TSTP Solution File: ITP160^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP160^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 : Mon May 20 22:23:30 EDT 2024
% Result : Theorem 29.65s 8.97s
% Output : Refutation 30.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 696
% Syntax : Number of formulae : 851 ( 172 unt; 543 typ; 0 def)
% Number of atoms : 666 ( 262 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 3760 ( 50 ~; 0 |; 34 &;3346 @)
% ( 0 <=>; 330 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 188 ( 187 usr)
% Number of type conns : 2369 (2369 >; 0 *; 0 +; 0 <<)
% Number of symbols : 358 ( 356 usr; 6 con; 0-5 aty)
% Number of variables : 1190 ( 148 ^1008 !; 34 ?;1190 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1614046668nres_d_type,type,
set_Pr1614046668nres_d: $tType ).
thf(produc819780758nres_d_type,type,
produc819780758nres_d: $tType ).
thf(set_Pr1712866168nres_d_type,type,
set_Pr1712866168nres_d: $tType ).
thf(set_Pr1710101992nres_d_type,type,
set_Pr1710101992nres_d: $tType ).
thf(produc1834705330nres_d_type,type,
produc1834705330nres_d: $tType ).
thf(set_Pr613277282nres_d_type,type,
set_Pr613277282nres_d: $tType ).
thf(produc809931564nres_d_type,type,
produc809931564nres_d: $tType ).
thf(set_Pr642586912nres_d_type,type,
set_Pr642586912nres_d: $tType ).
thf(set_Pr1436380704nres_b_type,type,
set_Pr1436380704nres_b: $tType ).
thf(set_Pr794589344nres_d_type,type,
set_Pr794589344nres_d: $tType ).
thf(set_Pr1652381728nres_c_type,type,
set_Pr1652381728nres_c: $tType ).
thf(set_Pr1245537056nres_c_type,type,
set_Pr1245537056nres_c: $tType ).
thf(set_Pr24800800nres_d_type,type,
set_Pr24800800nres_d: $tType ).
thf(set_Pr2039330848nres_a_type,type,
set_Pr2039330848nres_a: $tType ).
thf(set_Pr818594592nres_b_type,type,
set_Pr818594592nres_b: $tType ).
thf(set_Pr882593184nres_c_type,type,
set_Pr882593184nres_c: $tType ).
thf(set_Pr1824526846nres_d_type,type,
set_Pr1824526846nres_d: $tType ).
thf(produc235099114nres_d_type,type,
produc235099114nres_d: $tType ).
thf(produc1869490410nres_b_type,type,
produc1869490410nres_b: $tType ).
thf(produc2007659370nres_d_type,type,
produc2007659370nres_d: $tType ).
thf(produc1545802474nres_c_type,type,
produc1545802474nres_c: $tType ).
thf(produc1811455466nres_c_type,type,
produc1811455466nres_c: $tType ).
thf(produc2043357418nres_d_type,type,
produc2043357418nres_d: $tType ).
thf(produc1298363114nres_a_type,type,
produc1298363114nres_a: $tType ).
thf(produc1530265066nres_b_type,type,
produc1530265066nres_b: $tType ).
thf(produc1581500522nres_c_type,type,
produc1581500522nres_c: $tType ).
thf(set_Pr1125433775_nat_o_type,type,
set_Pr1125433775_nat_o: $tType ).
thf(produc416848975_nat_o_type,type,
produc416848975_nat_o: $tType ).
thf(set_Pr1413987240nres_d_type,type,
set_Pr1413987240nres_d: $tType ).
thf(set_Pr584391464nres_c_type,type,
set_Pr584391464nres_c: $tType ).
thf(set_Pr2080238504nres_d_type,type,
set_Pr2080238504nres_d: $tType ).
thf(set_Pr1358127528nres_b_type,type,
set_Pr1358127528nres_b: $tType ).
thf(set_Pr1250642728nres_c_type,type,
set_Pr1250642728nres_c: $tType ).
thf(produc1479083634nres_d_type,type,
produc1479083634nres_d: $tType ).
thf(produc1716397554nres_c_type,type,
produc1716397554nres_c: $tType ).
thf(produc1677145714nres_d_type,type,
produc1677145714nres_d: $tType ).
thf(produc96971890nres_b_type,type,
produc96971890nres_b: $tType ).
thf(produc1914459634nres_c_type,type,
produc1914459634nres_c: $tType ).
thf(set_Pr1146978466nres_d_type,type,
set_Pr1146978466nres_d: $tType ).
thf(set_Pr1402127136nres_b_type,type,
set_Pr1402127136nres_b: $tType ).
thf(set_Pr451158306nres_d_type,type,
set_Pr451158306nres_d: $tType ).
thf(set_Pr57594146nres_c_type,type,
set_Pr57594146nres_c: $tType ).
thf(set_Pr181592673nres_c_type,type,
set_Pr181592673nres_c: $tType ).
thf(set_Pr797615136nres_d_type,type,
set_Pr797615136nres_d: $tType ).
thf(set_Pr436741343nres_a_type,type,
set_Pr436741343nres_a: $tType ).
thf(set_Pr1052763806nres_b_type,type,
set_Pr1052763806nres_b: $tType ).
thf(set_Pr404050976nres_c_type,type,
set_Pr404050976nres_c: $tType ).
thf(set_Pr1602564423_nat_o_type,type,
set_Pr1602564423_nat_o: $tType ).
thf(produc1757587562nres_d_type,type,
produc1757587562nres_d: $tType ).
thf(set_Pr1537816964nres_d_type,type,
set_Pr1537816964nres_d: $tType ).
thf(set_Pr1351316363_int_o_type,type,
set_Pr1351316363_int_o: $tType ).
thf(produc1616993579_int_o_type,type,
produc1616993579_int_o: $tType ).
thf(set_Pr766923865_nat_o_type,type,
set_Pr766923865_nat_o: $tType ).
thf(set_Pr1435428853_int_o_type,type,
set_Pr1435428853_int_o: $tType ).
thf(set_Pr42712642nres_b_type,type,
set_Pr42712642nres_b: $tType ).
thf(set_Pr119249666nres_d_type,type,
set_Pr119249666nres_d: $tType ).
thf(set_Pr1345535106nres_b_type,type,
set_Pr1345535106nres_b: $tType ).
thf(set_Pr1812169344nres_c_type,type,
set_Pr1812169344nres_c: $tType ).
thf(set_Pr890971136nres_a_type,type,
set_Pr890971136nres_a: $tType ).
thf(set_Pr1434142398nres_d_type,type,
set_Pr1434142398nres_d: $tType ).
thf(set_Pr512944190nres_b_type,type,
set_Pr512944190nres_b: $tType ).
thf(set_Pr979578428nres_c_type,type,
set_Pr979578428nres_c: $tType ).
thf(set_Pr409172028nres_c_type,type,
set_Pr409172028nres_c: $tType ).
thf(set_Pr589481214nres_d_type,type,
set_Pr589481214nres_d: $tType ).
thf(set_Pr1635457468nres_a_type,type,
set_Pr1635457468nres_a: $tType ).
thf(set_Pr1815766654nres_b_type,type,
set_Pr1815766654nres_b: $tType ).
thf(set_Pr134917244nres_c_type,type,
set_Pr134917244nres_c: $tType ).
thf(set_Pr1361202684nres_a_type,type,
set_Pr1361202684nres_a: $tType ).
thf(produc1314004473_nat_o_type,type,
produc1314004473_nat_o: $tType ).
thf(set_Pr524661639_nat_o_type,type,
set_Pr524661639_nat_o: $tType ).
thf(set_Pr1774281699_o_o_o_type,type,
set_Pr1774281699_o_o_o: $tType ).
thf(set_Pr37069423_o_c_c_type,type,
set_Pr37069423_o_c_c: $tType ).
thf(produc13679884nres_b_type,type,
produc13679884nres_b: $tType ).
thf(produc2052210762nres_c_type,type,
produc2052210762nres_c: $tType ).
thf(produc1484956106nres_a_type,type,
produc1484956106nres_a: $tType ).
thf(produc1943257992nres_d_type,type,
produc1943257992nres_d: $tType ).
thf(produc1376003336nres_b_type,type,
produc1376003336nres_b: $tType ).
thf(produc1106446854nres_c_type,type,
produc1106446854nres_c: $tType ).
thf(produc2103861704nres_d_type,type,
produc2103861704nres_d: $tType ).
thf(produc1536607048nres_b_type,type,
produc1536607048nres_b: $tType ).
thf(produc1267050566nres_c_type,type,
produc1267050566nres_c: $tType ).
thf(produc699795910nres_a_type,type,
produc699795910nres_a: $tType ).
thf(produc1174115751_nat_o_type,type,
produc1174115751_nat_o: $tType ).
thf(set_Pr1920786322nres_d_type,type,
set_Pr1920786322nres_d: $tType ).
thf(set_Pr1176961680nres_b_type,type,
set_Pr1176961680nres_b: $tType ).
thf(set_Pr1408729042nres_c_type,type,
set_Pr1408729042nres_c: $tType ).
thf(set_Pr664904400nres_a_type,type,
set_Pr664904400nres_a: $tType ).
thf(set_Pr1640496404nres_d_type,type,
set_Pr1640496404nres_d: $tType ).
thf(set_Pr194842259nres_c_type,type,
set_Pr194842259nres_c: $tType ).
thf(set_Pr896671762nres_b_type,type,
set_Pr896671762nres_b: $tType ).
thf(set_Pr1598501265nres_a_type,type,
set_Pr1598501265nres_a: $tType ).
thf(set_Pr426609621nres_d_type,type,
set_Pr426609621nres_d: $tType ).
thf(set_Pr1128439124nres_c_type,type,
set_Pr1128439124nres_c: $tType ).
thf(set_Pr1830268627nres_b_type,type,
set_Pr1830268627nres_b: $tType ).
thf(set_Pr384614482nres_a_type,type,
set_Pr384614482nres_a: $tType ).
thf(set_Pr1524520971nt_o_o_type,type,
set_Pr1524520971nt_o_o: $tType ).
thf(set_Pr1371175689_o_o_o_type,type,
set_Pr1371175689_o_o_o: $tType ).
