,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)],[351]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',fact_214_ord__le__eq__subst) ).
thf(1289,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)],[272]) ).
thf(143,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_top_Oextremum__uniqueI) ).
thf(844,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
=> ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(88,axiom,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Id__refine) ).
thf(652,plain,
! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(69,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
( ( if_o_R1705037948nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T) ).
thf(588,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)],[69]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_301_RETURN__SPEC__refine) ).
thf(1253,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)],[260]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_300_RETURN__SPEC__refine) ).
thf(813,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)],[133]) ).
thf(299,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_RETURN__rule) ).
thf(1385,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)],[299]) ).
thf(179,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: refine432681134nres_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ord_le527798542nres_b @ ( refine122110613un_b_b @ A @ C ) @ ( refine122110613un_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_conc__fun__R__mono) ).
thf(963,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: refine432681134nres_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ord_le527798542nres_b @ ( refine122110613un_b_b @ A @ C ) @ ( refine122110613un_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(47,axiom,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_meta__le__everything__if__top) ).
thf(517,plain,
! [A: refine787176636t_unit,B: refine787176636t_unit] :
( ( A = top_to177290092t_unit )
=> ( ord_le1051254044t_unit @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(7,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( B = C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ord__le__eq__trans) ).
thf(378,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( B = C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(169,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_le516598614nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le516598614nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ord__le__eq__subst) ).
thf(929,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: ( $o > refine424419629nres_a ) > $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > refine424419629nres_a,F: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ E @ F )
=> ( ord_le516598614nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le516598614nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',fact_158_ord__le__eq__trans) ).
thf(1077,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)],[210]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_332_pw__le__iff) ).
thf(763,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)],[123]) ).
thf(8,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_order__class_Oorder_Oantisym) ).
thf(383,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_286_nres__order__simps_I5_J) ).
thf(536,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)],[51]) ).
thf(200,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_order_Otrans) ).
thf(1045,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(109,axiom,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_top_Oextremum__unique) ).
thf(716,plain,
! [A: refine787176636t_unit] :
( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
= ( A = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(55,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T) ).
thf(549,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( if_Ref1732808808nres_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(317,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_abs__trans__additional_I5_J) ).
thf(1444,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(226,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_meta__le__everything__if__top) ).
thf(1133,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = top_to231829469nres_a )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(287,axiom,
! [A: set_b] :
( top_to240090974nres_b
!= ( refine1198353289_RES_b @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_nres__inequalities_I1_J) ).
thf(1348,plain,
! [A: set_b] :
( top_to240090974nres_b
!= ( refine1198353289_RES_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(187,axiom,
! [A: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A )
=> ( A = top_to2046902534nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_top_Oextremum__uniqueI) ).
thf(999,plain,
! [A: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A )
=> ( A = top_to2046902534nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(26,axiom,
! [A: set_b,B: set_b,C: set_b,D: set_b,E: $o] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( if_set_b @ E @ A @ C ) @ ( if_set_b @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__mono__setup_Omono__if) ).
thf(447,plain,
! [A: set_b,B: set_b,C: set_b,D: set_b,E: $o] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( if_set_b @ E @ A @ C ) @ ( if_set_b @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(269,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_conc__trans__additional_I2_J) ).
thf(1280,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(16,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ C @ A )
=> ( ord_le1656162903nres_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_dual__order_Otrans) ).
thf(410,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ C @ A )
=> ( ord_le1656162903nres_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(251,axiom,
! [A: set_Pr712638521unit_b] :
( ( refine2043866375unit_b @ A @ top_to240090974nres_b )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_conc__fun__FAIL) ).
thf(1229,plain,
! [A: set_Pr712638521unit_b] :
( ( refine2043866375unit_b @ A @ top_to240090974nres_b )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(303,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_conc__trans__additional_I6_J) ).
thf(1395,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(297,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_top_Oextremum__uniqueI) ).
thf(1380,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
=> ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(275,axiom,
! [A: b] :
( top_to240090974nres_b
!= ( refine2063221605TURN_b @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_nres__inequalities_I3_J) ).
