TSTP Solution File: ITP156^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP156^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:19 EDT 2024
% Result : Theorem 14.47s 4.32s
% Output : Refutation 15.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 435
% Syntax : Number of formulae : 750 ( 398 unt; 122 typ; 0 def)
% Number of atoms : 1548 ( 748 equ; 4 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 5032 ( 68 ~; 30 |; 102 &;4364 @)
% ( 0 <=>; 468 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 33 ( 32 usr)
% Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 90 usr; 24 con; 0-2 aty)
% Number of variables : 1597 ( 32 ^1561 !; 4 ?;1597 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1741234931a_real_type,type,
set_Pr1741234931a_real: $tType ).
thf(produc1826081171a_real_type,type,
produc1826081171a_real: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(produc826782210l_real_type,type,
produc826782210l_real: $tType ).
thf(produc578556564l_real_type,type,
produc578556564l_real: $tType ).
thf(produc1286132450l_real_type,type,
produc1286132450l_real: $tType ).
thf(produc1088645164real_a_type,type,
produc1088645164real_a: $tType ).
thf(produc2096821232od_a_a_type,type,
produc2096821232od_a_a: $tType ).
thf(produc348734722a_real_type,type,
produc348734722a_real: $tType ).
thf(produc1921647824od_a_a_type,type,
produc1921647824od_a_a: $tType ).
thf(produc1016684094_a_a_a_type,type,
produc1016684094_a_a_a: $tType ).
thf(set_Pr147102617l_real_type,type,
set_Pr147102617l_real: $tType ).
thf(produc391212143l_real_type,type,
produc391212143l_real: $tType ).
thf(produc443621487t_real_type,type,
produc443621487t_real: $tType ).
thf(set_se1596668135od_a_a_type,type,
set_se1596668135od_a_a: $tType ).
thf(set_Pr1928503567a_real_type,type,
set_Pr1928503567a_real: $tType ).
thf(produc1396156303t_real_type,type,
produc1396156303t_real: $tType ).
thf(produc1232925073real_a_type,type,
produc1232925073real_a: $tType ).
thf(produc1923333543_set_a_type,type,
produc1923333543_set_a: $tType ).
thf(produc957004601l_real_type,type,
produc957004601l_real: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_a_set_a_type,type,
product_prod_a_set_a: $tType ).
thf(product_prod_a_real_type,type,
product_prod_a_real: $tType ).
thf(product_prod_real_a_type,type,
product_prod_real_a: $tType ).
thf(set_set_real_type,type,
set_set_real: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(real_type,type,
real: $tType ).
thf(a_type,type,
a: $tType ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(plus_p2005278886t_real_type,type,
plus_p2005278886t_real: produc443621487t_real > produc443621487t_real > produc443621487t_real ).
thf(plus_p125342128_set_a_type,type,
plus_p125342128_set_a: produc1923333543_set_a > produc1923333543_set_a > produc1923333543_set_a ).
thf(plus_p1243198544real_a_type,type,
plus_p1243198544real_a: product_prod_real_a > product_prod_real_a > product_prod_real_a ).
thf(plus_p1952869542l_real_type,type,
plus_p1952869542l_real: produc391212143l_real > produc391212143l_real > produc391212143l_real ).
thf(plus_p1582417306real_a_type,type,
plus_p1582417306real_a: produc1232925073real_a > produc1232925073real_a > produc1232925073real_a ).
thf(plus_p541014626a_real_type,type,
plus_p541014626a_real: product_prod_a_real > product_prod_a_real > product_prod_a_real ).
thf(plus_p1745648536t_real_type,type,
plus_p1745648536t_real: produc1396156303t_real > produc1396156303t_real > produc1396156303t_real ).
thf(plus_p1265825342_set_a_type,type,
plus_p1265825342_set_a: product_prod_a_set_a > product_prod_a_set_a > product_prod_a_set_a ).
thf(plus_p1505579230od_a_a_type,type,
plus_p1505579230od_a_a: product_prod_a_a > product_prod_a_a > product_prod_a_a ).
thf(plus_plus_real_type,type,
plus_plus_real: real > real > real ).
thf(plus_p130512152a_real_type,type,
plus_p130512152a_real: set_Pr1928503567a_real > set_Pr1928503567a_real > set_Pr1928503567a_real ).
thf(plus_p634297534od_a_a_type,type,
plus_p634297534od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(plus_plus_set_real_type,type,
plus_plus_set_real: set_real > set_real > set_real ).
thf(plus_p1613276318od_a_a_type,type,
plus_p1613276318od_a_a: set_se1596668135od_a_a > set_se1596668135od_a_a > set_se1596668135od_a_a ).
thf(plus_p768704801t_real_type,type,
plus_p768704801t_real: set_set_real > set_set_real > set_set_real ).
thf(plus_plus_set_set_a_type,type,
plus_plus_set_set_a: set_set_a > set_set_a > set_set_a ).
thf(plus_plus_set_a_type,type,
plus_plus_set_a: set_a > set_a > set_a ).
thf(plus_plus_a_type,type,
plus_plus_a: a > a > a ).
thf(zero_z342251165l_real_type,type,
zero_z342251165l_real: produc578556564l_real ).
thf(zero_z1937883107real_a_type,type,
zero_z1937883107real_a: produc1088645164real_a ).
thf(zero_z590476811l_real_type,type,
zero_z590476811l_real: produc826782210l_real ).
thf(zero_z396988537od_a_a_type,type,
zero_z396988537od_a_a: produc2096821232od_a_a ).
thf(zero_z659284464l_real_type,type,
zero_z659284464l_real: produc957004601l_real ).
thf(zero_z1407338960real_a_type,type,
zero_z1407338960real_a: product_prod_real_a ).
thf(zero_z2135370393l_real_type,type,
zero_z2135370393l_real: produc1286132450l_real ).
thf(zero_z53797895od_a_a_type,type,
zero_z53797895od_a_a: produc1921647824od_a_a ).
thf(zero_z705155042a_real_type,type,
zero_z705155042a_real: product_prod_a_real ).
thf(zero_z950819678od_a_a_type,type,
zero_z950819678od_a_a: product_prod_a_a ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(zero_z257140542od_a_a_type,type,
zero_z257140542od_a_a: set_Product_prod_a_a ).
thf(zero_zero_set_real_type,type,
zero_zero_set_real: set_real ).
thf(zero_zero_set_a_type,type,
zero_zero_set_a: set_a ).
thf(zero_zero_a_type,type,
zero_zero_a: a ).
thf(ord_less_real_type,type,
ord_less_real: real > real > $o ).
thf(ord_le108336051od_a_a_type,type,
ord_le108336051od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(ord_le1824328871od_a_a_type,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_less_eq_set_real_type,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(prefer1113819806a_real_type,type,
prefer1113819806a_real: set_Pr1741234931a_real > $o ).
thf(prefer225425826od_a_a_type,type,
prefer225425826od_a_a: set_Pr1948701895od_a_a > $o ).
thf(prefer1247792113f_real_type,type,
prefer1247792113f_real: set_Pr147102617l_real > $o ).
thf(prefer529818233pref_a_type,type,
prefer529818233pref_a: set_Product_prod_a_a > $o ).
thf(produc1175086478l_real_type,type,
produc1175086478l_real: produc957004601l_real > real > produc578556564l_real ).
thf(produc1430099868real_a_type,type,
produc1430099868real_a: produc957004601l_real > a > produc1088645164real_a ).
thf(produc886678603a_real_type,type,
produc886678603a_real: product_prod_a_real > product_prod_a_real > produc1826081171a_real ).
thf(produc1474507607od_a_a_type,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(produc454274172a_real_type,type,
produc454274172a_real: product_prod_a_a > real > produc348734722a_real ).
thf(produc2061588782_a_a_a_type,type,
produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a ).
thf(produc1926903988l_real_type,type,
produc1926903988l_real: real > produc957004601l_real > produc826782210l_real ).
thf(produc454550562od_a_a_type,type,
produc454550562od_a_a: real > product_prod_a_a > produc2096821232od_a_a ).
thf(produc705216881l_real_type,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(produc247649703t_real_type,type,
produc247649703t_real: real > set_real > produc443621487t_real ).
thf(produc1872317017_set_a_type,type,
produc1872317017_set_a: real > set_a > produc1923333543_set_a ).
thf(product_Pair_real_a_type,type,
product_Pair_real_a: real > a > product_prod_real_a ).
thf(produc1812461223l_real_type,type,
produc1812461223l_real: set_real > real > produc391212143l_real ).
thf(produc617496131real_a_type,type,
produc617496131real_a: set_real > a > produc1232925073real_a ).
thf(produc64206290l_real_type,type,
produc64206290l_real: a > produc957004601l_real > produc1286132450l_real ).
thf(produc1299253312od_a_a_type,type,
produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a ).
thf(product_Pair_a_real_type,type,
product_Pair_a_real: a > real > product_prod_a_real ).
thf(produc1391501065t_real_type,type,
produc1391501065t_real: a > set_real > produc1396156303t_real ).
thf(product_Pair_a_set_a_type,type,
product_Pair_a_set_a: a > set_a > product_prod_a_set_a ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(real_V368978776od_a_a_type,type,
real_V368978776od_a_a: real > produc1572603623od_a_a > produc1572603623od_a_a ).
thf(real_V195069393a_real_type,type,
real_V195069393a_real: real > produc348734722a_real > produc348734722a_real ).
thf(real_V1538726831_a_a_a_type,type,
real_V1538726831_a_a_a: real > produc1016684094_a_a_a > produc1016684094_a_a_a ).
thf(real_V1943155903od_a_a_type,type,
real_V1943155903od_a_a: real > produc2096821232od_a_a > produc2096821232od_a_a ).
thf(real_V1214981142real_a_type,type,
real_V1214981142real_a: real > product_prod_real_a > product_prod_real_a ).