thf(set_Pr68707591_o_o_o_type,type,
set_Pr68707591_o_o_o: $tType ).
thf(produc1410942426nres_b_type,type,
produc1410942426nres_b: $tType ).
thf(produc1565049884nres_c_type,type,
produc1565049884nres_c: $tType ).
thf(produc1433404954nres_a_type,type,
produc1433404954nres_a: $tType ).
thf(produc1719157342nres_d_type,type,
produc1719157342nres_d: $tType ).
thf(produc1587512412nres_b_type,type,
produc1587512412nres_b: $tType ).
thf(produc1741619870nres_c_type,type,
produc1741619870nres_c: $tType ).
thf(produc1609974940nres_a_type,type,
produc1609974940nres_a: $tType ).
thf(produc496448427nt_o_o_type,type,
produc496448427nt_o_o: $tType ).
thf(set_Pr807116335_c_c_c_type,type,
set_Pr807116335_c_c_c: $tType ).
thf(set_Pr1659864199_nat_o_type,type,
set_Pr1659864199_nat_o: $tType ).
thf(set_Pr1320171143_int_o_type,type,
set_Pr1320171143_int_o: $tType ).
thf(produc1039600167_o_o_o_type,type,
produc1039600167_o_o_o: $tType ).
thf(set_Pr46530663_o_c_c_type,type,
set_Pr46530663_o_c_c: $tType ).
thf(refine116648739nres_d_type,type,
refine116648739nres_d: $tType ).
thf(refine1696877731nres_b_type,type,
refine1696877731nres_b: $tType ).
thf(set_Pr2088790547_o_o_o_type,type,
set_Pr2088790547_o_o_o: $tType ).
thf(produc724473255_nat_o_type,type,
produc724473255_nat_o: $tType ).
thf(produc480790439_int_o_type,type,
produc480790439_int_o: $tType ).
thf(set_Pr2058424041at_o_o_type,type,
set_Pr2058424041at_o_o: $tType ).
thf(set_Pr1006121889nt_o_o_type,type,
set_Pr1006121889nt_o_o: $tType ).
thf(set_Pr1495585653nt_o_o_type,type,
set_Pr1495585653nt_o_o: $tType ).
thf(set_Pr1673989513_c_c_c_type,type,
set_Pr1673989513_c_c_c: $tType ).
thf(set_Pr1357842111at_nat_type,type,
set_Pr1357842111at_nat: $tType ).
thf(set_Pr1749533559at_int_type,type,
set_Pr1749533559at_int: $tType ).
thf(set_Pr1719254903nt_nat_type,type,
set_Pr1719254903nt_nat: $tType ).
thf(set_Pr2110946351nt_int_type,type,
set_Pr2110946351nt_int: $tType ).
thf(produc1839156403_o_o_o_type,type,
produc1839156403_o_o_o: $tType ).
thf(set_Pr1933985801_c_o_o_type,type,
set_Pr1933985801_c_o_o: $tType ).
thf(set_Pr1955643401_o_o_c_type,type,
set_Pr1955643401_o_o_c: $tType ).
thf(produc482595465at_o_o_type,type,
produc482595465at_o_o: $tType ).
thf(produc426758977nt_o_o_type,type,
produc426758977nt_o_o: $tType ).
thf(set_Pr618353415_o_o_o_type,type,
set_Pr618353415_o_o_o: $tType ).
thf(set_Pr933902153_nat_c_type,type,
set_Pr933902153_nat_c: $tType ).
thf(set_Pr1575377993_int_c_type,type,
set_Pr1575377993_int_c: $tType ).
thf(produc1281043295at_nat_type,type,
produc1281043295at_nat: $tType ).
thf(produc610583575at_int_type,type,
produc610583575at_int: $tType ).
thf(produc1389674519nt_nat_type,type,
produc1389674519nt_nat: $tType ).
thf(produc719214799nt_int_type,type,
produc719214799nt_int: $tType ).
thf(set_Pr310822599_nat_o_type,type,
set_Pr310822599_nat_o: $tType ).
thf(set_Pr94755271_int_o_type,type,
set_Pr94755271_int_o: $tType ).
thf(set_Pr343524935_o_nat_type,type,
set_Pr343524935_o_nat: $tType ).
thf(set_Pr1437791047_o_int_type,type,
set_Pr1437791047_o_int: $tType ).
thf(produc1838469673_c_o_o_type,type,
produc1838469673_c_o_o: $tType ).
thf(produc2056997417_o_o_c_type,type,
produc2056997417_o_o_c: $tType ).
thf(produc46704423_o_o_o_type,type,
produc46704423_o_o_o: $tType ).
thf(set_Pr1234209675_a_c_c_type,type,
set_Pr1234209675_a_c_c: $tType ).
thf(produc1144174441_nat_c_type,type,
produc1144174441_nat_c: $tType ).
thf(produc1769036905_int_c_type,type,
produc1769036905_int_c: $tType ).
thf(set_Pr709440729_a_o_c_type,type,
set_Pr709440729_a_o_c: $tType ).
thf(produc878596327_nat_o_type,type,
produc878596327_nat_o: $tType ).
thf(produc1620501479_int_o_type,type,
produc1620501479_int_o: $tType ).
thf(produc1991839847_o_nat_type,type,
produc1991839847_o_nat: $tType ).
thf(produc922271079_o_int_type,type,
produc922271079_o_int: $tType ).
thf(set_Pr934623755_o_o_o_type,type,
set_Pr934623755_o_o_o: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(set_Pr1858794777nt_int_type,type,
set_Pr1858794777nt_int: $tType ).
thf(product_prod_a_a_c_c_type,type,
product_prod_a_a_c_c: $tType ).
thf(product_prod_o_a_o_c_type,type,
product_prod_o_a_o_c: $tType ).
thf(product_prod_o_o_o_o_type,type,
product_prod_o_o_o_o: $tType ).
thf(refine449204144nres_d_type,type,
refine449204144nres_d: $tType ).
thf(refine440942639nres_c_type,type,
refine440942639nres_c: $tType ).
thf(refine432681134nres_b_type,type,
refine432681134nres_b: $tType ).
thf(refine424419629nres_a_type,type,
refine424419629nres_a: $tType ).
thf(set_Product_prod_d_d_type,type,
set_Product_prod_d_d: $tType ).
thf(set_Product_prod_d_b_type,type,
set_Product_prod_d_b: $tType ).
thf(set_Product_prod_c_c_type,type,
set_Product_prod_c_c: $tType ).
thf(set_Product_prod_c_a_type,type,
set_Product_prod_c_a: $tType ).
thf(set_Product_prod_b_d_type,type,
set_Product_prod_b_d: $tType ).
thf(set_Product_prod_b_c_type,type,
set_Product_prod_b_c: $tType ).
thf(set_Product_prod_b_b_type,type,
set_Product_prod_b_b: $tType ).
thf(set_Product_prod_b_a_type,type,
set_Product_prod_b_a: $tType ).
thf(set_Product_prod_a_d_type,type,
set_Product_prod_a_d: $tType ).
thf(set_Product_prod_a_c_type,type,
set_Product_prod_a_c: $tType ).
thf(set_Product_prod_a_b_type,type,
set_Product_prod_a_b: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(set_Product_prod_o_o_type,type,
set_Product_prod_o_o: $tType ).
thf(product_prod_b_d_type,type,
product_prod_b_d: $tType ).
thf(product_prod_a_c_type,type,
product_prod_a_c: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(autoref_annot_type,type,
autoref_annot: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(d_type,type,
d: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(autore867490625_o_c_c_type,type,
autore867490625_o_c_c: ( ( $o > $o ) > ( ( $o > $o ) > c ) > c ) > autoref_annot > ( $o > $o ) > ( ( $o > $o ) > c ) > c ).
thf(autore1290907938nres_b_type,type,
autore1290907938nres_b: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > autoref_annot > a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(autore1757597947_o_o_o_type,type,
autore1757597947_o_o_o: ( c > ( c > $o > $o ) > $o > $o ) > autoref_annot > c > ( c > $o > $o ) > $o > $o ).
thf(autore956520418nres_c_type,type,
autore956520418nres_c: ( c > ( c > refine440942639nres_c ) > refine440942639nres_c ) > autoref_annot > c > ( c > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore241567778nres_d_type,type,
autore241567778nres_d: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > autoref_annot > c > ( c > refine449204144nres_d ) > refine449204144nres_d ).
thf(autore1422848225_c_c_c_type,type,
autore1422848225_c_c_c: ( c > ( c > c ) > c ) > autoref_annot > c > ( c > c ) > c ).
thf(autore73061154nres_c_type,type,
autore73061154nres_c: ( d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > autoref_annot > d > ( d > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore1505592162nres_d_type,type,
autore1505592162nres_d: ( d > ( d > refine449204144nres_d ) > refine449204144nres_d ) > autoref_annot > d > ( d > refine449204144nres_d ) > refine449204144nres_d ).
thf(autoref_APP_o_o_c_c_type,type,
autoref_APP_o_o_c_c: ( ( ( $o > $o ) > c ) > c ) > ( ( $o > $o ) > c ) > c ).
thf(autore1733926270_o_c_c_type,type,
autore1733926270_o_c_c: ( ( $o > $o ) > ( ( $o > $o ) > c ) > c ) > ( $o > $o ) > ( ( $o > $o ) > c ) > c ).
thf(autoref_APP_o_o_a_type,type,
autoref_APP_o_o_a: ( ( $o > $o ) > a ) > ( $o > $o ) > a ).
thf(autoref_APP_o_o_c_type,type,
autoref_APP_o_o_c: ( ( $o > $o ) > c ) > ( $o > $o ) > c ).
thf(autore956252284nres_b_type,type,
autore956252284nres_b: ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(autore821920247_o_o_o_type,type,
autore821920247_o_o_o: ( ( c > $o > $o ) > $o > $o ) > ( c > $o > $o ) > $o > $o ).
thf(autore2084714426nres_c_type,type,
autore2084714426nres_c: ( ( c > refine440942639nres_c ) > refine440942639nres_c ) > ( c > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore1159379066nres_d_type,type,
autore1159379066nres_d: ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > ( c > refine449204144nres_d ) > refine449204144nres_d ).