thf(1303,plain,
! [A: b] :
( top_to240090974nres_b
!= ( refine2063221605TURN_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(337,axiom,
! [A: b > refine432681134nres_b] :
( ( refine1264602246nd_b_b @ top_to240090974nres_b @ A )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_bind__FAIL) ).
thf(1527,plain,
! [A: b > refine432681134nres_b] :
( ( refine1264602246nd_b_b @ top_to240090974nres_b @ A )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(18,axiom,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_dual__order_Orefl) ).
thf(422,plain,
! [A: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(328,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
=> ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_top_Oextremum__uniqueI) ).
thf(1480,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
=> ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(115,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a,E: $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( if_set_a @ E @ A @ C ) @ ( if_set_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_order__mono__setup_Omono__if) ).
thf(735,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a,E: $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( if_set_a @ E @ A @ C ) @ ( if_set_a @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ord__le__eq__trans) ).
thf(358,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(138,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
=> ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_abs__trans__additional_I2_J) ).
thf(828,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b,C: set_Product_prod_b_b,D: refine432681134nres_b] :
( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_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)],[138]) ).
thf(178,axiom,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_conc__fun__FAIL) ).
thf(960,plain,
! [A: set_Pr1720557880unit_a] :
( ( refine2043866374unit_a @ A @ top_to231829469nres_a )
= top_to177290092t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(206,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_dual__order_Oantisym) ).
thf(1065,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(176,axiom,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ top_to2046902534nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_top__greatest) ).
thf(955,plain,
! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ top_to2046902534nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_284_abs__trans__additional_I1_J) ).
thf(796,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)],[128]) ).
thf(156,axiom,
! [A: set_a,B: set_a] :
( ( A = top_top_set_a )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_meta__le__everything__if__top) ).
thf(886,plain,
! [A: set_a,B: set_a] :
( ( A = top_top_set_a )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',fact_271_SPEC__rule) ).
thf(1172,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)],[235]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_270_RES__rule) ).
thf(897,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)],[159]) ).
thf(35,axiom,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order__trans) ).
thf(474,plain,
! [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b,C: $o > refine432681134nres_b] :
( ( ord_le1656162903nres_b @ A @ B )
=> ( ( ord_le1656162903nres_b @ B @ C )
=> ( ord_le1656162903nres_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(254,axiom,
! [A: set_Pr1707992533t_unit] :
( ( refine2140306339t_unit @ A @ top_to177290092t_unit )
= top_to240090974nres_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_conc__fun__FAIL) ).
thf(1236,plain,
! [A: set_Pr1707992533t_unit] :
( ( refine2140306339t_unit @ A @ top_to177290092t_unit )
= top_to240090974nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',fact_232_le__rel__bool__arg__iff) ).
thf(1352,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)],[288]) ).
thf(265,axiom,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_top_Oextremum__unique) ).
thf(1268,plain,
! [A: refine432681134nres_b] :
( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
= ( A = top_to240090974nres_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(20,axiom,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
& ( ord_less_eq_set_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_eq__iff) ).
thf(427,plain,
( ( (=) @ set_b )
= ( ^ [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
& ( ord_less_eq_set_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(149,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(860,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(192,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = B )
=> ( ord_le527798542nres_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_eq__refl) ).
thf(1019,plain,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( A = B )
=> ( ord_le527798542nres_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(290,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ A )
=> ( ord_le519537037nres_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_dual__order_Otrans) ).
thf(1357,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)],[290]) ).
thf(136,axiom,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( top_to231829469nres_a
= ( refine2021053540t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_conc__fun__fail__iff_I2_J) ).
thf(822,plain,
! [A: set_Pr1628433942t_unit,B: refine787176636t_unit] :
( ( top_to231829469nres_a
= ( refine2021053540t_unit @ A @ B ) )
= ( B = top_to177290092t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(313,axiom,
! [A: refine432681134nres_b] :
( ( top_to240090974nres_b != A )
= ( refine412683990fail_b @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_intro__nofail_I2_J) ).