thf(real_V296206913od_a_a_type,type,
real_V296206913od_a_a: real > produc1921647824od_a_a > produc1921647824od_a_a ).
thf(real_V512797224a_real_type,type,
real_V512797224a_real: real > product_prod_a_real > product_prod_a_real ).
thf(real_V543523736od_a_a_type,type,
real_V543523736od_a_a: real > product_prod_a_a > product_prod_a_a ).
thf(real_V453051771R_real_type,type,
real_V453051771R_real: real > real > real ).
thf(real_V1035702895aleR_a_type,type,
real_V1035702895aleR_a: real > a > a ).
thf(collec645855634od_a_a_type,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(member384820540a_real_type,type,
member384820540a_real: produc1826081171a_real > set_Pr1741234931a_real > $o ).
thf(member2057358096od_a_a_type,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(member1068169442l_real_type,type,
member1068169442l_real: produc957004601l_real > set_Pr147102617l_real > $o ).
thf(member1103263856a_real_type,type,
member1103263856a_real: product_prod_a_real > set_Pr1928503567a_real > $o ).
thf(member449909584od_a_a_type,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_real_type,type,
member_real: real > set_real > $o ).
thf(member1838126896od_a_a_type,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(member_set_real_type,type,
member_set_real: set_real > set_set_real > $o ).
thf(member_set_a_type,type,
member_set_a: set_a > set_set_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(relation_type,type,
relation: set_Product_prod_a_a ).
thf(u_type,type,
u: real ).
thf(v_type,type,
v: real ).
thf(x_type,type,
x: a ).
thf(y_type,type,
y: a ).
thf(190,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_group__cancel_Oadd2) ).
thf(892,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(108,axiom,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_one__reorient) ).
thf(629,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(234,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Pair__inject) ).
thf(1024,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(280,axiom,
! [A: real] :
( ( real_V1035702895aleR_a @ A @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_scale__zero__right) ).
thf(1168,plain,
! [A: real] :
( ( real_V1035702895aleR_a @ A @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(257,axiom,
! [A: a,B: real,C: a] :
( ( ( plus_plus_a @ A @ ( real_V1035702895aleR_a @ B @ C ) )
= ( plus_plus_a @ C @ ( real_V1035702895aleR_a @ B @ A ) ) )
= ( ( C = A )
| ( B = one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_scaleR__eq__iff) ).
thf(1105,plain,
! [A: a,B: real,C: a] :
( ( ( plus_plus_a @ A @ ( real_V1035702895aleR_a @ B @ C ) )
= ( plus_plus_a @ C @ ( real_V1035702895aleR_a @ B @ A ) ) )
= ( ( C = A )
| ( B = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(14,axiom,
! [A: product_prod_a_a] :
( ( zero_z950819678od_a_a = A )
= ( A = zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_zero__reorient) ).
thf(347,plain,
! [A: product_prod_a_a] :
( ( zero_z950819678od_a_a = A )
= ( A = zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(72,axiom,
( zero_z1937883107real_a
= ( produc1430099868real_a @ zero_z659284464l_real @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_zero__prod__def) ).
thf(518,plain,
( zero_z1937883107real_a
= ( produc1430099868real_a @ zero_z659284464l_real @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(56,axiom,
! [A: set_Product_prod_a_a] :
( ( plus_p634297534od_a_a @ A @ zero_z257140542od_a_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add_Oright__neutral) ).
thf(468,plain,
! [A: set_Product_prod_a_a] :
( ( plus_p634297534od_a_a @ A @ zero_z257140542od_a_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(283,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer529818233pref_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_convex__ge__imp__conved) ).
thf(1179,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer529818233pref_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(154,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_is__num__normalize_I1_J) ).
thf(777,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(119,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_add__le__cancel__right) ).
thf(666,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(60,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ ( real_V453051771R_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_pth__c_I1_J) ).
thf(481,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ ( real_V453051771R_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(20,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_add__pos__nonneg) ).
thf(365,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(285,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_indiff__trans) ).
thf(1190,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(9,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_order__refl) ).
thf(333,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(235,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: real,E: real] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) )
=> ( prefer529818233pref_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_weak__convexI) ).
thf(1031,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: real,E: real] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) )
=> ( prefer529818233pref_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(288,axiom,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ C ) @ ( real_V1035702895aleR_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_scaleR__add__left) ).
thf(1200,plain,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ C ) @ ( real_V1035702895aleR_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_le__add__same__cancel2) ).
thf(379,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(46,axiom,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_scaleR__add__right) ).
thf(440,plain,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(97,axiom,
! [A: product_prod_a_real,B: set_Pr1928503567a_real,C: product_prod_a_real,D: set_Pr1928503567a_real] :
( ( member1103263856a_real @ A @ B )
=> ( ( member1103263856a_real @ C @ D )
=> ( member1103263856a_real @ ( plus_p541014626a_real @ A @ C ) @ ( plus_p130512152a_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_set__plus__intro) ).
thf(597,plain,
! [A: product_prod_a_real,B: set_Pr1928503567a_real,C: product_prod_a_real,D: set_Pr1928503567a_real] :
( ( member1103263856a_real @ A @ B )
=> ( ( member1103263856a_real @ C @ D )
=> ( member1103263856a_real @ ( plus_p541014626a_real @ A @ C ) @ ( plus_p130512152a_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(180,axiom,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ A @ zero_z950819678od_a_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add_Ocomm__neutral) ).
thf(861,plain,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ A @ zero_z950819678od_a_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(35,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__left__mono) ).
thf(408,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(219,axiom,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( real_V453051771R_real @ B @ A )
= ( real_V453051771R_real @ C @ A ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_scale__right__imp__eq) ).
thf(977,plain,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( real_V453051771R_real @ B @ A )
= ( real_V453051771R_real @ C @ A ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(74,axiom,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ A @ zero_z705155042a_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add_Oright__neutral) ).
thf(523,plain,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ A @ zero_z705155042a_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(92,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ ( real_V453051771R_real @ B @ C ) )
= ( plus_plus_real @ C @ ( real_V453051771R_real @ B @ A ) ) )
= ( ( C = A )
| ( B = one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_scaleR__eq__iff) ).
thf(582,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ ( real_V453051771R_real @ B @ C ) )
= ( plus_plus_real @ C @ ( real_V453051771R_real @ B @ A ) ) )
= ( ( C = A )
| ( B = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(184,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_double__add__le__zero__iff__single__add__le__zero) ).
thf(873,plain,
! [A: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(49,axiom,
ord_less_eq_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_zero__le__one) ).
thf(449,plain,
ord_less_eq_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(249,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add_Ogroup__left__neutral) ).
thf(1078,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(27,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_add__mono__thms__linordered__field_I5_J) ).
thf(385,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(81,axiom,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_split__scaleR__neg__le) ).
thf(550,plain,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) ) )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(135,axiom,
! [A: real,B: a,C: real,D: a] :
( ( ( product_Pair_real_a @ A @ B )
= ( product_Pair_real_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_old_Oprod_Oinject) ).
thf(715,plain,
! [A: real,B: a,C: real,D: a] :
( ( ( product_Pair_real_a @ A @ B )
= ( product_Pair_real_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(314,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__cancel__right__left) ).
thf(1275,plain,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(244,axiom,
! [A: a,B: a,C: a,D: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__Pair) ).
thf(1063,plain,
! [A: a,B: a,C: a,D: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(169,axiom,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ zero_z950819678od_a_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add_Ogroup__left__neutral) ).
thf(829,plain,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ zero_z950819678od_a_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(227,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add_Oright__cancel) ).
thf(1001,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(303,axiom,
! [A: real,B: a,C: real,D: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ C @ D ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ D ) @ ( real_V1035702895aleR_a @ C @ B ) ) )
=> ( ( A != C )
=> ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_add__scaleR__degen) ).
thf(1243,plain,
! [A: real,B: a,C: real,D: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ C @ D ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ D ) @ ( real_V1035702895aleR_a @ C @ B ) ) )
=> ( ( A != C )
=> ( D = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(133,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_scaleR__right__mono) ).
thf(709,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(188,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_eq_real @ B @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_add__le__same__cancel1) ).
thf(885,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_eq_real @ B @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(310,axiom,
( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062) ).
thf(1265,plain,
( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(173,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_scaleR__mono) ).
thf(841,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(38,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_zero__reorient) ).
thf(417,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(138,axiom,
ord_less_eq_real @ one_one_real @ one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_le__numeral__extra_I4_J) ).
thf(724,plain,
ord_less_eq_real @ one_one_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(88,axiom,
! [A: real,B: set_real,C: real,D: set_real] :
( ( member_real @ A @ B )
=> ( ( member_real @ C @ D )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_set__plus__intro) ).
thf(570,plain,
! [A: real,B: set_real,C: real,D: set_real] :
( ( member_real @ A @ B )
=> ( ( member_real @ C @ D )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(157,axiom,
! [A: set_Pr147102617l_real] :
( ! [B: real,C: real,D: real,E: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) )
=> ( prefer1247792113f_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_weak__convexI) ).
thf(785,plain,
! [A: set_Pr147102617l_real] :
( ! [B: real,C: real,D: real,E: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) )
=> ( prefer1247792113f_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(67,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ C @ ( real_V453051771R_real @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_pth__b_I2_J) ).
thf(504,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ C @ ( real_V453051771R_real @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(172,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__cancel__left__right) ).
thf(838,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(13,axiom,
! [A: real,B: real,C: product_prod_a_a] :
( ( real_V1943155903od_a_a @ A @ ( produc454550562od_a_a @ B @ C ) )
= ( produc454550562od_a_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_scaleR__Pair) ).