thf(autoref_APP_c_c_c_type,type,
autoref_APP_c_c_c: ( ( c > c ) > c ) > ( c > c ) > c ).
thf(autore964129529nres_c_type,type,
autore964129529nres_c: ( ( d > refine440942639nres_c ) > refine440942639nres_c ) > ( d > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore38794169nres_d_type,type,
autore38794169nres_d: ( ( d > refine449204144nres_d ) > refine449204144nres_d ) > ( d > refine449204144nres_d ) > refine449204144nres_d ).
thf(autore781669463nres_b_type,type,
autore781669463nres_b: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(autoref_APP_a_o_o_type,type,
autoref_APP_a_o_o: ( a > $o > $o ) > a > $o > $o ).
thf(autore1382402919nres_a_type,type,
autore1382402919nres_a: ( a > refine424419629nres_a ) > a > refine424419629nres_a ).
thf(autore1390664424nres_b_type,type,
autore1390664424nres_b: ( a > refine432681134nres_b ) > a > refine432681134nres_b ).
thf(autoref_APP_a_a_type,type,
autoref_APP_a_a: ( a > a ) > a > a ).
thf(autore1669652584nres_a_type,type,
autore1669652584nres_a: ( b > refine424419629nres_a ) > b > refine424419629nres_a ).
thf(autore1677914089nres_b_type,type,
autore1677914089nres_b: ( b > refine432681134nres_b ) > b > refine432681134nres_b ).
thf(autore1554881264_o_o_o_type,type,
autore1554881264_o_o_o: ( c > ( c > $o > $o ) > $o > $o ) > c > ( c > $o > $o ) > $o > $o ).
thf(autore224164375nres_c_type,type,
autore224164375nres_c: ( c > ( c > refine440942639nres_c ) > refine440942639nres_c ) > c > ( c > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore430131799nres_d_type,type,
autore430131799nres_d: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > c > ( c > refine449204144nres_d ) > refine449204144nres_d ).
thf(autoref_APP_c_c_c_c_type,type,
autoref_APP_c_c_c_c: ( c > ( c > c ) > c ) > c > ( c > c ) > c ).
thf(autoref_APP_c_o_o_type,type,
autoref_APP_c_o_o: ( c > $o > $o ) > c > $o > $o ).
thf(autore1973425259nres_c_type,type,
autore1973425259nres_c: ( c > refine440942639nres_c ) > c > refine440942639nres_c ).
thf(autore1981686764nres_d_type,type,
autore1981686764nres_d: ( c > refine449204144nres_d ) > c > refine449204144nres_d ).
thf(autoref_APP_c_c_type,type,
autoref_APP_c_c: ( c > c ) > c > c ).
thf(autore1989911767nres_c_type,type,
autore1989911767nres_c: ( d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > d > ( d > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore48395543nres_d_type,type,
autore48395543nres_d: ( d > ( d > refine449204144nres_d ) > refine449204144nres_d ) > d > ( d > refine449204144nres_d ) > refine449204144nres_d ).
thf(autore113191276nres_c_type,type,
autore113191276nres_c: ( d > refine440942639nres_c ) > d > refine440942639nres_c ).
thf(autore121452781nres_d_type,type,
autore121452781nres_d: ( d > refine449204144nres_d ) > d > refine449204144nres_d ).
thf(autore971224502_o_c_c_type,type,
autore971224502_o_c_c: ( ( $o > $o ) > ( ( $o > $o ) > c ) > c ) > ( $o > $o ) > ( ( $o > $o ) > c ) > c ).
thf(autore906565869nres_b_type,type,
autore906565869nres_b: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(autore1861331824_o_o_o_type,type,
autore1861331824_o_o_o: ( c > ( c > $o > $o ) > $o > $o ) > c > ( c > $o > $o ) > $o > $o ).
thf(autore572178349nres_c_type,type,
autore572178349nres_c: ( c > ( c > refine440942639nres_c ) > refine440942639nres_c ) > c > ( c > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore2004709357nres_d_type,type,
autore2004709357nres_d: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > c > ( c > refine449204144nres_d ) > refine449204144nres_d ).
thf(autoref_OP_c_c_c_c_type,type,
autoref_OP_c_c_c_c: ( c > ( c > c ) > c ) > c > ( c > c ) > c ).
thf(autore1836202733nres_c_type,type,
autore1836202733nres_c: ( d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > d > ( d > refine440942639nres_c ) > refine440942639nres_c ).
thf(autore1121250093nres_d_type,type,
autore1121250093nres_d: ( d > ( d > refine449204144nres_d ) > refine449204144nres_d ) > d > ( d > refine449204144nres_d ) > refine449204144nres_d ).
thf(autore821969498_o_c_c_type,type,
autore821969498_o_c_c: set_Pr37069423_o_c_c > autoref_annot ).
thf(autore1424734926_o_o_o_type,type,
autore1424734926_o_o_o: set_Pr1774281699_o_o_o > autoref_annot ).
thf(autore1545784985nres_c_type,type,
autore1545784985nres_c: set_Pr1250642728nres_c > autoref_annot ).
thf(autore16598297nres_b_type,type,
autore16598297nres_b: set_Pr1358127528nres_b > autoref_annot ).
thf(autore349294361nres_d_type,type,
autore349294361nres_d: set_Pr2080238504nres_d > autoref_annot ).
thf(autore464253722_c_c_c_type,type,
autore464253722_c_c_c: set_Pr807116335_c_c_c > autoref_annot ).
thf(autore1683160729nres_c_type,type,
autore1683160729nres_c: set_Pr584391464nres_c > autoref_annot ).
thf(autore486670105nres_d_type,type,
autore486670105nres_d: set_Pr1413987240nres_d > autoref_annot ).
thf(autore1113312320RNAL_o_type,type,
autore1113312320RNAL_o: $o > $o ).
thf(autore233619284nres_b_type,type,
autore233619284nres_b: ( ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(autore1360171649nres_b_type,type,
autore1360171649nres_b: ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(autore1318775848nres_b_type,type,
autore1318775848nres_b: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(autore519998265nres_b_type,type,
autore519998265nres_b: ( a > refine432681134nres_b ) > ( a > refine432681134nres_b ) > $o ).
thf(autore1904863386L_EQ_a_type,type,
autore1904863386L_EQ_a: a > a > $o ).
thf(produc2068274457_o_o_c_type,type,
produc2068274457_o_o_c: ( ( $o > $o ) > a ) > ( ( $o > $o ) > c ) > produc2056997417_o_o_c ).
thf(produc1910095910nres_d_type,type,
produc1910095910nres_d: ( ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ) > ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > produc809931564nres_d ).
thf(produc2075136412nres_d_type,type,
produc2075136412nres_d: ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > produc1757587562nres_d ).
thf(product_Pair_o_o_o_o_type,type,
product_Pair_o_o_o_o: ( $o > $o ) > ( $o > $o ) > product_prod_o_o_o_o ).
thf(produc973126316nres_d_type,type,
produc973126316nres_d: ( refine1696877731nres_b > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ) > ( refine116648739nres_d > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > produc1834705330nres_d ).
thf(produc912866704nres_d_type,type,
produc912866704nres_d: ( refine424419629nres_a > ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( refine440942639nres_c > ( refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > ( c > refine449204144nres_d ) > refine449204144nres_d ) > produc819780758nres_d ).
thf(produc2073916516nres_c_type,type,
produc2073916516nres_c: ( refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ) > ( refine440942639nres_c > ( c > refine440942639nres_c ) > refine440942639nres_c ) > produc1581500522nres_c ).
thf(produc1992182244nres_b_type,type,
produc1992182244nres_b: ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > produc1530265066nres_b ).
thf(produc1066811108nres_a_type,type,
produc1066811108nres_a: ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ) > produc1298363114nres_a ).
thf(produc1576596708nres_d_type,type,
produc1576596708nres_d: ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > produc2043357418nres_d ).
thf(produc651225572nres_c_type,type,
produc651225572nres_c: ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( refine449204144nres_d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > produc1811455466nres_c ).
thf(produc385572580nres_c_type,type,
produc385572580nres_c: ( refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ) > ( refine449204144nres_d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > produc1545802474nres_c ).
thf(produc2035736420nres_d_type,type,
produc2035736420nres_d: ( refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ) > ( refine449204144nres_d > ( d > refine449204144nres_d ) > refine449204144nres_d ) > produc2007659370nres_d ).
thf(produc183923940nres_b_type,type,
produc183923940nres_b: ( refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > ( refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > produc1869490410nres_b ).
thf(produc1915822052nres_d_type,type,
produc1915822052nres_d: ( refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > ( refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > produc235099114nres_d ).
thf(produc1824358636nres_c_type,type,
produc1824358636nres_c: ( a > ( a > refine424419629nres_a ) > refine424419629nres_a ) > ( c > ( c > refine440942639nres_c ) > refine440942639nres_c ) > produc1914459634nres_c ).
thf(produc295171948nres_b_type,type,
produc295171948nres_b: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > produc96971890nres_b ).
thf(produc627868012nres_d_type,type,
produc627868012nres_d: ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > produc1677145714nres_d ).
thf(produc1393542937_c_o_o_type,type,
produc1393542937_c_o_o: ( a > $o > $o ) > ( c > $o > $o ) > produc1838469673_c_o_o ).
thf(produc278407104nres_a_type,type,
produc278407104nres_a: ( a > refine424419629nres_a ) > ( a > refine424419629nres_a ) > produc699795910nres_a ).
thf(produc1827604032nres_c_type,type,
produc1827604032nres_c: ( a > refine424419629nres_a ) > ( c > refine440942639nres_c ) > produc1267050566nres_c ).
thf(produc809128386nres_b_type,type,
produc809128386nres_b: ( a > refine432681134nres_b ) > ( a > refine432681134nres_b ) > produc1536607048nres_b ).
thf(produc210841666nres_d_type,type,
produc210841666nres_d: ( a > refine432681134nres_b ) > ( c > refine449204144nres_d ) > produc2103861704nres_d ).
thf(product_Pair_a_a_c_c_type,type,
product_Pair_a_a_c_c: ( a > a ) > ( c > c ) > product_prod_a_a_c_c ).