thf(1431,plain,
! [A: refine432681134nres_b] :
( ( top_to240090974nres_b != A )
= ( refine412683990fail_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(12,axiom,
( ord_le1656162903nres_b
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
! [C: $o] : ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__fun__def) ).
thf(395,plain,
( ord_le1656162903nres_b
= ( ^ [A: $o > refine432681134nres_b,B: $o > refine432681134nres_b] :
! [C: $o] : ( ord_le527798542nres_b @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(141,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_eq__iff) ).
thf(839,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(130,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( B = C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_ord__le__eq__trans) ).
thf(803,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( B = C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_288_less__eq__nres_Osimps_I2_J) ).
thf(923,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)],[167]) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',fact_213_ord__le__eq__subst) ).
thf(1416,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)],[310]) ).
thf(319,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 @ ( refine1441824853un_a_a @ id_a @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_conc__trans__additional_I3_J) ).
thf(1449,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 @ ( refine1441824853un_a_a @ id_a @ D ) )
=> ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(106,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_dual__order_Orefl) ).
thf(708,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(182,axiom,
! [A: refine424419629nres_a] :
( ( A != top_to231829469nres_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_nres__cases) ).
thf(972,plain,
! [A: refine424419629nres_a] :
( ( A != top_to231829469nres_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(282,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ( refine412683989fail_a @ B )
& ! [C: a] :
( ( refine1001002027nres_a @ B @ C )
=> ( refine1001002027nres_a @ A @ C ) ) ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_pw__leI) ).
thf(1331,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)],[282]) ).
thf(356,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 @ ( refine122110613un_b_b @ id_b @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_conc__trans__additional_I3_J) ).
thf(1606,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 @ ( refine122110613un_b_b @ id_b @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(33,axiom,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_dual__order_Oantisym) ).
thf(469,plain,
! [A: set_b,B: set_b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(293,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
=> ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ B ) @ D )
=> ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_abs__trans__additional_I2_J) ).
thf(1367,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: set_Product_prod_a_b,D: refine432681134nres_b] :
( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_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)],[293]) ).
thf(171,axiom,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order__trans) ).
thf(940,plain,
! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
( ( ord_le516598614nres_a @ A @ B )
=> ( ( ord_le516598614nres_a @ B @ C )
=> ( ord_le516598614nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(197,axiom,
! [A: refine432681134nres_b,B: refine432681134nres_b] :