thf(344,plain,
! [A: real,B: real,C: product_prod_a_a] :
( ( real_V1943155903od_a_a @ A @ ( produc454550562od_a_a @ B @ C ) )
= ( produc454550562od_a_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(267,axiom,
! [A: real,B: a,C: real] :
( ( real_V512797224a_real @ A @ ( product_Pair_a_real @ B @ C ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_scaleR__Pair) ).
thf(1132,plain,
! [A: real,B: a,C: real] :
( ( real_V512797224a_real @ A @ ( product_Pair_a_real @ B @ C ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(197,axiom,
( zero_z2135370393l_real
= ( produc64206290l_real @ zero_zero_a @ zero_z659284464l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_zero__prod__def) ).
thf(917,plain,
( zero_z2135370393l_real
= ( produc64206290l_real @ zero_zero_a @ zero_z659284464l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(131,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__right__imp__eq) ).
thf(702,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(164,axiom,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_scaleR__left_Oadd) ).
thf(817,plain,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(84,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ B @ A ) )
= ( B = zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__cancel__right__left) ).
thf(559,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ B @ A ) )
= ( B = zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(252,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ A @ C ) @ ( plus_p634297534od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_set__plus__intro) ).
thf(1087,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ A @ C ) @ ( plus_p634297534od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(183,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_add__less__same__cancel2) ).
thf(870,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(100,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_scaleR__le__cancel__left__pos) ).
thf(606,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(151,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_add__mono__thms__linordered__field_I3_J) ).
thf(770,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(6,axiom,
! [A: real,B: product_prod_a_a,C: product_prod_a_a] :
( ( real_V368978776od_a_a @ A @ ( produc1474507607od_a_a @ B @ C ) )
= ( produc1474507607od_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_scale__prod) ).
thf(325,plain,
! [A: real,B: product_prod_a_a,C: product_prod_a_a] :
( ( real_V368978776od_a_a @ A @ ( produc1474507607od_a_a @ B @ C ) )
= ( produc1474507607od_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( produc705216881l_real @ A @ B )
= ( produc705216881l_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Oprod_Oinject) ).
thf(316,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( produc705216881l_real @ A @ B )
= ( produc705216881l_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(256,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( plus_p634297534od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ D @ E ) )
=> ( ( member449909584od_a_a @ D @ B )
=> ~ ( member449909584od_a_a @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_set__plus__elim) ).
thf(1100,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( plus_p634297534od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ D @ E ) )
=> ( ( member449909584od_a_a @ D @ B )
=> ~ ( member449909584od_a_a @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(300,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_subsetI) ).
thf(1232,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(112,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= ( plus_p1505579230od_a_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__left__cancel) ).
thf(638,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= ( plus_p1505579230od_a_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(177,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_add__mono1) ).
thf(853,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(146,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__le__imp__le__right) ).
thf(756,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(95,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_add__nonpos__nonpos) ).
thf(591,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(47,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_comm__monoid__add__class_Oadd__0) ).
thf(443,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(24,axiom,
! [A: real,B: product_prod_a_a,C: real] :
( ( real_V195069393a_real @ A @ ( produc454274172a_real @ B @ C ) )
= ( produc454274172a_real @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_scaleR__Pair) ).
thf(376,plain,
! [A: real,B: product_prod_a_a,C: real] :
( ( real_V195069393a_real @ A @ ( produc454274172a_real @ B @ C ) )
= ( produc454274172a_real @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(274,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_surj__pair) ).
thf(1151,plain,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(166,axiom,
~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_not__one__le__zero) ).
thf(821,plain,
~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(193,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_add__less__cancel__left) ).
thf(905,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(16,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add_Oright__cancel) ).
thf(353,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(215,axiom,
ord_less_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_zero__less__one) ).
thf(966,plain,
ord_less_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(220,axiom,
! [A: real,B: real,C: real,D: real,E: real,F: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) )
= ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_pth__c_I4_J) ).
thf(981,plain,
! [A: real,B: real,C: real,D: real,E: real,F: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) )
= ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(293,axiom,
! [A: real,B: product_prod_a_a,C: a] :
( ( real_V1538726831_a_a_a @ A @ ( produc2061588782_a_a_a @ B @ C ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_scale__prod) ).
thf(1215,plain,
! [A: real,B: product_prod_a_a,C: a] :
( ( real_V1538726831_a_a_a @ A @ ( produc2061588782_a_a_a @ B @ C ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(128,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_add__nonpos__eq__0__iff) ).
thf(692,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(262,axiom,
ord_less_eq_real @ zero_zero_real @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_assms_I3_J) ).
thf(1119,plain,
ord_less_eq_real @ zero_zero_real @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(226,axiom,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ A @ zero_z950819678od_a_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add_Oright__neutral) ).
thf(998,plain,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ A @ zero_z950819678od_a_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(36,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_zero__neq__one) ).
thf(411,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_add__strict__increasing2) ).
thf(428,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(68,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_add__le__imp__le__left) ).
thf(507,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(31,axiom,
! [A: set_real] :
( ( plus_plus_set_real @ zero_zero_set_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add_Oleft__neutral) ).
thf(397,plain,
! [A: set_real] :
( ( plus_plus_set_real @ zero_zero_set_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(126,axiom,
! [A: set_a] :
( ( plus_plus_set_a @ A @ zero_zero_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_add_Oright__neutral) ).
thf(687,plain,
! [A: set_a] :
( ( plus_plus_set_a @ A @ zero_zero_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(247,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ zero_z950819678od_a_a @ A )
=> ( ord_le1824328871od_a_a @ B @ ( plus_p634297534od_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_set__zero__plus2) ).
thf(1072,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ zero_z950819678od_a_a @ A )
=> ( ord_le1824328871od_a_a @ B @ ( plus_p634297534od_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(51,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add__increasing2) ).
thf(453,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(290,axiom,
! [A: real,B: a,C: product_prod_a_a] :
( ( real_V296206913od_a_a @ A @ ( produc1299253312od_a_a @ B @ C ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_scaleR__Pair) ).
thf(1206,plain,
! [A: real,B: a,C: product_prod_a_a] :
( ( real_V296206913od_a_a @ A @ ( produc1299253312od_a_a @ B @ C ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(70,axiom,
! [A: real,B: real,C: real] :
( ( ( real_V453051771R_real @ A @ B )
= ( real_V453051771R_real @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_scale__cancel__right) ).
thf(512,plain,
! [A: real,B: real,C: real] :
( ( ( real_V453051771R_real @ A @ B )
= ( real_V453051771R_real @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_pth__c_I2_J) ).
thf(529,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(158,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add__le__same__cancel2) ).
thf(793,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(200,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_less__add__same__cancel2) ).
thf(925,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(148,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add_Ogroup__left__neutral) ).
thf(761,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(162,axiom,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_field__le__epsilon) ).
thf(810,plain,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(242,axiom,
! [A: a,B: set_real,C: a,D: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ A @ B ) @ ( produc1391501065t_real @ C @ D ) )
= ( produc1391501065t_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__Pair) ).
thf(1057,plain,
! [A: a,B: set_real,C: a,D: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ A @ B ) @ ( produc1391501065t_real @ C @ D ) )
= ( produc1391501065t_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(278,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_subset__eq) ).
thf(1163,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(237,axiom,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_add_Oleft__commute) ).
thf(1042,plain,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(264,axiom,
! [A: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ A )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_scale__zero__left) ).
thf(1123,plain,
! [A: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ A )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(282,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( plus_plus_set_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( A
= ( plus_plus_a @ D @ E ) )
=> ( ( member_a @ D @ B )
=> ~ ( member_a @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_set__plus__elim) ).
thf(1174,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( plus_plus_set_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( A
= ( plus_plus_a @ D @ E ) )
=> ( ( member_a @ D @ B )
=> ~ ( member_a @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(165,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_pth__b_I1_J) ).
thf(820,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(302,axiom,
! [A: a,B: a,C: a,D: a] :
( ( A
= ( plus_plus_a @ B @ C ) )
=> ( ( plus_plus_a @ A @ D )
= ( plus_plus_a @ B @ ( plus_plus_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_group__cancel_Oadd1) ).
thf(1238,plain,
! [A: a,B: a,C: a,D: a] :
( ( A
= ( plus_plus_a @ B @ C ) )
=> ( ( plus_plus_a @ A @ D )
= ( plus_plus_a @ B @ ( plus_plus_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(211,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_antisym) ).
thf(957,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(296,axiom,
ord_less_eq_real @ zero_zero_real @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I4_J) ).
thf(1223,plain,
ord_less_eq_real @ zero_zero_real @ v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(64,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_add__neg__neg) ).
thf(493,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(52,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_add__strict__left__mono) ).
thf(456,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(218,axiom,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ zero_z705155042a_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add_Ogroup__left__neutral) ).
thf(974,plain,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ zero_z705155042a_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(231,axiom,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= B )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__cancel__left__left) ).
thf(1012,plain,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= B )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(175,axiom,
! [A: real,B: product_prod_a_a,C: real] :
( ( real_V195069393a_real @ A @ ( produc454274172a_real @ B @ C ) )
= ( produc454274172a_real @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_scale__prod) ).
thf(847,plain,
! [A: real,B: product_prod_a_a,C: real] :
( ( real_V195069393a_real @ A @ ( produc454274172a_real @ B @ C ) )
= ( produc454274172a_real @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(86,axiom,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_less__add__one) ).
thf(566,plain,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(61,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(484,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(259,axiom,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add_Oassoc) ).
thf(1111,plain,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(139,axiom,
! [A: set_real,B: set_real] :
( ( member_real @ zero_zero_real @ A )
=> ( ord_less_eq_set_real @ B @ ( plus_plus_set_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_set__zero__plus2) ).
thf(725,plain,
! [A: set_real,B: set_real] :
( ( member_real @ zero_zero_real @ A )
=> ( ord_less_eq_set_real @ B @ ( plus_plus_set_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(101,axiom,
ord_less_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_less__numeral__extra_I1_J) ).