thf(produc1961734380nres_c_type,type,
produc1961734380nres_c: ( b > ( b > refine424419629nres_a ) > refine424419629nres_a ) > ( d > ( d > refine440942639nres_c ) > refine440942639nres_c ) > produc1716397554nres_c ).
thf(produc765243756nres_d_type,type,
produc765243756nres_d: ( b > ( b > refine432681134nres_b ) > refine432681134nres_b ) > ( d > ( d > refine449204144nres_d ) > refine449204144nres_d ) > produc1479083634nres_d ).
thf(produc316577664nres_c_type,type,
produc316577664nres_c: ( b > refine424419629nres_a ) > ( d > refine440942639nres_c ) > produc1106446854nres_c ).
thf(produc1445585666nres_b_type,type,
produc1445585666nres_b: ( b > refine432681134nres_b ) > ( b > refine432681134nres_b ) > produc1376003336nres_b ).
thf(produc847298946nres_d_type,type,
produc847298946nres_d: ( b > refine432681134nres_b ) > ( d > refine449204144nres_d ) > produc1943257992nres_d ).
thf(produc1063567300nres_a_type,type,
produc1063567300nres_a: ( c > refine440942639nres_c ) > ( a > refine424419629nres_a ) > produc1484956106nres_a ).
thf(produc465280580nres_c_type,type,
produc465280580nres_c: ( c > refine440942639nres_c ) > ( c > refine440942639nres_c ) > produc2052210762nres_c ).
thf(produc83262214nres_b_type,type,
produc83262214nres_b: ( d > refine449204144nres_d ) > ( b > refine432681134nres_b ) > produc13679884nres_b ).
thf(produc1136923598nres_a_type,type,
produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
thf(produc1153446608nres_c_type,type,
produc1153446608nres_c: refine424419629nres_a > refine440942639nres_c > produc1741619870nres_c ).
thf(produc2130641934nres_b_type,type,
produc2130641934nres_b: refine432681134nres_b > refine432681134nres_b > produc1587512412nres_b ).
thf(produc2147164944nres_d_type,type,
produc2147164944nres_d: refine432681134nres_b > refine449204144nres_d > produc1719157342nres_d ).
thf(produc960353612nres_a_type,type,
produc960353612nres_a: refine440942639nres_c > refine424419629nres_a > produc1433404954nres_a ).
thf(produc976876622nres_c_type,type,
produc976876622nres_c: refine440942639nres_c > refine440942639nres_c > produc1565049884nres_c ).
thf(produc1954071948nres_b_type,type,
produc1954071948nres_b: refine449204144nres_d > refine432681134nres_b > produc1410942426nres_b ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(product_Pair_a_c_type,type,
product_Pair_a_c: a > c > product_prod_a_c ).
thf(product_Pair_b_d_type,type,
product_Pair_b_d: b > d > product_prod_b_d ).
thf(refine2063221604TURN_a_type,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine2063221605TURN_b_type,type,
refine2063221605TURN_b: b > refine432681134nres_b ).
thf(refine2063221606TURN_c_type,type,
refine2063221606TURN_c: c > refine440942639nres_c ).
thf(refine2063221607TURN_d_type,type,
refine2063221607TURN_d: d > refine449204144nres_d ).
thf(refine1985319227es_b_b_type,type,
refine1985319227es_b_b: refine1696877731nres_b > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine1129534141es_d_d_type,type,
refine1129534141es_d_d: refine116648739nres_d > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ).
thf(refine436832838nd_a_a_type,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine436832839nd_a_b_type,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine1264602245nd_b_a_type,type,
refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine1264602246nd_b_b_type,type,
refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
thf(refine2092371654nd_c_c_type,type,
refine2092371654nd_c_c: refine440942639nres_c > ( c > refine440942639nres_c ) > refine440942639nres_c ).
thf(refine2092371655nd_c_d_type,type,
refine2092371655nd_c_d: refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d ).
thf(refine772657413nd_d_c_type,type,
refine772657413nd_d_c: refine449204144nres_d > ( d > refine440942639nres_c ) > refine440942639nres_c ).
thf(refine772657414nd_d_d_type,type,
refine772657414nd_d_d: refine449204144nres_d > ( d > refine449204144nres_d ) > refine449204144nres_d ).
thf(refine1711024813nres_d_type,type,
refine1711024813nres_d: set_Pr613277282nres_d > ( ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > $o ) > ( ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(refine1958703523nres_d_type,type,
refine1958703523nres_d: set_Pr797615136nres_d > ( ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(refine408412177nres_d_type,type,
refine408412177nres_d: set_Pr2080238504nres_d > ( ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o ) > ( a > ( a > refine432681134nres_b ) > refine432681134nres_b ) > $o ).
thf(refine746536475nres_d_type,type,
refine746536475nres_d: set_Pr589481214nres_d > ( ( c > refine449204144nres_d ) > $o ) > ( a > refine432681134nres_b ) > $o ).
thf(refine321891363sn_a_c_type,type,
refine321891363sn_a_c: set_Product_prod_a_c > ( c > $o ) > a > $o ).
thf(refine1535302424nres_d_type,type,
refine1535302424nres_d: set_Pr589481214nres_d > set_Pr1537816964nres_d ).
thf(refine737062558el_a_a_type,type,
refine737062558el_a_a: set_Product_prod_a_a > set_Pr384614482nres_a ).
thf(refine737062559el_a_b_type,type,
refine737062559el_a_b: set_Product_prod_a_b > set_Pr1830268627nres_b ).
thf(refine737062560el_a_c_type,type,
refine737062560el_a_c: set_Product_prod_a_c > set_Pr1128439124nres_c ).
thf(refine737062561el_a_d_type,type,
refine737062561el_a_d: set_Product_prod_a_d > set_Pr426609621nres_d ).
thf(refine1564831965el_b_a_type,type,
refine1564831965el_b_a: set_Product_prod_b_a > set_Pr1598501265nres_a ).
thf(refine1564831966el_b_b_type,type,
refine1564831966el_b_b: set_Product_prod_b_b > set_Pr896671762nres_b ).
thf(refine1564831967el_b_c_type,type,
refine1564831967el_b_c: set_Product_prod_b_c > set_Pr194842259nres_c ).
thf(refine1564831968el_b_d_type,type,
refine1564831968el_b_d: set_Product_prod_b_d > set_Pr1640496404nres_d ).
thf(refine245117724el_c_a_type,type,
refine245117724el_c_a: set_Product_prod_c_a > set_Pr664904400nres_a ).
thf(refine245117726el_c_c_type,type,
refine245117726el_c_c: set_Product_prod_c_c > set_Pr1408729042nres_c ).
thf(refine1072887132el_d_b_type,type,
refine1072887132el_d_b: set_Product_prod_d_b > set_Pr1176961680nres_b ).
thf(refine1072887134el_d_d_type,type,
refine1072887134el_d_d: set_Product_prod_d_d > set_Pr1920786322nres_d ).
thf(refine1437029927_bnd_a_type,type,
refine1437029927_bnd_a: $o > refine424419629nres_a > refine424419629nres_a ).
thf(refine1437029928_bnd_b_type,type,
refine1437029928_bnd_b: $o > refine432681134nres_b > refine432681134nres_b ).
thf(refine1437029929_bnd_c_type,type,
refine1437029929_bnd_c: $o > refine440942639nres_c > refine440942639nres_c ).
thf(refine1437029930_bnd_d_type,type,
refine1437029930_bnd_d: $o > refine449204144nres_d > refine449204144nres_d ).
thf(id_a_R351071993nres_b_type,type,
id_a_R351071993nres_b: set_Pr1815766654nres_b ).
thf(id_Ref1256934482nres_b_type,type,
id_Ref1256934482nres_b: set_Pr896671762nres_b ).
thf(id_a_type,type,
id_a: set_Product_prod_a_a ).
thf(fun_re1859931662_c_a_c_type,type,
fun_re1859931662_c_a_c: set_Pr1955643401_o_o_c > set_Product_prod_a_c > set_Pr46530663_o_c_c ).
thf(fun_re2071856555nres_d_type,type,
fun_re2071856555nres_d: set_Pr797615136nres_d > set_Pr1640496404nres_d > set_Pr1824526846nres_d ).
thf(fun_re1144975870_o_c_c_type,type,
fun_re1144975870_o_c_c: set_Pr934623755_o_o_o > set_Pr46530663_o_c_c > set_Pr37069423_o_c_c ).
thf(fun_rel_o_o_o_o_a_c_type,type,
fun_rel_o_o_o_o_a_c: set_Pr934623755_o_o_o > set_Product_prod_a_c > set_Pr1955643401_o_o_c ).
thf(fun_re692194867nres_d_type,type,
fun_re692194867nres_d: set_Pr24800800nres_d > set_Pr797615136nres_d > set_Pr1712866168nres_d ).
thf(fun_re2021699288_o_o_o_type,type,
fun_re2021699288_o_o_o: set_Pr1933985801_c_o_o > set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o ).
thf(fun_re1877185935nres_c_type,type,
fun_re1877185935nres_c: set_Pr134917244nres_c > set_Pr1128439124nres_c > set_Pr404050976nres_c ).
thf(fun_re1579405647nres_b_type,type,
fun_re1579405647nres_b: set_Pr1815766654nres_b > set_Pr896671762nres_b > set_Pr1052763806nres_b ).
thf(fun_re1140323340nres_a_type,type,
fun_re1140323340nres_a: set_Pr1635457468nres_a > set_Pr1598501265nres_a > set_Pr436741343nres_a ).
thf(fun_re1306413669nres_d_type,type,
fun_re1306413669nres_d: set_Pr589481214nres_d > set_Pr1824526846nres_d > set_Pr613277282nres_d ).
thf(fun_re1394577105nres_d_type,type,
fun_re1394577105nres_d: set_Pr589481214nres_d > set_Pr1640496404nres_d > set_Pr797615136nres_d ).
thf(fun_re955494798nres_c_type,type,
fun_re955494798nres_c: set_Pr409172028nres_c > set_Pr194842259nres_c > set_Pr181592673nres_c ).
thf(fun_rel_a_a_c_c_a_c_type,type,
fun_rel_a_a_c_c_a_c: set_Pr1234209675_a_c_c > set_Product_prod_a_c > set_Pr1673989513_c_c_c ).