( ( ord_le527798542nres_b @ A @ B )
=> ( ( ord_le527798542nres_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_dual__order_Oantisym) ).
thf(1037,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)],[197]) ).
thf(59,axiom,
! [A: refine424419629nres_a] :
( ( sup_su2034729561nres_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_sup__top__left) ).
thf(560,plain,
! [A: refine424419629nres_a] :
( ( sup_su2034729561nres_a @ top_to231829469nres_a @ A )
= top_to231829469nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1627,plain,
$false,
inference(e,[status(thm)],[1322,1501,1469,1190,760,1559,1031,1179,555,1005,683,730,1068,994,1401,1569,741,1205,1437,614,677,1310,500,472,1260,1342,945,1354,1458,1127,1441,841,436,389,1298,719,1313,1455,357,949,724,1055,1409,1511,917,1545,638,1087,1247,1319,1398,1232,969,1572,591,1040,646,514,1383,966,480,485,834,1183,1283,602,1377,1215,877,1447,866,660,1345,527,1169,397,1242,849,1074,452,546,1153,366,1274,825,952,1580,1255,598,820,424,429,1370,815,1387,910,957,894,746,1091,407,630,625,852,665,1210,757,710,1106,847,566,583,522,1159,461,1195,1407,1360,578,1143,1227,1425,1138,783,697,1089,1234,1534,1017,753,1461,1414,1028,1082,901,686,622,738,654,1192,1002,569,393,1114,1263,997,1530,1539,1060,1050,605,1393,1434,938,633,541,765,1286,1167,1185,773,662,926,1563,657,558,1071,750,1483,573,444,375,904,732,1124,413,1503,1271,611,713,1058,1239,466,919,1464,641,1428,831,1524,1048,1603,1542,1122,1307,863,509,880,649,1043,434,477,811,1339,594,483,700,1556,943,668,1112,858,552,799,1162,912,1198,399,1474,1594,868,563,1477,1102,505,431,695,1245,455,883,1176,608,1364,1250,1034,675,1203,680,1277,487,458,1547,855,1516,1566,705,1156,673,791,1188,585,576,808,1130,1218,907,1300,1452,1336,643,1404,1257,1536,1023,727,1008,497,1485,1506,1585,386,1094,978,1372,595,363,539,671,976,495,891,1108,1316,450,1084,524,581,1390,1575,1289,844,652,588,1253,813,1385,963,517,378,929,1077,763,383,536,1045,716,549,1444,1133,1348,999,447,1280,410,1229,1395,1380,1303,1527,422,1480,735,358,828,960,1065,955,796,886,1172,897,474,1236,1352,1268,427,860,1019,1357,822,1431,395,839,803,923,1416,1449,708,972,1331,1606,469,1367,940,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP159^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.20 % Computer : n016.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 20:08:35 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.66/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/0.93 % [INFO] Parsing done (413ms).
% 2.06/0.95 % [INFO] Running in sequential loop mode.
% 3.55/1.34 % [INFO] eprover registered as external prover.
% 3.55/1.35 % [INFO] Scanning for conjecture ...
% 3.76/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 362 axioms. Running axiom selection ...
% 4.25/1.64 % [INFO] Axiom selection finished. Selected 354 axioms (removed 8 axioms).
% 5.25/1.94 % [INFO] Problem is higher-order (TPTP THF).
% 5.25/1.97 % [INFO] Type checking passed.
% 5.25/1.97 % [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 ...
% 20.30/5.48 % External prover 'e' found a proof!
% 20.30/5.48 % [INFO] Killing All external provers ...
% 20.30/5.49 % Time passed: 5195ms (effective reasoning time: 4531ms)
% 20.30/5.49 % 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)>