thf(610,plain,
ord_less_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(66,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_group__cancel_Oadd1) ).
thf(499,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(223,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_add__le__less__mono) ).
thf(989,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(312,axiom,
! [A: a] :
( ( real_V1035702895aleR_a @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_scaleR__one) ).
thf(1270,plain,
! [A: a] :
( ( real_V1035702895aleR_a @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(308,axiom,
( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_u__0) ).
thf(1259,plain,
( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(115,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ zero_zero_real @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_pth__a) ).
thf(650,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ zero_zero_real @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(208,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ C @ B ) @ ( real_V453051771R_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_scaleR__left__mono__neg) ).
thf(948,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ C @ B ) @ ( real_V453051771R_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(269,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_add__right__cancel) ).
thf(1138,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(17,axiom,
! [A: real,B: real,C: product_prod_a_a] :
( ( real_V1943155903od_a_a @ A @ ( produc454550562od_a_a @ B @ C ) )
= ( produc454550562od_a_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_scale__prod) ).
thf(356,plain,
! [A: real,B: real,C: product_prod_a_a] :
( ( real_V1943155903od_a_a @ A @ ( produc454550562od_a_a @ B @ C ) )
= ( produc454550562od_a_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(156,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_order__class_Oorder_Oeq__iff) ).
thf(783,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(39,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_scaleR__mono_H) ).
thf(420,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(277,axiom,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ A @ ( real_V1035702895aleR_a @ B @ C ) )
= ( real_V1035702895aleR_a @ B @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_scale__left__commute) ).
thf(1160,plain,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ A @ ( real_V1035702895aleR_a @ B @ C ) )
= ( real_V1035702895aleR_a @ B @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(203,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__cancel__right__right) ).
thf(933,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(145,axiom,
! [A: set_a] :
( ( plus_plus_set_a @ zero_zero_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add_Oleft__neutral) ).
thf(753,plain,
! [A: set_a] :
( ( plus_plus_set_a @ zero_zero_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(120,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_le__add__same__cancel1) ).
thf(669,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(248,axiom,
! [A: real,B: a] :
( ( ( real_V1035702895aleR_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_real )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_scale__eq__0__iff) ).
thf(1075,plain,
! [A: real,B: a] :
( ( ( real_V1035702895aleR_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_real )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(75,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ A @ B ) )
= ( B = zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_add__cancel__right__right) ).
thf(526,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( A
= ( plus_p1505579230od_a_a @ A @ B ) )
= ( B = zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(80,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ C @ A ) @ ( real_V453051771R_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_scaleR__left__mono) ).
thf(547,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ C @ A ) @ ( real_V453051771R_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(132,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_add__nonneg__nonneg) ).
thf(706,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(7,axiom,
( zero_z659284464l_real
= ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_zero__prod__def) ).
thf(328,plain,
( zero_z659284464l_real
= ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,axiom,
! [A: real,B: set_real,C: real,D: set_real] :
( ( plus_p2005278886t_real @ ( produc247649703t_real @ A @ B ) @ ( produc247649703t_real @ C @ D ) )
= ( produc247649703t_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__Pair) ).
thf(471,plain,
! [A: real,B: set_real,C: real,D: set_real] :
( ( plus_p2005278886t_real @ ( produc247649703t_real @ A @ B ) @ ( produc247649703t_real @ C @ D ) )
= ( produc247649703t_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(123,axiom,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add_Ocommute) ).
thf(679,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(236,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ A @ B ) @ ( product_Pair_a_set_a @ C @ D ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__Pair) ).
thf(1039,plain,
! [A: a,B: set_a,C: a,D: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ A @ B ) @ ( product_Pair_a_set_a @ C @ D ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(217,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__mono__thms__linordered__semiring_I4_J) ).
thf(970,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(260,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_old_Oprod_Oinject) ).
thf(1114,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(71,axiom,
! [A: real] :
( ( real_V453051771R_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_pth__4_I1_J) ).
thf(515,plain,
! [A: real] :
( ( real_V453051771R_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(221,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_le__cases) ).
thf(984,plain,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(137,axiom,
! [A: set_real,B: real,C: set_real,D: real] :
( ( plus_p1952869542l_real @ ( produc1812461223l_real @ A @ B ) @ ( produc1812461223l_real @ C @ D ) )
= ( produc1812461223l_real @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__Pair) ).
thf(721,plain,
! [A: set_real,B: real,C: set_real,D: real] :
( ( plus_p1952869542l_real @ ( produc1812461223l_real @ A @ B ) @ ( produc1812461223l_real @ C @ D ) )
= ( produc1812461223l_real @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(304,axiom,
! [A: a,B: real,C: real] :
( ( A != zero_zero_a )
=> ( ( ( real_V1035702895aleR_a @ B @ A )
= ( real_V1035702895aleR_a @ C @ A ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_scale__right__imp__eq) ).
thf(1246,plain,
! [A: a,B: real,C: real] :
( ( A != zero_zero_a )
=> ( ( ( real_V1035702895aleR_a @ B @ A )
= ( real_V1035702895aleR_a @ C @ A ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(22,axiom,
! [A: real,B: set_a,C: real,D: set_a] :
( ( plus_p125342128_set_a @ ( produc1872317017_set_a @ A @ B ) @ ( produc1872317017_set_a @ C @ D ) )
= ( produc1872317017_set_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__Pair) ).
thf(371,plain,
! [A: real,B: set_a,C: real,D: set_a] :
( ( plus_p125342128_set_a @ ( produc1872317017_set_a @ A @ B ) @ ( produc1872317017_set_a @ C @ D ) )
= ( produc1872317017_set_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(243,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_old_Oprod_Oinducts) ).
thf(1060,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(240,axiom,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__cancel__left__right) ).
thf(1050,plain,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(136,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_double__zero) ).
thf(718,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(189,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_add__mono__thms__linordered__semiring_I3_J) ).
thf(888,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(268,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_in__mono) ).
thf(1135,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(214,axiom,
ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_zero__less__two) ).
thf(965,plain,
ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(272,axiom,
! [A: a,B: real,C: a,D: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ A @ B ) @ ( product_Pair_a_real @ C @ D ) )
= ( product_Pair_a_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__Pair) ).
thf(1146,plain,
! [A: a,B: real,C: a,D: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ A @ B ) @ ( product_Pair_a_real @ C @ D ) )
= ( product_Pair_a_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(313,axiom,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_indifferent__imp__weak__pref_I2_J) ).
thf(1273,plain,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(89,axiom,
! [A: real,B: a,C: real,D: a] :
( ( ( product_Pair_real_a @ A @ B )
= ( product_Pair_real_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_prod_Oinject) ).
thf(573,plain,
! [A: real,B: a,C: real,D: a] :
( ( ( product_Pair_real_a @ A @ B )
= ( product_Pair_real_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(275,axiom,
! [A: real,B: a,C: real] :
( ( real_V512797224a_real @ A @ ( product_Pair_a_real @ B @ C ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_scale__prod) ).
thf(1154,plain,
! [A: real,B: a,C: real] :
( ( real_V512797224a_real @ A @ ( product_Pair_a_real @ B @ C ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(40,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ D ) @ ( real_V453051771R_real @ C @ B ) ) )
=> ( ( A != C )
=> ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_add__scaleR__degen) ).
thf(423,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ D ) @ ( real_V453051771R_real @ C @ B ) ) )
=> ( ( A != C )
=> ( D = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(229,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_add__left__imp__eq) ).
thf(1007,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(33,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add__le__cancel__left) ).
thf(402,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(141,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= B )
= ( A = zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__cancel__left__left) ).
thf(732,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= B )
= ( A = zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(152,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Oright__neutral) ).
thf(772,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(168,axiom,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_split__scaleR__pos__le) ).
thf(826,plain,
! [A: real,B: real] :
( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_eq_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(91,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_add__increasing) ).
thf(579,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(307,axiom,
! [A: real,B: a,C: real,D: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ A @ B ) @ ( product_Pair_real_a @ C @ D ) )
= ( product_Pair_real_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__Pair) ).
thf(1256,plain,
! [A: real,B: a,C: real,D: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ A @ B ) @ ( product_Pair_real_a @ C @ D ) )
= ( product_Pair_real_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(85,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_order__subst1) ).
thf(562,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(192,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_pth__b_I3_J) ).
thf(904,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(113,axiom,
( zero_z705155042a_real
= ( product_Pair_a_real @ zero_zero_a @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_zero__prod__def) ).
thf(641,plain,
( zero_z705155042a_real
= ( product_Pair_a_real @ zero_zero_a @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(29,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Collect__mem__eq) ).
thf(391,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(204,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_add_Ocomm__neutral) ).
thf(936,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(26,axiom,
! [A: product_prod_a_real,B: product_prod_a_real,C: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= ( plus_p541014626a_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__right__cancel) ).
thf(382,plain,
! [A: product_prod_a_real,B: product_prod_a_real,C: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= ( plus_p541014626a_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(102,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_add__less__imp__less__left) ).
thf(611,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(10,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_antisym__conv) ).
thf(335,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(253,axiom,
! [A: real,B: a,C: a] :
( ( A != zero_zero_real )
=> ( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_scale__left__imp__eq) ).
thf(1090,plain,
! [A: real,B: a,C: a] :
( ( A != zero_zero_real )
=> ( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(297,axiom,
member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_assms_I2_J) ).
thf(1224,plain,
member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(15,axiom,
! [A: set_Product_prod_a_a] :
( ( plus_p634297534od_a_a @ zero_z257140542od_a_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_add_Oleft__neutral) ).
thf(350,plain,
! [A: set_Product_prod_a_a] :
( ( plus_p634297534od_a_a @ zero_z257140542od_a_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(121,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_add__nonneg__eq__0__iff) ).
thf(672,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(198,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_scaleR__nonpos__nonpos) ).