thf(fun_re1366722255nres_c_type,type,
fun_re1366722255nres_c: set_Pr979578428nres_c > set_Pr1128439124nres_c > set_Pr57594146nres_c ).
thf(fun_re884113425nres_d_type,type,
fun_re884113425nres_d: set_Pr1434142398nres_d > set_Pr1640496404nres_d > set_Pr451158306nres_d ).
thf(fun_re1925572817nres_b_type,type,
fun_re1925572817nres_b: set_Pr1345535106nres_b > set_Pr1176961680nres_b > set_Pr1402127136nres_b ).
thf(fun_re1740744275nres_d_type,type,
fun_re1740744275nres_d: set_Pr119249666nres_d > set_Pr1920786322nres_d > set_Pr1146978466nres_d ).
thf(fun_re1732033515nres_d_type,type,
fun_re1732033515nres_d: set_Pr1537816964nres_d > set_Pr1824526846nres_d > set_Pr1710101992nres_d ).
thf(fun_re2045802267nres_b_type,type,
fun_re2045802267nres_b: set_Pr384614482nres_a > set_Pr1052763806nres_b > set_Pr818594592nres_b ).
thf(fun_re1904331357nres_a_type,type,
fun_re1904331357nres_a: set_Pr1830268627nres_b > set_Pr436741343nres_a > set_Pr2039330848nres_a ).
thf(fun_re1190106143nres_d_type,type,
fun_re1190106143nres_d: set_Pr1128439124nres_c > set_Pr1712866168nres_d > set_Pr1614046668nres_d ).
thf(fun_re1915547295nres_c_type,type,
fun_re1915547295nres_c: set_Pr1128439124nres_c > set_Pr404050976nres_c > set_Pr882593184nres_c ).
thf(fun_re439246495nres_d_type,type,
fun_re439246495nres_d: set_Pr1128439124nres_c > set_Pr797615136nres_d > set_Pr24800800nres_d ).
thf(fun_re297775585nres_c_type,type,
fun_re297775585nres_c: set_Pr426609621nres_d > set_Pr181592673nres_c > set_Pr1245537056nres_c ).
thf(fun_re816936095nres_c_type,type,
fun_re816936095nres_c: set_Pr1640496404nres_d > set_Pr57594146nres_c > set_Pr1652381728nres_c ).
thf(fun_re1488118943nres_d_type,type,
fun_re1488118943nres_d: set_Pr1640496404nres_d > set_Pr451158306nres_d > set_Pr794589344nres_d ).
thf(fun_re650017687nres_b_type,type,
fun_re650017687nres_b: set_Pr664904400nres_a > set_Pr1402127136nres_b > set_Pr1436380704nres_b ).
thf(fun_re1190945563nres_d_type,type,
fun_re1190945563nres_d: set_Pr1408729042nres_c > set_Pr1146978466nres_d > set_Pr642586912nres_d ).
thf(fun_re1165441639nres_b_type,type,
fun_re1165441639nres_b: set_Product_prod_a_a > set_Pr1052763806nres_b > set_Pr1358127528nres_b ).
thf(fun_re843975451nres_a_type,type,
fun_re843975451nres_a: set_Product_prod_a_a > set_Pr384614482nres_a > set_Pr1361202684nres_a ).
thf(fun_re1837693787nres_b_type,type,
fun_re1837693787nres_b: set_Product_prod_a_a > set_Pr896671762nres_b > set_Pr1815766654nres_b ).
thf(fun_re708847385nres_a_type,type,
fun_re708847385nres_a: set_Product_prod_a_b > set_Pr1598501265nres_a > set_Pr1635457468nres_a ).
thf(fun_re362844942_o_o_o_type,type,
fun_re362844942_o_o_o: set_Product_prod_a_c > set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o ).
thf(fun_re418666087nres_c_type,type,
fun_re418666087nres_c: set_Product_prod_a_c > set_Pr404050976nres_c > set_Pr1250642728nres_c ).
thf(fun_re1089848935nres_d_type,type,
fun_re1089848935nres_d: set_Product_prod_a_c > set_Pr797615136nres_d > set_Pr2080238504nres_d ).
thf(fun_re836380558_c_c_c_type,type,
fun_re836380558_c_c_c: set_Product_prod_a_c > set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c ).
thf(fun_rel_a_c_o_o_o_o_type,type,
fun_rel_a_c_o_o_o_o: set_Product_prod_a_c > set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o ).
thf(fun_re766812315nres_c_type,type,
fun_re766812315nres_c: set_Product_prod_a_c > set_Pr1128439124nres_c > set_Pr134917244nres_c ).
thf(fun_re1760530651nres_d_type,type,
fun_re1760530651nres_d: set_Product_prod_a_c > set_Pr1640496404nres_d > set_Pr589481214nres_d ).
thf(fun_rel_a_c_a_c_type,type,
fun_rel_a_c_a_c: set_Product_prod_a_c > set_Product_prod_a_c > set_Pr1234209675_a_c_c ).
thf(fun_re631684249nres_c_type,type,
fun_re631684249nres_c: set_Product_prod_a_d > set_Pr194842259nres_c > set_Pr409172028nres_c ).
thf(fun_re132614427nres_b_type,type,
fun_re132614427nres_b: set_Product_prod_b_b > set_Pr896671762nres_b > set_Pr512944190nres_b ).
thf(fun_re430551721nres_c_type,type,
fun_re430551721nres_c: set_Product_prod_b_d > set_Pr57594146nres_c > set_Pr584391464nres_c ).
thf(fun_re1101734569nres_d_type,type,
fun_re1101734569nres_d: set_Product_prod_b_d > set_Pr451158306nres_d > set_Pr1413987240nres_d ).
thf(fun_re1209216603nres_c_type,type,
fun_re1209216603nres_c: set_Product_prod_b_d > set_Pr1128439124nres_c > set_Pr979578428nres_c ).
thf(fun_re55451291nres_d_type,type,
fun_re55451291nres_d: set_Product_prod_b_d > set_Pr1640496404nres_d > set_Pr1434142398nres_d ).
thf(fun_re1645900187nres_a_type,type,
fun_re1645900187nres_a: set_Product_prod_c_a > set_Pr664904400nres_a > set_Pr890971136nres_a ).
thf(fun_re492134875nres_b_type,type,
fun_re492134875nres_b: set_Product_prod_c_a > set_Pr1176961680nres_b > set_Pr1345535106nres_b ).
thf(fun_re1568737051nres_c_type,type,
fun_re1568737051nres_c: set_Product_prod_c_c > set_Pr1408729042nres_c > set_Pr1812169344nres_c ).
thf(fun_re414971739nres_d_type,type,
fun_re414971739nres_d: set_Product_prod_c_c > set_Pr1920786322nres_d > set_Pr119249666nres_d ).
thf(fun_re934539163nres_b_type,type,
fun_re934539163nres_b: set_Product_prod_d_b > set_Pr1176961680nres_b > set_Pr42712642nres_b ).
thf(relAPP1562327022_o_c_c_type,type,
relAPP1562327022_o_c_c: ( set_Pr46530663_o_c_c > set_Pr37069423_o_c_c ) > set_Pr46530663_o_c_c > set_Pr37069423_o_c_c ).
thf(relAPP1388319497nres_d_type,type,
relAPP1388319497nres_d: ( set_Pr1824526846nres_d > set_Pr613277282nres_d ) > set_Pr1824526846nres_d > set_Pr613277282nres_d ).
thf(relAPP745136137nres_d_type,type,
relAPP745136137nres_d: ( set_Pr1824526846nres_d > set_Pr1710101992nres_d ) > set_Pr1824526846nres_d > set_Pr1710101992nres_d ).
thf(relAPP412764446_o_c_c_type,type,
relAPP412764446_o_c_c: ( set_Pr1955643401_o_o_c > set_Product_prod_a_c > set_Pr46530663_o_c_c ) > set_Pr1955643401_o_o_c > set_Product_prod_a_c > set_Pr46530663_o_c_c ).
thf(relAPP1095654971nres_d_type,type,
relAPP1095654971nres_d: ( set_Pr1712866168nres_d > set_Pr1614046668nres_d ) > set_Pr1712866168nres_d > set_Pr1614046668nres_d ).
thf(relAPP1723270664_o_o_o_type,type,
relAPP1723270664_o_o_o: ( set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o ) > set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o ).
thf(relAPP765626983nres_c_type,type,
relAPP765626983nres_c: ( set_Pr404050976nres_c > set_Pr882593184nres_c ) > set_Pr404050976nres_c > set_Pr882593184nres_c ).
thf(relAPP998488211nres_c_type,type,
relAPP998488211nres_c: ( set_Pr404050976nres_c > set_Pr1250642728nres_c ) > set_Pr404050976nres_c > set_Pr1250642728nres_c ).
thf(relAPP869047273nres_b_type,type,
relAPP869047273nres_b: ( set_Pr1052763806nres_b > set_Pr818594592nres_b ) > set_Pr1052763806nres_b > set_Pr818594592nres_b ).
thf(relAPP91071253nres_b_type,type,
relAPP91071253nres_b: ( set_Pr1052763806nres_b > set_Pr1358127528nres_b ) > set_Pr1052763806nres_b > set_Pr1358127528nres_b ).
thf(relAPP1102334824nres_a_type,type,
relAPP1102334824nres_a: ( set_Pr436741343nres_a > set_Pr2039330848nres_a ) > set_Pr436741343nres_a > set_Pr2039330848nres_a ).
thf(relAPP1953591565nres_d_type,type,
relAPP1953591565nres_d: ( set_Pr797615136nres_d > set_Pr1640496404nres_d > set_Pr1824526846nres_d ) > set_Pr797615136nres_d > set_Pr1640496404nres_d > set_Pr1824526846nres_d ).
thf(relAPP1659518317nres_d_type,type,
relAPP1659518317nres_d: ( set_Pr797615136nres_d > set_Pr1712866168nres_d ) > set_Pr797615136nres_d > set_Pr1712866168nres_d ).
thf(relAPP511982311nres_d_type,type,
relAPP511982311nres_d: ( set_Pr797615136nres_d > set_Pr24800800nres_d ) > set_Pr797615136nres_d > set_Pr24800800nres_d ).