% 20.30/5.49 % Axioms used in derivation (354): fact_204_eq__iff, fact_163_ord__eq__le__trans, fact_202_eq__iff, fact_12_conc__fun__fail__iff_I1_J, fact_27_conc__fun__FAIL, fact_19_conc__fun__fail__iff_I1_J, fact_293_nres__inequalities_I3_J, fact_69_top_Oextremum__unique, fact_108_order__mono__setup_Omono__if, fact_107_order__mono__setup_Omono__if, fact_235_ord__eq__le__eq__trans, fact_74_top_Oextremum__unique, fact_118_dual__order_Oeq__iff, fact_93_Refine__Misc_Oif__mono, fact_38_conc__trans, fact_124_dual__order_Otrans, fact_193_eq__refl, fact_7_conc__fun__fail__iff_I2_J, fact_238_conc__trans__additional_I2_J, fact_63_meta__le__everything__if__top, fact_232_le__rel__bool__arg__iff, fact_159_ord__eq__le__trans, fact_213_ord__le__eq__subst, fact_42_conc__trans, fact_251_Id__SPEC__refine, fact_307_intro__nofail_I2_J, fact_229_Greatest__equality, fact_314_pwD1, fact_99_conc__fun__R__mono, fact_216_ord__eq__le__subst, fact_227_order__subst1, fact_286_nres__order__simps_I5_J, fact_4_conc__fun__fail__iff_I2_J, fact_208_ord__le__eq__subst, help_If_2_1_If_001t__Set__Oset_Itf__a_J_T, fact_58_top__greatest, fact_9_conc__fun__fail__iff_I2_J, fact_139_order__trans, fact_285_nres__order__simps_I5_J, fact_342_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_188_eq__refl, fact_177_antisym__conv, fact_174_antisym__conv, fact_194_antisym, fact_150_order__class_Oorder_Oantisym, fact_83_top_Oextremum__uniqueI, fact_66_meta__le__everything__if__top, fact_22_conc__fun__FAIL, fact_0_nres__order__simps_I4_J, fact_326_pwD2, fact_47_order__mono__setup_Orefl, help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_200_antisym, fact_294_nres__inequalities_I3_J, fact_109_order__mono__setup_Omono__if, fact_102_conc__fun__R__mono, fact_14_conc__fun__fail__iff_I1_J, fact_276_SPEC__cons__rule, fact_340_ibind__strict_I2_J, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_81_top_Oextremum__uniqueI, fact_161_ord__eq__le__trans, fact_145_order__class_Oorder_Oantisym, fact_279_nres__cases, fact_151_order__class_Oorder_Oantisym, fact_28_conc__fun__FAIL, fact_101_conc__fun__R__mono, fact_113_dual__order_Oantisym, fact_95_Refine__Misc_Oif__mono, fact_1_nres__order__simps_I4_J, fact_98_le__fun__def, fact_165_ord__eq__le__trans, fact_254_abs__trans__additional_I2_J, fact_112_dual__order_Oantisym, fact_123_dual__order_Oeq__iff, fact_283_abs__trans__additional_I1_J, fact_278_nres__inequalities_I1_J, fact_96_Refine__Misc_Oif__mono, fact_329_pw__leI_H, fact_8_conc__fun__fail__iff_I2_J, help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T, fact_333_inres__def, fact_319_RES__refine, fact_242_conc__trans__additional_I3_J, fact_41_conc__trans, fact_30_nres__order__simps_I3_J, fact_52_top__greatest, fact_215_ord__le__eq__subst, fact_248_conc__trans__additional_I5_J, fact_37_conc__trans, fact_203_eq__iff, fact_43_conc__trans, fact_341_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_346_sup__top__left, fact_269_RES__rule, fact_6_conc__fun__fail__iff_I2_J, fact_135_dual__order_Orefl, fact_120_dual__order_Oeq__iff, fact_298_RETURN__rule, fact_272_SPEC__rule, fact_299_RETURN__SPEC__refine, fact_249_conc__trans__additional_I4_J, fact_129_dual__order_Otrans, fact_257_abs__trans__additional_I4_J, fact_60_meta__le__everything__if__top, fact_241_conc__trans__additional_I3_J, fact_97_le__fun__def, fact_126_dual__order_Otrans, fact_166_order__class_Oorder_Oeq__iff, fact_184_order_Otrans, fact_137_dual__order_Orefl, fact_196_antisym, fact_205_eq__iff, fact_158_ord__le__eq__trans, fact_29_conc__fun__FAIL, fact_323_inres__simps_I1_J, fact_217_ord__eq__le__subst, fact_61_meta__le__everything__if__top, help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_170_order__class_Oorder_Oeq__iff, fact_176_antisym__conv, fact_89_le__funI, fact_53_top__greatest, fact_338_bind__FAIL, fact_147_order__class_Oorder_Oantisym, fact_100