thf(919,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(160,axiom,
! [A: a,B: real,C: a,D: real] :
( ( ( product_Pair_a_real @ A @ B )
= ( product_Pair_a_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_old_Oprod_Oinject) ).
thf(804,plain,
! [A: a,B: real,C: a,D: real] :
( ( ( product_Pair_a_real @ A @ B )
= ( product_Pair_a_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(149,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ B ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ D ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_pth__9_I1_J) ).
thf(764,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( real_V453051771R_real @ D @ B ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ D ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(286,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Oleft__neutral) ).
thf(1194,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(291,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_add_Ocomm__neutral) ).
thf(1209,plain,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(124,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_scaleR__nonneg__nonpos) ).
thf(681,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(261,axiom,
( prefer529818233pref_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_real @ zero_zero_real @ D )
& ( ord_less_real @ zero_zero_real @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_weak__convex__pref__def) ).
thf(1117,plain,
( prefer529818233pref_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_real @ zero_zero_real @ D )
& ( ord_less_real @ zero_zero_real @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(230,axiom,
prefer529818233pref_a @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(1011,plain,
prefer529818233pref_a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(239,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_subset__iff) ).
thf(1048,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(19,axiom,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= A )
= ( B = zero_z705155042a_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__cancel__left__right) ).
thf(362,plain,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= A )
= ( B = zero_z705155042a_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(271,axiom,
( ( plus_plus_real @ u @ v )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_assms_I5_J) ).
thf(1144,plain,
( ( plus_plus_real @ u @ v )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(143,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
| ( ord_less_real @ B @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_add__less__zeroD) ).
thf(737,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real )
=> ( ( ord_less_real @ A @ zero_zero_real )
| ( ord_less_real @ B @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(104,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( plus_plus_set_real @ B @ C ) )
=> ~ ! [D: real,E: real] :
( ( A
= ( plus_plus_real @ D @ E ) )
=> ( ( member_real @ D @ B )
=> ~ ( member_real @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_set__plus__elim) ).
thf(616,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( plus_plus_set_real @ B @ C ) )
=> ~ ! [D: real,E: real] :
( ( A
= ( plus_plus_real @ D @ E ) )
=> ( ( member_real @ D @ B )
=> ~ ( member_real @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(69,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add_Oleft__commute) ).
thf(509,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(186,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_add__less__imp__less__right) ).
thf(880,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(44,axiom,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_pth__6) ).
thf(434,plain,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(59,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_eq__refl) ).
thf(477,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_add__mono__thms__linordered__semiring_I2_J) ).
thf(387,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(147,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_add__nonpos__neg) ).
thf(758,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(179,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_add__less__same__cancel1) ).
thf(858,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(78,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ord_less_eq_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_scaleR__le__cancel__left__neg) ).
thf(535,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ord_less_eq_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(96,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_add__nonneg__pos) ).
thf(594,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(105,axiom,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( A
= ( plus_p541014626a_real @ A @ B ) )
= ( B = zero_z705155042a_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__cancel__right__right) ).
thf(621,plain,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( A
= ( plus_p541014626a_real @ A @ B ) )
= ( B = zero_z705155042a_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(73,axiom,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( A
= ( plus_p541014626a_real @ B @ A ) )
= ( B = zero_z705155042a_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__cancel__right__left) ).
thf(520,plain,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( A
= ( plus_p541014626a_real @ B @ A ) )
= ( B = zero_z705155042a_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(273,axiom,
( plus_plus_a
= ( ^ [A: a,B: a] : ( plus_plus_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add_Ocommute) ).
thf(1149,plain,
( plus_plus_a
= ( ^ [A: a,B: a] : ( plus_plus_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(206,axiom,
! [A: real] :
( ( real_V453051771R_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_scale__zero__left) ).
thf(943,plain,
! [A: real] :
( ( real_V453051771R_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(8,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( produc705216881l_real @ A @ B )
= ( produc705216881l_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_prod_Oinject) ).
thf(330,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( produc705216881l_real @ A @ B )
= ( produc705216881l_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_scaleR__add__left) ).
thf(462,plain,
! [A: real,B: real,C: real] :
( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ C ) @ ( real_V453051771R_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(111,axiom,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_less__numeral__extra_I3_J) ).
thf(636,plain,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(245,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_prod_Oinject) ).
thf(1066,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(155,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pth__7_I1_J) ).
thf(780,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(232,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_add__right__imp__eq) ).
thf(1015,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(305,axiom,
! [A: real,B: a,C: a] :
( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_scale__cancel__left) ).
thf(1250,plain,
! [A: real,B: a,C: a] :
( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(43,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add__less__cancel__right) ).
thf(431,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(116,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_pos__add__strict) ).
thf(653,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(199,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add__pos__pos) ).
thf(922,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(195,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_add__mono__thms__linordered__semiring_I1_J) ).
thf(912,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(281,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__cancel__right__right) ).
thf(1171,plain,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(30,axiom,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= B )
= ( A = zero_z705155042a_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__cancel__left__left) ).
thf(394,plain,
! [A: product_prod_a_real,B: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= B )
= ( A = zero_z705155042a_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(222,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_order_Otrans) ).
thf(986,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(63,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_add__right__mono) ).
thf(490,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_not__one__less__zero) ).
thf(426,plain,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(289,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_comm__monoid__add__class_Oadd__0) ).
thf(1203,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(23,axiom,
( zero_z53797895od_a_a
= ( produc1299253312od_a_a @ zero_zero_a @ zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_zero__prod__def) ).
thf(374,plain,
( zero_z53797895od_a_a
= ( produc1299253312od_a_a @ zero_zero_a @ zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(62,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_zero__le__scaleR__iff) ).
thf(487,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(250,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Collect__mem__eq) ).
thf(1081,plain,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(205,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( C = D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_add__mono__thms__linordered__field_I1_J) ).
thf(939,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( C = D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(82,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_zero__le__double__add__iff__zero__le__single__add) ).
thf(553,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(167,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add_Oleft__neutral) ).
thf(823,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(134,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_pth__9_I2_J) ).
thf(712,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(178,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ B ) )
= ( real_V453051771R_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_pth__8) ).
thf(855,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ C @ B ) )
= ( real_V453051771R_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(127,axiom,
( zero_z1407338960real_a
= ( product_Pair_real_a @ zero_zero_real @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_zero__prod__def) ).
thf(690,plain,
( zero_z1407338960real_a
= ( product_Pair_real_a @ zero_zero_real @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(298,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_strict__trans) ).
thf(1225,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(37,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_less__add__same__cancel1) ).
thf(414,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(210,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ one_one_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_scaleR__left__le__one__le) ).
thf(954,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ one_one_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(144,axiom,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_le__cases3) ).
thf(739,plain,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(241,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: real,E: real] :
( ( prefer529818233pref_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_weak__convexD) ).
thf(1053,plain,
! [A: set_Product_prod_a_a,B: a,C: a,D: real,E: real] :
( ( prefer529818233pref_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ D @ B ) @ ( real_V1035702895aleR_a @ E @ C ) ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(284,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_old_Oprod_Oexhaust) ).
thf(1186,plain,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(93,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_scaleR__nonpos__nonneg) ).
thf(585,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(11,axiom,
! [A: set_Product_prod_a_a,B: set_se1596668135od_a_a,C: set_Product_prod_a_a,D: set_se1596668135od_a_a] :
( ( member1838126896od_a_a @ A @ B )
=> ( ( member1838126896od_a_a @ C @ D )
=> ( member1838126896od_a_a @ ( plus_p634297534od_a_a @ A @ C ) @ ( plus_p1613276318od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_set__plus__intro) ).
thf(338,plain,
! [A: set_Product_prod_a_a,B: set_se1596668135od_a_a,C: set_Product_prod_a_a,D: set_se1596668135od_a_a] :
( ( member1838126896od_a_a @ A @ B )
=> ( ( member1838126896od_a_a @ C @ D )
=> ( member1838126896od_a_a @ ( plus_p634297534od_a_a @ A @ C ) @ ( plus_p1613276318od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(90,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_add__neg__nonpos) ).
thf(576,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(209,axiom,
! [A: real] :
( ( real_V453051771R_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_scale__zero__right) ).
thf(951,plain,
! [A: real] :
( ( real_V453051771R_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(18,axiom,
! [A: set_a] :
( ( plus_plus_set_a @ A @ zero_zero_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add_Ocomm__neutral) ).
thf(359,plain,
! [A: set_a] :
( ( plus_plus_set_a @ A @ zero_zero_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(294,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add_Oleft__cancel) ).
thf(1218,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(114,axiom,
! [A: set_Pr147102617l_real] :
( ! [B: real,C: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer1247792113f_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_convex__ge__imp__conved) ).
thf(643,plain,
! [A: set_Pr147102617l_real] :
( ! [B: real,C: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer1247792113f_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(309,axiom,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1262,plain,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(301,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add_Oright__neutral) ).
thf(1235,plain,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(270,axiom,
! [A: real,B: product_prod_a_a,C: a] :
( ( real_V1538726831_a_a_a @ A @ ( produc2061588782_a_a_a @ B @ C ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_scaleR__Pair) ).
thf(1141,plain,
! [A: real,B: product_prod_a_a,C: a] :
( ( real_V1538726831_a_a_a @ A @ ( produc2061588782_a_a_a @ B @ C ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(117,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_zero__reorient) ).
thf(656,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(103,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_add__strict__increasing) ).
thf(613,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(295,axiom,
( zero_z950819678od_a_a
= ( product_Pair_a_a @ zero_zero_a @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_zero__prod__def) ).
thf(1221,plain,
( zero_z950819678od_a_a
= ( product_Pair_a_a @ zero_zero_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(98,axiom,
! [A: product_prod_a_real,B: product_prod_a_real,C: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= ( plus_p541014626a_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__left__cancel) ).