thf(relAPP1354295571nres_d_type,type,
relAPP1354295571nres_d: ( set_Pr797615136nres_d > set_Pr2080238504nres_d ) > set_Pr797615136nres_d > set_Pr2080238504nres_d ).
thf(relAPP745269862nres_c_type,type,
relAPP745269862nres_c: ( set_Pr181592673nres_c > set_Pr1245537056nres_c ) > set_Pr181592673nres_c > set_Pr1245537056nres_c ).
thf(relAPP1804623572_c_c_c_type,type,
relAPP1804623572_c_c_c: ( set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c ) > set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c ).
thf(relAPP944912869nres_c_type,type,
relAPP944912869nres_c: ( set_Pr57594146nres_c > set_Pr1652381728nres_c ) > set_Pr57594146nres_c > set_Pr1652381728nres_c ).
thf(relAPP131141393nres_c_type,type,
relAPP131141393nres_c: ( set_Pr57594146nres_c > set_Pr584391464nres_c ) > set_Pr57594146nres_c > set_Pr584391464nres_c ).
thf(relAPP691268197nres_d_type,type,
relAPP691268197nres_d: ( set_Pr451158306nres_d > set_Pr794589344nres_d ) > set_Pr451158306nres_d > set_Pr794589344nres_d ).
thf(relAPP486948753nres_d_type,type,
relAPP486948753nres_d: ( set_Pr451158306nres_d > set_Pr1413987240nres_d ) > set_Pr451158306nres_d > set_Pr1413987240nres_d ).
thf(relAPP1077394663nres_b_type,type,
relAPP1077394663nres_b: ( set_Pr1402127136nres_b > set_Pr1436380704nres_b ) > set_Pr1402127136nres_b > set_Pr1436380704nres_b ).
thf(relAPP720329701nres_d_type,type,
relAPP720329701nres_d: ( set_Pr1146978466nres_d > set_Pr642586912nres_d ) > set_Pr1146978466nres_d > set_Pr642586912nres_d ).
thf(relAPP2129980178_o_c_c_type,type,
relAPP2129980178_o_c_c: ( set_Pr934623755_o_o_o > set_Pr46530663_o_c_c > set_Pr37069423_o_c_c ) > set_Pr934623755_o_o_o > set_Pr46530663_o_c_c > set_Pr37069423_o_c_c ).
thf(relAPP1750172554_o_o_c_type,type,
relAPP1750172554_o_o_c: ( set_Pr934623755_o_o_o > set_Product_prod_a_c > set_Pr1955643401_o_o_c ) > set_Pr934623755_o_o_o > set_Product_prod_a_c > set_Pr1955643401_o_o_c ).
thf(relAPP829628004_o_o_o_type,type,
relAPP829628004_o_o_o: ( set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o ) > set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o ).
thf(relAPP1525934692_c_o_o_type,type,
relAPP1525934692_c_o_o: ( set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o ) > set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o ).
thf(relAPP759382665nres_d_type,type,
relAPP759382665nres_d: ( set_Pr24800800nres_d > set_Pr797615136nres_d > set_Pr1712866168nres_d ) > set_Pr24800800nres_d > set_Pr797615136nres_d > set_Pr1712866168nres_d ).
thf(relAPP1210499902_o_o_o_type,type,
relAPP1210499902_o_o_o: ( set_Pr1933985801_c_o_o > set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o ) > set_Pr1933985801_c_o_o > set_Pr934623755_o_o_o > set_Pr1371175689_o_o_o ).
thf(relAPP483050597nres_c_type,type,
relAPP483050597nres_c: ( set_Pr134917244nres_c > set_Pr1128439124nres_c > set_Pr404050976nres_c ) > set_Pr134917244nres_c > set_Pr1128439124nres_c > set_Pr404050976nres_c ).
thf(relAPP1293188647nres_b_type,type,
relAPP1293188647nres_b: ( set_Pr1815766654nres_b > set_Pr896671762nres_b > set_Pr1052763806nres_b ) > set_Pr1815766654nres_b > set_Pr896671762nres_b > set_Pr1052763806nres_b ).
thf(relAPP811277159nres_a_type,type,
relAPP811277159nres_a: ( set_Pr1635457468nres_a > set_Pr1598501265nres_a > set_Pr436741343nres_a ) > set_Pr1635457468nres_a > set_Pr1598501265nres_a > set_Pr436741343nres_a ).
thf(relAPP1716516381nres_d_type,type,
relAPP1716516381nres_d: ( set_Pr589481214nres_d > set_Pr1824526846nres_d > set_Pr613277282nres_d ) > set_Pr589481214nres_d > set_Pr1824526846nres_d > set_Pr613277282nres_d ).
thf(relAPP98076839nres_d_type,type,
relAPP98076839nres_d: ( set_Pr589481214nres_d > set_Pr1640496404nres_d > set_Pr797615136nres_d ) > set_Pr589481214nres_d > set_Pr1640496404nres_d > set_Pr797615136nres_d ).
thf(relAPP1482036727nres_d_type,type,
relAPP1482036727nres_d: ( set_Pr589481214nres_d > set_Pr1537816964nres_d ) > set_Pr589481214nres_d > set_Pr1537816964nres_d ).
thf(relAPP1763648999nres_c_type,type,
relAPP1763648999nres_c: ( set_Pr409172028nres_c > set_Pr194842259nres_c > set_Pr181592673nres_c ) > set_Pr409172028nres_c > set_Pr194842259nres_c > set_Pr181592673nres_c ).
thf(relAPP981449866_c_c_c_type,type,
relAPP981449866_c_c_c: ( set_Pr1234209675_a_c_c > set_Product_prod_a_c > set_Pr1673989513_c_c_c ) > set_Pr1234209675_a_c_c > set_Product_prod_a_c > set_Pr1673989513_c_c_c ).
thf(relAPP1790450405nres_c_type,type,
relAPP1790450405nres_c: ( set_Pr979578428nres_c > set_Pr1128439124nres_c > set_Pr57594146nres_c ) > set_Pr979578428nres_c > set_Pr1128439124nres_c > set_Pr57594146nres_c ).
thf(relAPP1405476647nres_d_type,type,
relAPP1405476647nres_d: ( set_Pr1434142398nres_d > set_Pr1640496404nres_d > set_Pr451158306nres_d ) > set_Pr1434142398nres_d > set_Pr1640496404nres_d > set_Pr451158306nres_d ).
thf(relAPP38185259nres_b_type,type,
relAPP38185259nres_b: ( set_Pr1345535106nres_b > set_Pr1176961680nres_b > set_Pr1402127136nres_b ) > set_Pr1345535106nres_b > set_Pr1176961680nres_b > set_Pr1402127136nres_b ).
thf(relAPP990557099nres_d_type,type,
relAPP990557099nres_d: ( set_Pr119249666nres_d > set_Pr1920786322nres_d > set_Pr1146978466nres_d ) > set_Pr119249666nres_d > set_Pr1920786322nres_d > set_Pr1146978466nres_d ).
thf(relAPP1787540131nres_d_type,type,
relAPP1787540131nres_d: ( set_Pr1537816964nres_d > set_Pr1824526846nres_d > set_Pr1710101992nres_d ) > set_Pr1537816964nres_d > set_Pr1824526846nres_d > set_Pr1710101992nres_d ).
thf(relAPP1111247343nres_b_type,type,
relAPP1111247343nres_b: ( set_Pr384614482nres_a > set_Pr1052763806nres_b > set_Pr818594592nres_b ) > set_Pr384614482nres_a > set_Pr1052763806nres_b > set_Pr818594592nres_b ).
thf(relAPP907138281nres_a_type,type,
relAPP907138281nres_a: ( set_Pr384614482nres_a > set_Pr1361202684nres_a ) > set_Pr384614482nres_a > set_Pr1361202684nres_a ).
thf(relAPP1042385007nres_a_type,type,
relAPP1042385007nres_a: ( set_Pr1830268627nres_b > set_Pr436741343nres_a > set_Pr2039330848nres_a ) > set_Pr1830268627nres_b > set_Pr436741343nres_a > set_Pr2039330848nres_a ).
thf(relAPP422583323nres_d_type,type,
relAPP422583323nres_d: ( set_Pr1128439124nres_c > set_Pr1712866168nres_d > set_Pr1614046668nres_d ) > set_Pr1128439124nres_c > set_Pr1712866168nres_d > set_Pr1614046668nres_d ).
thf(relAPP177337967nres_c_type,type,
relAPP177337967nres_c: ( set_Pr1128439124nres_c > set_Pr404050976nres_c > set_Pr882593184nres_c ) > set_Pr1128439124nres_c > set_Pr404050976nres_c > set_Pr882593184nres_c ).
thf(relAPP1396672239nres_d_type,type,
relAPP1396672239nres_d: ( set_Pr1128439124nres_c > set_Pr797615136nres_d > set_Pr24800800nres_d ) > set_Pr1128439124nres_c > set_Pr797615136nres_d > set_Pr24800800nres_d ).
thf(relAPP1774615993nres_c_type,type,
relAPP1774615993nres_c: ( set_Pr1128439124nres_c > set_Pr404050976nres_c ) > set_Pr1128439124nres_c > set_Pr404050976nres_c ).
thf(relAPP489595641nres_c_type,type,
relAPP489595641nres_c: ( set_Pr1128439124nres_c > set_Pr57594146nres_c ) > set_Pr1128439124nres_c > set_Pr57594146nres_c ).
thf(relAPP2018433511nres_c_type,type,
relAPP2018433511nres_c: ( set_Pr1128439124nres_c > set_Pr134917244nres_c ) > set_Pr1128439124nres_c > set_Pr134917244nres_c ).
thf(relAPP1564590053nres_c_type,type,
relAPP1564590053nres_c: ( set_Pr1128439124nres_c > set_Pr979578428nres_c ) > set_Pr1128439124nres_c > set_Pr979578428nres_c ).
thf(relAPP1327809903nres_c_type,type,
relAPP1327809903nres_c: ( set_Pr426609621nres_d > set_Pr181592673nres_c > set_Pr1245537056nres_c ) > set_Pr426609621nres_d > set_Pr181592673nres_c > set_Pr1245537056nres_c ).