_conc__fun__R__mono, fact_262_abs__trans__additional_I6_J, fact_79_top_Oextremum__uniqueI, fact_160_ord__eq__le__trans, fact_284_abs__trans__additional_I1_J, fact_316_le__nofailI, fact_332_pw__le__iff, fact_88_le__funI, fact_308_intro__nofail_I2_J, fact_312_not__nofail__iff, fact_167_order__class_Oorder_Oeq__iff, fact_281_abs__trans__additional_I1_J, fact_265_abs__fun__simps_I1_J, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T, fact_45_order__mono__setup_Orefl, fact_206_eq__iff, fact_115_dual__order_Oantisym, fact_274_SPEC__trans, fact_295_RETURN__to__SPEC__rule, fact_17_conc__fun__fail__iff_I1_J, fact_33_conc__trans__additional_I1_J, fact_300_RETURN__SPEC__refine, fact_18_conc__fun__fail__iff_I1_J, fact_116_dual__order_Oantisym, fact_94_Refine__Misc_Oif__mono, fact_15_conc__fun__fail__iff_I1_J, fact_255_abs__trans__additional_I2_J, fact_197_antisym, help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T, fact_201_eq__iff, fact_304_pw__conc__nofail, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T, fact_86_le__funE, fact_211_ord__le__eq__subst, fact_237_Id__refine, fact_76_top_Oextremum__uniqueI, fact_68_top_Oextremum__unique, fact_230_GreatestI2__order, fact_199_antisym, fact_317_RES__refine, fact_169_order__class_Oorder_Oeq__iff, fact_136_dual__order_Orefl, fact_221_order__subst2, fact_260_abs__trans__additional_I5_J, fact_65_meta__le__everything__if__top, fact_187_eq__refl, fact_268_if__rule, fact_104_order__mono__setup_Omono__if, fact_48_order__mono__setup_Orefl, fact_25_conc__fun__FAIL, fact_178_antisym__conv, fact_180_order_Otrans, fact_49_order__mono__setup_Orefl, fact_214_ord__le__eq__subst, fact_287_less__eq__nres_Osimps_I2_J, help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T, fact_91_Refine__Misc_Oif__mono, fact_244_conc__trans__additional_I3_J, fact_228_Greatest__equality, fact_50_order__mono__setup_Orefl, help_If_2_1_If_001t__Set__Oset_Itf__b_J_T, fact_172_order__class_Oorder_Oeq__iff, fact_122_dual__order_Oeq__iff, fact_114_dual__order_Oantisym, fact_71_top_Oextremum__unique, fact_130_dual__order_Otrans, fact_259_abs__trans__additional_I5_J, fact_275_SPEC__cons__rule, fact_273_SPEC__trans, fact_142_order__trans, fact_117_dual__order_Oeq__iff, fact_282_abs__trans__additional_I1_J, fact_143_order__trans, fact_252_Id__SPEC__refine, fact_321_RETURN__refine, fact_337_bind__FAIL, fact_345_sup__top__left, fact_121_dual__order_Oeq__iff, fact_128_dual__order_Otrans, fact_288_less__eq__nres_Osimps_I2_J, fact_175_antisym__conv, fact_226_order__subst1, fact_224_order__subst1, fact_127_dual__order_Otrans, fact_75_top_Oextremum__unique, fact_245_conc__trans__additional_I6_J, fact_13_conc__fun__fail__iff_I1_J, fact_125_dual__order_Otrans, fact_153_ord__le__eq__trans, fact_131_dual__order_Orefl, fact_309_nofail__def, fact_149_order__class_Oorder_Oantisym, fact_132_dual__order_Orefl, fact_270_RES__rule, fact_258_abs__trans__additional_I4_J, fact_40_conc__trans, fact_303_nofail__simps_I1_J, fact_59_top__greatest, fact_164_ord__eq__le__trans, fact_92_Refine__Misc_Oif__mono, fact_35_conc__trans__additional_I1_J, fact_134_dual__order_Orefl, fact_198_antisym, fact_110_dual__order_Oantisym, fact_297_RETURN__rule, fact_36_conc__trans__additional_I1_J, fact_218_ord__eq__le__subst, fact_148_order__class_Oorder_Oantisym, fact_85_le__funD, fact_344_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_290_nres__order__simps_I21_J, fact_31_nres__order__simps_I3_J, fact_271_SPEC__rule, fact_330_pw__leI_H, fact_246_conc__trans__additional_I6_J, fact_133_dual__order_Orefl, fact_152_ord__le__eq__trans, fact_20_conc__fun__fail__iff_I1_J, fact_267_if__rule, fact_315_le__nofailI, fact_44_conc__trans, fact_106_order__mono__setup_Omono__if, fact_335_bind__FAIL, fact_32_nres__order__simps_I3_J, fact_209_ord__le__eq__subst, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_105_order__mono__setup_Omono__if, fact_82_top_Oextremum__uniqueI, fact_16_conc__fun__fail__iff_I1_J, fact_173_antisym__conv, fact_324_inres__simps_I1_J, fact_111_dual__order_Oantisym, fact_189_eq__refl, fact_26_conc__fun__FAIL, fact_264_abs__fun__simps_I1_J, fact_191_eq__refl, fact_310_nofail__def, fact_280_nres__cases, fact_182_order_Otrans, help_If_3_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T, fact_55_top__greatest, fact_233_le__rel__bool__arg__iff, fact_140_order__trans, fact_186_order_Otrans, fact_138_order__trans, fact_327_pw__leI, fact_103_order__mono__setup_Omono__if, fact_39_conc__trans, fact_179_antisym__conv, fact_306_pw__conc__nofail, fact_157_ord__le__eq__trans, fact_84_le__funD, fact_192_eq__refl, fact_277_nres__inequalities_I1_J, fact_240_conc__trans__additional_I2_J, fact_57_top__greatest, fact_266_abs__fun__simps_I1_J, fact_261_abs__trans__additional_I6_J, fact_336_bind__FAIL, fact_181_order_Otrans, fact_77_top_Oextremum__uniqueI, help_If_1_1_If_001t__Set__Oset_Itf__a_J_T, fact_210_ord__le__eq__subst, fact_302_nofail__simps_I1_J, fact_225_order__subst1, fact_343_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_339_ibind__strict_I2_J, fact_247_conc__trans__additional_I5_J, fact_46_order__mono__setup_Orefl, fact_328_pw__leI, fact_10_conc__fun__fail__iff_I2_J, fact_320_RETURN__refine, fact_207_eq__iff, fact_331_pw__le__iff, fact_190_eq__refl, fact_162_ord__eq__le__trans, fact_325_pwD2, fact_156_ord__le__eq__trans, fact_24_conc__fun__FAIL, fact_2_nres__order__simps_I4_J, fact_87_le__funE, help_If_1_1_If_001t__Set__Oset_Itf__b_J_T, fact_219_ord__eq__le__subst, fact_67_meta__le__everything__if__top, fact_236_Id__refine, fact_21_conc__fun__FAIL, fact_220_order__subst2, fact_322_RETURN__refine, fact_313_pwD1, fact_119_dual__order_Oeq__iff, fact_144_order__trans, fact_168_order__class_Oorder_Oeq__iff, fact_23_conc__fun__FAIL, fact_183_order_Otrans, fact_185_order_Otrans, fact_195_antisym, fact_3_conc__fun__fail__iff_I2_J, fact_212_ord__le__eq__subst, fact_292_nres__order__simps_I20_J, fact_73_top_Oextremum__unique, fact_250_conc__trans__additional_I4_J, fact_263_abs__fun__simps_I1_J, fact_243_conc__trans__additional_I3_J, fact_5_conc__fun__fail__iff_I2_J, help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T, fact_223_order__subst2, fact_90_Refine__Misc_Oif__mono, fact_301_RETURN__SPEC__refine, fact_222_order__subst2, fact_334_inres__def, fact_11_conc__fun__fail__iff_I2_J, fact_296_RETURN__to__SPEC__rule, fact_291_nres__order__simps_I20_J, fact_146_order__class_Oorder_Oantisym, fact_305_pw__conc__nofail, fact_34_conc__trans__additional_I1_J, fact_256_abs__trans__additional_I2_J, fact_155_ord__le__eq__trans, fact_289_nres__order__simps_I21_J, fact_141_order__trans, fact_171_order__class_Oorder_Oeq__iff, fact_318_RES__refine, fact_154_ord__le__eq__trans, fact_239_conc__trans__additional_I2_J, fact_231_GreatestI2__order, fact_51_order__mono__setup_Orefl, fact_311_not__nofail__iff, fact_234_ord__eq__le__eq__trans, fact_253_abs__trans__additional_I2_J
% 20.30/5.49 % No. of inferences in proof: 712
% 20.30/5.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5195 ms resp. 4531 ms w/o parsing
% 22.34/5.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.34/5.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------