thf(600,plain,
! [A: product_prod_a_real,B: product_prod_a_real,C: product_prod_a_real] :
( ( ( plus_p541014626a_real @ A @ B )
= ( plus_p541014626a_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(181,axiom,
! [A: set_real] :
( ( plus_plus_set_real @ A @ zero_zero_set_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add_Oright__neutral) ).
thf(864,plain,
! [A: set_real] :
( ( plus_plus_set_real @ A @ zero_zero_set_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(254,axiom,
! [A: real,B: a,C: real] :
( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_scale__cancel__right) ).
thf(1094,plain,
! [A: real,B: a,C: real] :
( ( ( real_V1035702895aleR_a @ A @ B )
= ( real_V1035702895aleR_a @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(48,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add_Oleft__cancel) ).
thf(446,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(185,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_add__left__imp__eq) ).
thf(876,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(55,axiom,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_double__zero__sym) ).
thf(465,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(107,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_eq__iff) ).
thf(627,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(83,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_scaleR__nonneg__nonneg) ).
thf(556,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( real_V453051771R_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(276,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__left__cancel) ).
thf(1157,plain,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(265,axiom,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ C ) @ ( real_V1035702895aleR_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_scaleR__left_Oadd) ).
thf(1126,plain,
! [A: real,B: real,C: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ C ) @ ( real_V1035702895aleR_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(258,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_prod__cases) ).
thf(1108,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(50,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= ( plus_p1505579230od_a_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add__right__cancel) ).
thf(450,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= ( plus_p1505579230od_a_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(251,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subsetD) ).
thf(1084,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(202,axiom,
( zero_z590476811l_real
= ( produc1926903988l_real @ zero_zero_real @ zero_z659284464l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_zero__prod__def) ).
thf(931,plain,
( zero_z590476811l_real
= ( produc1926903988l_real @ zero_zero_real @ zero_z659284464l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(79,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_ord__eq__le__subst) ).
thf(539,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(21,axiom,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ zero_z950819678od_a_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Oleft__neutral) ).
thf(368,plain,
! [A: product_prod_a_a] :
( ( plus_p1505579230od_a_a @ zero_z950819678od_a_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(174,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_zero__less__double__add__iff__zero__less__single__add) ).
thf(844,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(163,axiom,
! [A: set_Pr147102617l_real,B: real,C: real,D: real,E: real] :
( ( prefer1247792113f_real @ A )
=> ( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_weak__convexD) ).
thf(813,plain,
! [A: set_Pr147102617l_real,B: real,C: real,D: real,E: real] :
( ( prefer1247792113f_real @ A )
=> ( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ( ( ord_less_real @ zero_zero_real @ D )
=> ( ( ord_less_real @ zero_zero_real @ E )
=> ( ( ( plus_plus_real @ D @ E )
= one_one_real )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(213,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_add__mono__thms__linordered__field_I4_J) ).
thf(963,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(4,axiom,
! [A: produc957004601l_real] :
( ( zero_z659284464l_real = A )
= ( A = zero_z659284464l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_zero__reorient) ).
thf(319,plain,
! [A: produc957004601l_real] :
( ( zero_z659284464l_real = A )
= ( A = zero_z659284464l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(207,axiom,
( zero_z396988537od_a_a
= ( produc454550562od_a_a @ zero_zero_real @ zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_zero__prod__def) ).
thf(946,plain,
( zero_z396988537od_a_a
= ( produc454550562od_a_a @ zero_zero_real @ zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(109,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_scaleR__le__0__iff) ).
thf(632,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_eq_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_eq_real @ zero_zero_real @ B ) )
| ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(225,axiom,
! [A: set_real,B: set_set_real,C: set_real,D: set_set_real] :
( ( member_set_real @ A @ B )
=> ( ( member_set_real @ C @ D )
=> ( member_set_real @ ( plus_plus_set_real @ A @ C ) @ ( plus_p768704801t_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_set__plus__intro) ).
thf(995,plain,
! [A: set_real,B: set_set_real,C: set_real,D: set_set_real] :
( ( member_set_real @ A @ B )
=> ( ( member_set_real @ C @ D )
=> ( member_set_real @ ( plus_plus_set_real @ A @ C ) @ ( plus_p768704801t_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(94,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( plus_plus_real @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pth__9_I3_J) ).
thf(588,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( plus_plus_real @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(306,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ C @ D )
=> ( member_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_set__plus__intro) ).
thf(1253,plain,
! [A: a,B: set_a,C: a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ C @ D )
=> ( member_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(130,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add__right__cancel) ).
thf(699,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(87,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_linear) ).
thf(568,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(196,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= A )
= ( B = zero_z950819678od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__cancel__left__right) ).
thf(914,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( plus_p1505579230od_a_a @ A @ B )
= A )
= ( B = zero_z950819678od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(292,axiom,
! [A: real,B: real,C: a] :
( ( real_V1214981142real_a @ A @ ( product_Pair_real_a @ B @ C ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_scale__prod) ).
thf(1212,plain,
! [A: real,B: real,C: a] :
( ( real_V1214981142real_a @ A @ ( product_Pair_real_a @ B @ C ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(238,axiom,
! [A: real,B: a,C: a] :
( ( real_V543523736od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_scaleR__Pair) ).
thf(1045,plain,
! [A: real,B: a,C: a] :
( ( real_V543523736od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(170,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add__decreasing2) ).
thf(832,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(125,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_add__less__le__mono) ).
thf(684,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(315,plain,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(216,axiom,
! [A: real,B: real,C: real,D: real,E: real,F: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ C @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_pth__b_I4_J) ).
thf(967,plain,
! [A: real,B: real,C: real,D: real,E: real,F: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) )
= ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ C @ ( plus_plus_real @ ( real_V453051771R_real @ D @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(299,axiom,
! [A: real,B: a,C: a] :
( ( real_V543523736od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_scale__prod) ).
thf(1229,plain,
! [A: real,B: a,C: a] :
( ( real_V543523736od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(34,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_add__mono) ).
thf(405,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(182,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_add__left__cancel) ).
thf(867,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(99,axiom,
! [A: set_a,B: set_set_a,C: set_a,D: set_set_a] :
( ( member_set_a @ A @ B )
=> ( ( member_set_a @ C @ D )
=> ( member_set_a @ ( plus_plus_set_a @ A @ C ) @ ( plus_plus_set_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_set__plus__intro) ).
thf(603,plain,
! [A: set_a,B: set_set_a,C: set_a,D: set_set_a] :
( ( member_set_a @ A @ B )
=> ( ( member_set_a @ C @ D )
=> ( member_set_a @ ( plus_plus_set_a @ A @ C ) @ ( plus_plus_set_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(142,axiom,
~ ( ord_less_real @ one_one_real @ one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_less__numeral__extra_I4_J) ).
thf(735,plain,
~ ( ord_less_real @ one_one_real @ one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(255,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: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ( member449909584od_a_a @ E @ ( plus_p634297534od_a_a @ A @ C ) )
=> ( member449909584od_a_a @ E @ ( plus_p634297534od_a_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_set__plus__mono2__b) ).
thf(1097,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: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ( member449909584od_a_a @ E @ ( plus_p634297534od_a_a @ A @ C ) )
=> ( member449909584od_a_a @ E @ ( plus_p634297534od_a_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(171,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_add_Oassoc) ).
thf(835,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(12,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__cancel__right__left) ).
thf(341,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(161,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_double__add__less__zero__iff__single__add__less__zero) ).
thf(807,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(45,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_add__strict__right__mono) ).
thf(437,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(77,axiom,
! [A: real,B: real] :
( ( ( real_V453051771R_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_scale__eq__0__iff) ).
thf(532,plain,
! [A: real,B: real] :
( ( ( real_V453051771R_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(129,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Collect__cong) ).
thf(696,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(279,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le108336051od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_psubsetD) ).
thf(1165,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le108336051od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(159,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_ord__le__eq__subst) ).
thf(796,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(201,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pth__d) ).
thf(928,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(191,axiom,
! [A: set_Pr1741234931a_real] :
( ! [B: product_prod_a_real,C: product_prod_a_real] :
( ( member384820540a_real @ ( produc886678603a_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member384820540a_real @ ( produc886678603a_real @ ( plus_p541014626a_real @ ( real_V512797224a_real @ D @ B ) @ ( real_V512797224a_real @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer1113819806a_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_convex__ge__imp__conved) ).
thf(897,plain,
! [A: set_Pr1741234931a_real] :
( ! [B: product_prod_a_real,C: product_prod_a_real] :
( ( member384820540a_real @ ( produc886678603a_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member384820540a_real @ ( produc886678603a_real @ ( plus_p541014626a_real @ ( real_V512797224a_real @ D @ B ) @ ( real_V512797224a_real @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer1113819806a_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(58,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ B @ C ) @ ( real_V453051771R_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_scaleR__right__mono__neg) ).
thf(474,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ ( real_V453051771R_real @ B @ C ) @ ( real_V453051771R_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(150,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__decreasing) ).
thf(767,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(32,axiom,
( zero_z342251165l_real
= ( produc1175086478l_real @ zero_z659284464l_real @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_zero__prod__def) ).
thf(400,plain,
( zero_z342251165l_real
= ( produc1175086478l_real @ zero_z659284464l_real @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(287,axiom,
! [A: real,B: a,C: a] :
( ( real_V1035702895aleR_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_scaleR__add__right) ).
thf(1197,plain,
! [A: real,B: a,C: a] :
( ( real_V1035702895aleR_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(212,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__Collect__eq) ).
thf(960,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(110,axiom,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_le__numeral__extra_I3_J) ).
thf(635,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(106,axiom,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ zero_z705155042a_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_add_Oleft__neutral) ).
thf(624,plain,
! [A: product_prod_a_real] :
( ( plus_p541014626a_real @ zero_z705155042a_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(140,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_order__subst2) ).