thf(relAPP919190011nres_a_type,type,
relAPP919190011nres_a: ( set_Pr1598501265nres_a > set_Pr436741343nres_a ) > set_Pr1598501265nres_a > set_Pr436741343nres_a ).
thf(relAPP587861290nres_a_type,type,
relAPP587861290nres_a: ( set_Pr1598501265nres_a > set_Pr1635457468nres_a ) > set_Pr1598501265nres_a > set_Pr1635457468nres_a ).
thf(relAPP2095637113nres_b_type,type,
relAPP2095637113nres_b: ( set_Pr896671762nres_b > set_Pr1052763806nres_b ) > set_Pr896671762nres_b > set_Pr1052763806nres_b ).
thf(relAPP1936960811nres_b_type,type,
relAPP1936960811nres_b: ( set_Pr896671762nres_b > set_Pr1815766654nres_b ) > set_Pr896671762nres_b > set_Pr1815766654nres_b ).
thf(relAPP1483117353nres_b_type,type,
relAPP1483117353nres_b: ( set_Pr896671762nres_b > set_Pr512944190nres_b ) > set_Pr896671762nres_b > set_Pr512944190nres_b ).
thf(relAPP1784890619nres_c_type,type,
relAPP1784890619nres_c: ( set_Pr194842259nres_c > set_Pr181592673nres_c ) > set_Pr194842259nres_c > set_Pr181592673nres_c ).
thf(relAPP1699156520nres_c_type,type,
relAPP1699156520nres_c: ( set_Pr194842259nres_c > set_Pr409172028nres_c ) > set_Pr194842259nres_c > set_Pr409172028nres_c ).
thf(relAPP492592111nres_c_type,type,
relAPP492592111nres_c: ( set_Pr1640496404nres_d > set_Pr57594146nres_c > set_Pr1652381728nres_c ) > set_Pr1640496404nres_d > set_Pr57594146nres_c > set_Pr1652381728nres_c ).
thf(relAPP1711926383nres_d_type,type,
relAPP1711926383nres_d: ( set_Pr1640496404nres_d > set_Pr451158306nres_d > set_Pr794589344nres_d ) > set_Pr1640496404nres_d > set_Pr451158306nres_d > set_Pr794589344nres_d ).
thf(relAPP1552964229nres_d_type,type,
relAPP1552964229nres_d: ( set_Pr1640496404nres_d > set_Pr1824526846nres_d ) > set_Pr1640496404nres_d > set_Pr1824526846nres_d ).
thf(relAPP813854073nres_d_type,type,
relAPP813854073nres_d: ( set_Pr1640496404nres_d > set_Pr797615136nres_d ) > set_Pr1640496404nres_d > set_Pr797615136nres_d ).
thf(relAPP1676317369nres_d_type,type,
relAPP1676317369nres_d: ( set_Pr1640496404nres_d > set_Pr451158306nres_d ) > set_Pr1640496404nres_d > set_Pr451158306nres_d ).
thf(relAPP900772393nres_d_type,type,
relAPP900772393nres_d: ( set_Pr1640496404nres_d > set_Pr589481214nres_d ) > set_Pr1640496404nres_d > set_Pr589481214nres_d ).
thf(relAPP446928935nres_d_type,type,
relAPP446928935nres_d: ( set_Pr1640496404nres_d > set_Pr1434142398nres_d ) > set_Pr1640496404nres_d > set_Pr1434142398nres_d ).
thf(relAPP1747515631nres_b_type,type,
relAPP1747515631nres_b: ( set_Pr664904400nres_a > set_Pr1402127136nres_b > set_Pr1436380704nres_b ) > set_Pr664904400nres_a > set_Pr1402127136nres_b > set_Pr1436380704nres_b ).
thf(relAPP947801195nres_a_type,type,
relAPP947801195nres_a: ( set_Pr664904400nres_a > set_Pr890971136nres_a ) > set_Pr664904400nres_a > set_Pr890971136nres_a ).
thf(relAPP2032940527nres_d_type,type,
relAPP2032940527nres_d: ( set_Pr1408729042nres_c > set_Pr1146978466nres_d > set_Pr642586912nres_d ) > set_Pr1408729042nres_c > set_Pr1146978466nres_d > set_Pr642586912nres_d ).
thf(relAPP2059096425nres_c_type,type,
relAPP2059096425nres_c: ( set_Pr1408729042nres_c > set_Pr1812169344nres_c ) > set_Pr1408729042nres_c > set_Pr1812169344nres_c ).
thf(relAPP1033339257nres_b_type,type,
relAPP1033339257nres_b: ( set_Pr1176961680nres_b > set_Pr1402127136nres_b ) > set_Pr1176961680nres_b > set_Pr1402127136nres_b ).
thf(relAPP1977623725nres_b_type,type,
relAPP1977623725nres_b: ( set_Pr1176961680nres_b > set_Pr1345535106nres_b ) > set_Pr1176961680nres_b > set_Pr1345535106nres_b ).
thf(relAPP1523780267nres_b_type,type,
relAPP1523780267nres_b: ( set_Pr1176961680nres_b > set_Pr42712642nres_b ) > set_Pr1176961680nres_b > set_Pr42712642nres_b ).
thf(relAPP1899039865nres_d_type,type,
relAPP1899039865nres_d: ( set_Pr1920786322nres_d > set_Pr1146978466nres_d ) > set_Pr1920786322nres_d > set_Pr1146978466nres_d ).
thf(relAPP941435307nres_d_type,type,
relAPP941435307nres_d: ( set_Pr1920786322nres_d > set_Pr119249666nres_d ) > set_Pr1920786322nres_d > set_Pr119249666nres_d ).
thf(relAPP1740535279nres_b_type,type,
relAPP1740535279nres_b: ( set_Product_prod_a_a > set_Pr1052763806nres_b > set_Pr1358127528nres_b ) > set_Product_prod_a_a > set_Pr1052763806nres_b > set_Pr1358127528nres_b ).
thf(relAPP439940547nres_a_type,type,
relAPP439940547nres_a: ( set_Product_prod_a_a > set_Pr384614482nres_a > set_Pr1361202684nres_a ) > set_Product_prod_a_a > set_Pr384614482nres_a > set_Pr1361202684nres_a ).
thf(relAPP1536875909nres_b_type,type,
relAPP1536875909nres_b: ( set_Product_prod_a_a > set_Pr896671762nres_b > set_Pr1815766654nres_b ) > set_Product_prod_a_a > set_Pr896671762nres_b > set_Pr1815766654nres_b ).
thf(relAPP1642956907nres_a_type,type,
relAPP1642956907nres_a: ( set_Product_prod_a_a > set_Pr384614482nres_a ) > set_Product_prod_a_a > set_Pr384614482nres_a ).
thf(relAPP456341443nres_a_type,type,
relAPP456341443nres_a: ( set_Product_prod_a_b > set_Pr1598501265nres_a > set_Pr1635457468nres_a ) > set_Product_prod_a_b > set_Pr1598501265nres_a > set_Pr1635457468nres_a ).
thf(relAPP11374829nres_b_type,type,
relAPP11374829nres_b: ( set_Product_prod_a_b > set_Pr1830268627nres_b ) > set_Product_prod_a_b > set_Pr1830268627nres_b ).
thf(relAPP913737114_o_o_o_type,type,
relAPP913737114_o_o_o: ( set_Product_prod_a_c > set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o ) > set_Product_prod_a_c > set_Pr1371175689_o_o_o > set_Pr1774281699_o_o_o ).
thf(relAPP1155943915nres_c_type,type,
relAPP1155943915nres_c: ( set_Product_prod_a_c > set_Pr404050976nres_c > set_Pr1250642728nres_c ) > set_Product_prod_a_c > set_Pr404050976nres_c > set_Pr1250642728nres_c ).
thf(relAPP1135042155nres_d_type,type,
relAPP1135042155nres_d: ( set_Product_prod_a_c > set_Pr797615136nres_d > set_Pr2080238504nres_d ) > set_Product_prod_a_c > set_Pr797615136nres_d > set_Pr2080238504nres_d ).
thf(relAPP1889825126_c_c_c_type,type,
relAPP1889825126_c_c_c: ( set_Product_prod_a_c > set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c ) > set_Product_prod_a_c > set_Pr1673989513_c_c_c > set_Pr807116335_c_c_c ).
thf(relAPP589338430_c_o_o_type,type,
relAPP589338430_c_o_o: ( set_Product_prod_a_c > set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o ) > set_Product_prod_a_c > set_Pr934623755_o_o_o > set_Pr1933985801_c_o_o ).
thf(relAPP173519167nres_c_type,type,
relAPP173519167nres_c: ( set_Product_prod_a_c > set_Pr1128439124nres_c > set_Pr134917244nres_c ) > set_Product_prod_a_c > set_Pr1128439124nres_c > set_Pr134917244nres_c ).
thf(relAPP1270454529nres_d_type,type,
relAPP1270454529nres_d: ( set_Product_prod_a_c > set_Pr1640496404nres_d > set_Pr589481214nres_d ) > set_Product_prod_a_c > set_Pr1640496404nres_d > set_Pr589481214nres_d ).
thf(relAPP887115074_a_c_c_type,type,
relAPP887115074_a_c_c: ( set_Product_prod_a_c > set_Product_prod_a_c > set_Pr1234209675_a_c_c ) > set_Product_prod_a_c > set_Product_prod_a_c > set_Pr1234209675_a_c_c ).
thf(relAPP1774770060_o_c_c_type,type,
relAPP1774770060_o_c_c: ( set_Product_prod_a_c > set_Pr46530663_o_c_c ) > set_Product_prod_a_c > set_Pr46530663_o_c_c ).
thf(relAPP970620078_o_o_c_type,type,
relAPP970620078_o_o_c: ( set_Product_prod_a_c > set_Pr1955643401_o_o_c ) > set_Product_prod_a_c > set_Pr1955643401_o_o_c ).
thf(relAPP1311785006_c_c_c_type,type,
relAPP1311785006_c_c_c: ( set_Product_prod_a_c > set_Pr1673989513_c_c_c ) > set_Product_prod_a_c > set_Pr1673989513_c_c_c ).
thf(relAPP237429680_a_c_c_type,type,
relAPP237429680_a_c_c: ( set_Product_prod_a_c > set_Pr1234209675_a_c_c ) > set_Product_prod_a_c > set_Pr1234209675_a_c_c ).