thf(728,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(266,axiom,
! [A: real,B: a,C: product_prod_a_a] :
( ( real_V296206913od_a_a @ A @ ( produc1299253312od_a_a @ B @ C ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_scale__prod) ).
thf(1129,plain,
! [A: real,B: a,C: product_prod_a_a] :
( ( real_V296206913od_a_a @ A @ ( produc1299253312od_a_a @ B @ C ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(311,axiom,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_indifferent__imp__weak__pref_I1_J) ).
thf(1268,plain,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(233,axiom,
! [A: a,B: a,C: a,D: a] :
( ( A
= ( plus_plus_a @ B @ C ) )
=> ( ( plus_plus_a @ D @ A )
= ( plus_plus_a @ B @ ( plus_plus_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_group__cancel_Oadd2) ).
thf(1019,plain,
! [A: a,B: a,C: a,D: a] :
( ( A
= ( plus_plus_a @ B @ C ) )
=> ( ( plus_plus_a @ D @ A )
= ( plus_plus_a @ B @ ( plus_plus_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(53,axiom,
! [A: a,B: real,C: a,D: real] :
( ( ( product_Pair_a_real @ A @ B )
= ( product_Pair_a_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod_Oinject) ).
thf(459,plain,
! [A: a,B: real,C: a,D: real] :
( ( ( product_Pair_a_real @ A @ B )
= ( product_Pair_a_real @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(176,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_pth__c_I3_J) ).
thf(850,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ E ) )
= ( plus_plus_real @ ( real_V453051771R_real @ C @ D ) @ ( plus_plus_real @ ( real_V453051771R_real @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(228,axiom,
! [A: real,B: real,C: a] :
( ( real_V1214981142real_a @ A @ ( product_Pair_real_a @ B @ C ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_scaleR__Pair) ).
thf(1004,plain,
! [A: real,B: real,C: a] :
( ( real_V1214981142real_a @ A @ ( product_Pair_real_a @ B @ C ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ A @ B ) @ ( real_V1035702895aleR_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(263,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mem__Collect__eq) ).
thf(1120,plain,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(194,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_add__mono__thms__linordered__field_I2_J) ).
thf(908,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(224,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_add__strict__mono) ).
thf(992,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(5,axiom,
! [A: real,B: product_prod_a_a,C: product_prod_a_a] :
( ( real_V368978776od_a_a @ A @ ( produc1474507607od_a_a @ B @ C ) )
= ( produc1474507607od_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_scaleR__Pair) ).
thf(322,plain,
! [A: real,B: product_prod_a_a,C: product_prod_a_a] :
( ( real_V368978776od_a_a @ A @ ( produc1474507607od_a_a @ B @ C ) )
= ( produc1474507607od_a_a @ ( real_V543523736od_a_a @ A @ B ) @ ( real_V543523736od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(118,axiom,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a,C: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( plus_p1505579230od_a_a @ ( real_V543523736od_a_a @ D @ B ) @ ( real_V543523736od_a_a @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer225425826od_a_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_convex__ge__imp__conved) ).
thf(659,plain,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a,C: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_eq_real @ zero_zero_real @ D )
& ( ord_less_eq_real @ zero_zero_real @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( plus_p1505579230od_a_a @ ( real_V543523736od_a_a @ D @ B ) @ ( real_V543523736od_a_a @ E @ C ) ) @ C ) @ A ) ) )
=> ( prefer225425826od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(153,axiom,
( prefer1247792113f_real
= ( ^ [A: set_Pr147102617l_real] :
! [B: real,C: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_real @ zero_zero_real @ D )
& ( ord_less_real @ zero_zero_real @ E ) )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_weak__convex__pref__def) ).
thf(775,plain,
( prefer1247792113f_real
= ( ^ [A: set_Pr147102617l_real] :
! [B: real,C: real] :
( ( member1068169442l_real @ ( produc705216881l_real @ B @ C ) @ A )
=> ! [D: real,E: real] :
( ( ( ( plus_plus_real @ D @ E )
= one_one_real )
& ( ord_less_real @ zero_zero_real @ D )
& ( ord_less_real @ zero_zero_real @ E ) )
=> ( member1068169442l_real @ ( produc705216881l_real @ ( plus_plus_real @ ( real_V453051771R_real @ D @ B ) @ ( real_V453051771R_real @ E @ C ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(122,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ B @ C ) )
& ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_scaleR__le__cancel__left) ).
thf(676,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( real_V453051771R_real @ A @ B ) @ ( real_V453051771R_real @ A @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ B @ C ) )
& ( ( ord_less_real @ A @ zero_zero_real )
=> ( ord_less_eq_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(187,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__cancel__left__left) ).
thf(882,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(65,axiom,
! [A: real] :
( ( real_V453051771R_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pth__4_I2_J) ).
thf(496,plain,
! [A: real] :
( ( real_V453051771R_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(246,axiom,
! [A: set_real,B: a,C: set_real,D: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ A @ B ) @ ( produc617496131real_a @ C @ D ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__Pair) ).
thf(1069,plain,
! [A: set_real,B: a,C: set_real,D: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ A @ B ) @ ( produc617496131real_a @ C @ D ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1389,plain,
$false,
inference(cvc4,[status(thm)],[892,629,1024,1168,1105,347,518,468,1179,777,666,481,365,1190,333,1031,1200,379,440,597,861,408,977,523,582,873,449,1078,385,550,715,1275,1063,829,1001,1243,709,885,1265,841,417,724,570,785,504,838,344,1132,917,702,817,559,1087,870,606,770,325,316,1100,1232,638,853,756,591,443,376,1151,821,905,353,966,981,1215,692,1119,998,411,428,507,397,687,1072,453,1206,512,529,793,925,761,810,1057,1163,1042,1123,1174,820,1238,957,1223,493,456,974,1012,847,566,484,1111,725,610,499,989,1270,1259,650,948,1138,356,783,420,1160,933,753,669,1075,526,547,706,328,471,679,1039,970,1114,515,984,721,1246,371,1060,1050,718,888,1135,965,1146,1273,573,1154,423,1007,402,732,772,826,579,1256,562,904,641,391,936,382,611,335,1090,1224,350,672,919,804,764,1194,1209,681,1117,1011,1048,362,1144,737,616,509,880,434,477,387,758,858,535,594,621,520,1149,943,330,462,636,1066,780,1015,1250,431,653,922,912,1171,394,986,490,426,1203,374,487,1081,939,553,823,712,855,690,1225,414,954,739,1053,1186,585,338,576,951,359,1218,643,1262,1235,1141,656,613,1221,600,864,1094,446,876,465,627,556,1157,1126,1108,450,1084,931,539,368,844,813,963,319,946,632,995,588,1253,699,568,914,1212,1045,832,684,315,967,1229,405,867,603,735,1097,835,341,807,437,532,696,1165,796,928,897,474,767,400,1197,960,635,624,728,1129,1268,1019,459,850,1004,1120,908,992,322,659,775,676,882,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ITP156^1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon May 6 14:32:24 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.71/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/0.97 % [INFO] Parsing done (234ms).
% 1.39/0.98 % [INFO] Running in sequential loop mode.
% 2.07/1.18 % [INFO] eprover registered as external prover.
% 2.07/1.19 % [INFO] cvc4 registered as external prover.
% 2.07/1.19 % [INFO] Scanning for conjecture ...
% 2.26/1.28 % [INFO] Found a conjecture and 353 axioms. Running axiom selection ...
% 2.72/1.37 % [INFO] Axiom selection finished. Selected 312 axioms (removed 41 axioms).
% 3.04/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 3.34/1.54 % [INFO] Type checking passed.
% 3.34/1.54 % [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 ...
% 14.47/4.31 % External prover 'cvc4' found a proof!
% 14.47/4.31 % [INFO] Killing All external provers ...
% 14.47/4.31 % Time passed: 3899ms (effective reasoning time: 3326ms)
% 14.47/4.31 % 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)>
% 14.47/4.31 % Axioms used in derivation (312): fact_223_pth__8, fact_104_add_Oleft__neutral, fact_281_add__less__cancel__right, fact_72_add__cancel__right__right, fact_77_add__cancel__right__left, fact_34_add__Pair, fact_285_less__add__same__cancel1, fact_191_pth__7_I1_J, fact_232_pth__b_I4_J, fact_169_add__mono__thms__linordered__semiring_I2_J, fact_263_scaleR__right__mono, fact_135_add__nonpos__nonpos, fact_45_old_Oprod_Oinject, fact_352_order__class_Oorder_Oeq__iff, fact_221_surj__pair, fact_73_add__cancel__right__left, fact_293_add__strict__mono, fact_62_add__right__cancel, fact_307_add__mono1, fact_225_pth__c_I1_J, fact_265_scaleR__left__mono, fact_96_add_Oright__neutral, fact_211_group__cancel_Oadd2, fact_313_add__nonneg__pos, fact_117_zero__reorient, fact_55_add__left__cancel, fact_24_scale__prod, fact_21_scale__prod, fact_161_add__right__mono, fact_28_scale__prod, fact_78_add__cancel__left__right, fact_251_set__zero__plus2, fact_118_zero__reorient, fact_103_add_Oleft__neutral, fact_348_le__cases, fact_231_pth__b_I3_J, fact_255_scale__right__imp__eq, fact_22_scale__prod, fact_150_zero__prod__def, fact_349_order_Otrans, fact_15_scaleR__Pair, fact_159_add__le__imp__le__left, fact_326_weak__convexD, fact_237_scale__zero__left, fact_247_scale__zero__right, fact_59_add__right__cancel, fact_197_add_Oleft__commute, fact_30_add__Pair, fact_253_scale__left__commute, fact_61_add__right__cancel, fact_187_add_Ocomm__neutral, fact_258_scale__left__imp__eq, fact_147_zero__prod__def, fact_81_add__cancel__left__right, fact_217_old_Oprod_Oinducts, fact_130_Collect__mem__eq, fact_250_set__plus__mono2__b, fact_224_pth__6, fact_180_add_Ogroup__left__neutral, fact_310_add__strict__increasing, fact_303_pos__add__strict, fact_206_add_Oassoc, fact_40_prod_Oinject, fact_314_add__neg__nonpos, fact_39_prod_Oinject, fact_241_scaleR__one, fact_120_zero__reorient, fact_331_psubsetD, fact_176_convex__ge__imp__conved, fact_320_subset__eq, fact_333_le__numeral__extra_I3_J, fact_205_add_Oassoc, fact_214_add__mono__thms__linordered__semiring_I4_J, fact_311_add__pos__nonneg, fact_137_add__nonneg__nonneg, fact_328_weak__convex__pref__def, fact_248_split__scaleR__neg__le, fact_113_add__le__same__cancel2, fact_228_pth__c_I4_J, fact_270_scaleR__nonpos__nonneg, fact_284_add__less__same__cancel2, fact_239_scale__eq__0__iff, fact_54_set__plus__intro, fact_297_add__less__le__mono, fact_202_add_Oright__cancel, fact_306_not__one__less__zero, fact_196_add__left__imp__eq, fact_254_scale__right__imp__eq, fact_242_scale__cancel__left, fact_148_zero__prod__def, fact_286_less__add__same__cancel2, fact_86_add__cancel__left__left, fact_163_add__left__mono, fact_262_scaleR__add__left, fact_82_add__cancel__left__right, fact_257_scaleR__add__right, fact_275_zero__le__one, fact_246_scale__zero__right, fact_213_group__cancel_Oadd1, fact_244_scale__cancel__right, fact_318_scaleR__le__cancel__left, fact_155_zero__prod__def, fact_11_scaleR__Pair, fact_109_le__add__same__cancel2, fact_216_ab__semigroup__add__class_Oadd__ac_I1_J, fact_267_scaleR__mono_H, fact_289_add__less__imp__less__right, fact_165_add__mono, fact_342_ord__eq__le__subst, fact_304_add__less__zeroD, fact_268_scaleR__mono, fact_278_weak__convexI, fact_122_add__nonpos__eq__0__iff, fact_152_zero__prod__def, fact_131_Collect__cong, fact_23_scale__prod, fact_65_add__le__cancel__right, fact_16_scaleR__Pair, fact_48_set__plus__intro, fact_195_add__left__imp__eq, fact_189_comm__monoid__add__class_Oadd__0, fact_53_set__plus__intro, fact_98_add_Oleft__neutral, fact_236_scaleR__eq__iff, fact_87_add__cancel__left__left, fact_52_set__plus__intro, fact_12_scaleR__Pair, fact_100_add_Oleft__neutral, fact_29_add__Pair, fact_334_less__numeral__extra_I3_J, fact_128_Collect__mem__eq, fact_332_is__num__normalize_I1_J, fact_105_add_Oleft__neutral, fact_345_antisym, fact_309_add__strict__increasing2, fact_220_prod__cases, fact_44_old_Oprod_Oinject, fact_312_add__nonpos__neg, fact_143_add__increasing, fact_264_scaleR__right__mono__neg, fact_80_add__cancel__left__right, fact_37_add__Pair, fact_175_convex__ge__imp__conved, fact_42_prod_Oinject, fact_298_add__le__less__mono, fact_141_add__decreasing2, fact_38_add__Pair, fact_13_scaleR__Pair, fact_290_add__less__imp__less__left, fact_95_add_Oright__neutral, fact_271_scaleR__nonneg__nonpos, fact_89_double__zero, fact_340_order__subst1, fact_190_pth__d, fact_10_assms_I3_J, fact_347_eq__refl, fact_229_pth__b_I1_J, fact_200_add_Ocommute, fact_154_zero__prod__def, fact_296_add__mono__thms__linordered__field_I5_J, fact_288_zero__less__double__add__iff__zero__less__single__add, fact_269_scaleR__nonpos__nonpos, fact_76_add__cancel__right__left, fact_335_le__numeral__extra_I4_J, fact_302_add__pos__pos, fact_339_add__scaleR__degen, fact_83_add__cancel__left__left, fact_204_add_Oleft__cancel, fact_222_pth__a, fact_41_prod_Oinject, fact_316_scaleR__le__cancel__left__pos, fact_325_weak__convexD, fact_351_antisym__conv, fact_292_add__strict__left__mono, fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062, fact_171_add__mono__thms__linordered__semiring_I3_J, fact_36_add__Pair, fact_183_add_Ocomm__neutral, fact_341_order__subst2, fact_238_scale__zero__left, fact_173_pth__4_I1_J, fact_2_indifferent__imp__weak__pref_I1_J, fact_324_scaleR__le__0__iff, fact_174_convex__ge__imp__conved, fact_209_set__plus__elim, fact_26_scale__prod, fact_194_add__right__imp__eq, fact_287_double__add__less__zero__iff__single__add__less__zero, fact_343_ord__le__eq__subst, fact_234_pth__9_I2_J, fact_299_add__mono__thms__linordered__field_I3_J, fact_227_pth__c_I3_J, fact_235_scaleR__eq__iff, fact_1_indifferent__imp__weak__pref_I2_J, fact_199_add_Ocommute, fact_9_assms_I5_J, fact_203_add_Oleft__cancel, fact_157_add__le__imp__le__right, fact_60_add__right__cancel, fact_71_add__cancel__right__right, fact_256_scaleR__add__right, fact_99_add_Oleft__neutral, fact_185_add_Ocomm__neutral, fact_20_scale__prod, fact_186_add_Ocomm__neutral, fact_218_old_Oprod_Oexhaust, fact_56_add__left__cancel, fact_272_scaleR__nonneg__nonneg, fact_31_add__Pair, fact_68_add__cancel__right__right, fact_295_add__mono__thms__linordered__field_I2_J, fact_305_zero__less__one, fact_300_add__mono__thms__linordered__field_I4_J, fact_260_scaleR__left_Oadd, fact_126_mem__Collect__eq, fact_90_add_Oright__neutral, fact_282_add__less__cancel__left, fact_188_comm__monoid__add__class_Oadd__0, fact_97_add_Oright__neutral, fact_192_pth__4_I2_J, fact_116_one__reorient, fact_3_indiff__trans, fact_92_add_Oright__neutral, fact_133_add__nonneg__eq__0__iff, fact_70_add__cancel__right__right, fact_279_weak__convexI, fact_344_eq__iff, fact_91_add_Oright__neutral, fact_240_scale__eq__0__iff, fact_106_zero__le__double__add__iff__zero__le__single__add, fact_215_ab__semigroup__add__class_Oadd__ac_I1_J, fact_167_add__mono__thms__linordered__semiring_I1_J, fact_139_add__increasing2, fact_208_set__plus__elim, fact_252_set__zero__plus2, fact_7_u__0, fact_57_add__left__cancel, fact_146_zero__prod__def, fact_124_mem__Collect__eq, fact_4_strict__trans, fact_75_add__cancel__right__left, fact_43_old_Oprod_Oinject, fact_329_field__le__epsilon, fact_107_double__add__le__zero__iff__single__add__le__zero, fact_336_less__numeral__extra_I4_J, fact_207_set__plus__elim, fact_280_subsetI, fact_151_zero__prod__def, fact_88_double__zero__sym, fact_5_assms_I2_J, fact_149_zero__prod__def, fact_346_linear, fact_67_add__le__cancel__left, fact_226_pth__c_I2_J, fact_330_less__numeral__extra_I1_J, fact_266_scaleR__left__mono__neg, fact_291_add__strict__right__mono, fact_319_subset__iff, fact_243_scaleR__left__le__one__le, fact_276_zero__neq__one, fact_337_order__refl, fact_17_scaleR__Pair, fact_101_add_Oleft__neutral, fact_233_pth__9_I1_J, fact_178_add_Ogroup__left__neutral, fact_327_weak__convex__pref__def, fact_181_add_Ogroup__left__neutral, fact_93_add_Oright__neutral, fact_301_add__neg__neg, fact_119_zero__reorient, fact_193_add__right__imp__eq, fact_0_assms_I1_J, fact_201_add_Oright__cancel, fact_210_group__cancel_Oadd2, fact_46_old_Oprod_Oinject, fact_111_le__add__same__cancel1, fact_153_zero__prod__def, fact_322_in__mono, fact_115_add__le__same__cancel1, fact_230_pth__b_I2_J, fact_294_add__mono__thms__linordered__field_I1_J, fact_321_subsetD, fact_283_add__less__same__cancel1, fact_49_set__plus__intro, fact_274_not__one__le__zero, fact_33_add__Pair, fact_63_pth__9_I3_J, fact_19_scaleR__Pair, fact_323_zero__le__scaleR__iff, fact_85_add__cancel__left__left, fact_338_add__scaleR__degen, fact_50_set__plus__intro, fact_25_scale__prod, fact_145_add__decreasing, fact_35_add__Pair, fact_315_zero__less__two, fact_58_add__left__cancel, fact_198_add_Oleft__commute, fact_317_scaleR__le__cancel__left__neg, fact_8_assms_I4_J, fact_219_Pair__inject, fact_261_scaleR__add__left, fact_350_le__cases3, fact_259_scaleR__left_Oadd, fact_308_less__add__one, fact_177_convex__ge__imp__conved, fact_212_group__cancel_Oadd1, fact_14_scaleR__Pair, fact_249_split__scaleR__pos__le, fact_182_add_Ogroup__left__neutral, fact_245_scale__cancel__right, fact_51_set__plus__intro
% 14.47/4.31 % No. of inferences in proof: 628
% 14.47/4.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3899 ms resp. 3326 ms w/o parsing
% 15.59/4.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.59/4.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------