thf(relAPP527276399nres_c_type,type,
relAPP527276399nres_c: ( set_Product_prod_a_c > set_Pr1128439124nres_c ) > set_Product_prod_a_c > set_Pr1128439124nres_c ).
thf(relAPP189920063nres_c_type,type,
relAPP189920063nres_c: ( set_Product_prod_a_d > set_Pr194842259nres_c > set_Pr409172028nres_c ) > set_Product_prod_a_d > set_Pr194842259nres_c > set_Pr409172028nres_c ).
thf(relAPP1043177969nres_d_type,type,
relAPP1043177969nres_d: ( set_Product_prod_a_d > set_Pr426609621nres_d ) > set_Product_prod_a_d > set_Pr426609621nres_d ).
thf(relAPP1912873449nres_a_type,type,
relAPP1912873449nres_a: ( set_Product_prod_b_a > set_Pr1598501265nres_a ) > set_Product_prod_b_a > set_Pr1598501265nres_a ).
thf(relAPP2073227843nres_b_type,type,
relAPP2073227843nres_b: ( set_Product_prod_b_b > set_Pr896671762nres_b > set_Pr512944190nres_b ) > set_Product_prod_b_b > set_Pr896671762nres_b > set_Pr512944190nres_b ).
thf(relAPP281291371nres_b_type,type,
relAPP281291371nres_b: ( set_Product_prod_b_b > set_Pr896671762nres_b ) > set_Product_prod_b_b > set_Pr896671762nres_b ).
thf(relAPP797192941nres_c_type,type,
relAPP797192941nres_c: ( set_Product_prod_b_c > set_Pr194842259nres_c ) > set_Product_prod_b_c > set_Pr194842259nres_c ).
thf(relAPP2017502121nres_c_type,type,
relAPP2017502121nres_c: ( set_Product_prod_b_d > set_Pr57594146nres_c > set_Pr584391464nres_c ) > set_Product_prod_b_d > set_Pr57594146nres_c > set_Pr584391464nres_c ).
thf(relAPP1996600361nres_d_type,type,
relAPP1996600361nres_d: ( set_Product_prod_b_d > set_Pr451158306nres_d > set_Pr1413987240nres_d ) > set_Product_prod_b_d > set_Pr451158306nres_d > set_Pr1413987240nres_d ).
thf(relAPP709871101nres_c_type,type,
relAPP709871101nres_c: ( set_Product_prod_b_d > set_Pr1128439124nres_c > set_Pr979578428nres_c ) > set_Product_prod_b_d > set_Pr1128439124nres_c > set_Pr979578428nres_c ).
thf(relAPP1806806463nres_d_type,type,
relAPP1806806463nres_d: ( set_Product_prod_b_d > set_Pr1640496404nres_d > set_Pr1434142398nres_d ) > set_Product_prod_b_d > set_Pr1640496404nres_d > set_Pr1434142398nres_d ).
thf(relAPP1313094511nres_d_type,type,
relAPP1313094511nres_d: ( set_Product_prod_b_d > set_Pr1640496404nres_d ) > set_Product_prod_b_d > set_Pr1640496404nres_d ).
thf(relAPP1825452871nres_a_type,type,
relAPP1825452871nres_a: ( set_Product_prod_c_a > set_Pr664904400nres_a > set_Pr890971136nres_a ) > set_Product_prod_c_a > set_Pr664904400nres_a > set_Pr890971136nres_a ).
thf(relAPP774904585nres_b_type,type,
relAPP774904585nres_b: ( set_Product_prod_c_a > set_Pr1176961680nres_b > set_Pr1345535106nres_b ) > set_Product_prod_c_a > set_Pr1176961680nres_b > set_Pr1345535106nres_b ).
thf(relAPP35306343nres_a_type,type,
relAPP35306343nres_a: ( set_Product_prod_c_a > set_Pr664904400nres_a ) > set_Product_prod_c_a > set_Pr664904400nres_a ).
thf(relAPP1559031491nres_c_type,type,
relAPP1559031491nres_c: ( set_Product_prod_c_c > set_Pr1408729042nres_c > set_Pr1812169344nres_c ) > set_Product_prod_c_c > set_Pr1408729042nres_c > set_Pr1812169344nres_c ).
thf(relAPP508483205nres_d_type,type,
relAPP508483205nres_d: ( set_Product_prod_c_c > set_Pr1920786322nres_d > set_Pr119249666nres_d ) > set_Product_prod_c_c > set_Pr1920786322nres_d > set_Pr119249666nres_d ).
thf(relAPP1067109483nres_c_type,type,
relAPP1067109483nres_c: ( set_Product_prod_c_c > set_Pr1408729042nres_c ) > set_Product_prod_c_c > set_Pr1408729042nres_c ).
thf(relAPP1311256519nres_b_type,type,
relAPP1311256519nres_b: ( set_Product_prod_d_b > set_Pr1176961680nres_b > set_Pr42712642nres_b ) > set_Product_prod_d_b > set_Pr1176961680nres_b > set_Pr42712642nres_b ).
thf(relAPP821124455nres_b_type,type,
relAPP821124455nres_b: ( set_Product_prod_d_b > set_Pr1176961680nres_b ) > set_Product_prod_d_b > set_Pr1176961680nres_b ).
thf(relAPP1852927595nres_d_type,type,
relAPP1852927595nres_d: ( set_Product_prod_d_d > set_Pr1920786322nres_d ) > set_Product_prod_d_d > set_Pr1920786322nres_d ).
thf(collec1321668993nres_d_type,type,
collec1321668993nres_d: ( produc809931564nres_d > $o ) > set_Pr613277282nres_d ).
thf(collec1671161663nres_d_type,type,
collec1671161663nres_d: ( produc1757587562nres_d > $o ) > set_Pr797615136nres_d ).
thf(collec554837959nres_d_type,type,
collec554837959nres_d: ( produc1677145714nres_d > $o ) > set_Pr2080238504nres_d ).
thf(collec1639315997nres_d_type,type,
collec1639315997nres_d: ( produc2103861704nres_d > $o ) > set_Pr589481214nres_d ).
thf(collec662378644od_a_c_type,type,
collec662378644od_a_c: ( product_prod_a_c > $o ) > set_Product_prod_a_c ).
thf(member1270020946_o_o_c_type,type,
member1270020946_o_o_c: produc2056997417_o_o_c > set_Pr1955643401_o_o_c > $o ).
thf(member660096835nres_d_type,type,
member660096835nres_d: produc809931564nres_d > set_Pr613277282nres_d > $o ).
thf(member461830657nres_d_type,type,
member461830657nres_d: produc1757587562nres_d > set_Pr797615136nres_d > $o ).
thf(member250723412_o_o_o_type,type,
member250723412_o_o_o: product_prod_o_o_o_o > set_Pr934623755_o_o_o > $o ).
thf(member449974729nres_d_type,type,
member449974729nres_d: produc1834705330nres_d > set_Pr1710101992nres_d > $o ).
thf(member508530605nres_d_type,type,
member508530605nres_d: produc819780758nres_d > set_Pr1614046668nres_d > $o ).
thf(member1751415169nres_c_type,type,
member1751415169nres_c: produc1581500522nres_c > set_Pr882593184nres_c > $o ).
thf(member1700179713nres_b_type,type,
member1700179713nres_b: produc1530265066nres_b > set_Pr818594592nres_b > $o ).
thf(member1468277761nres_a_type,type,
member1468277761nres_a: produc1298363114nres_a > set_Pr2039330848nres_a > $o ).
thf(member65788417nres_d_type,type,
member65788417nres_d: produc2043357418nres_d > set_Pr24800800nres_d > $o ).
thf(member1981370113nres_c_type,type,
member1981370113nres_c: produc1811455466nres_c > set_Pr1245537056nres_c > $o ).
thf(member1715717121nres_c_type,type,
member1715717121nres_c: produc1545802474nres_c > set_Pr1652381728nres_c > $o ).
thf(member30090369nres_d_type,type,
member30090369nres_d: produc2007659370nres_d > set_Pr794589344nres_d > $o ).
thf(member2039405057nres_b_type,type,
member2039405057nres_b: produc1869490410nres_b > set_Pr1436380704nres_b > $o ).
thf(member405013761nres_d_type,type,
member405013761nres_d: produc235099114nres_d > set_Pr642586912nres_d > $o ).
thf(member427035401nres_c_type,type,
member427035401nres_c: produc1914459634nres_c > set_Pr1250642728nres_c > $o ).
thf(member757031305nres_b_type,type,
member757031305nres_b: produc96971890nres_b > set_Pr1358127528nres_b > $o ).
thf(member189721481nres_d_type,type,
member189721481nres_d: produc1677145714nres_d > set_Pr2080238504nres_d > $o ).
thf(member1051493202_c_o_o_type,type,
member1051493202_c_o_o: produc1838469673_c_o_o > set_Pr1933985801_c_o_o > $o ).
thf(member1680325597nres_a_type,type,
member1680325597nres_a: produc699795910nres_a > set_Pr1361202684nres_a > $o ).
thf(member100096605nres_c_type,type,
member100096605nres_c: produc1267050566nres_c > set_Pr134917244nres_c > $o ).
thf(member369653087nres_b_type,type,
member369653087nres_b: produc1536607048nres_b > set_Pr1815766654nres_b > $o ).
thf(member936907743nres_d_type,type,
member936907743nres_d: produc2103861704nres_d > set_Pr589481214nres_d > $o ).
thf(member1010099668_a_c_c_type,type,
member1010099668_a_c_c: product_prod_a_a_c_c > set_Pr1234209675_a_c_c > $o ).
thf(member228973321nres_c_type,type,
member228973321nres_c: produc1716397554nres_c > set_Pr584391464nres_c > $o ).
thf(member2139143049nres_d_type,type,
member2139143049nres_d: produc1479083634nres_d > set_Pr1413987240nres_d > $o ).
thf(member2086976541nres_c_type,type,
member2086976541nres_c: produc1106446854nres_c > set_Pr979578428nres_c > $o ).
thf(member209049375nres_b_type,type,
member209049375nres_b: produc1376003336nres_b > set_Pr512944190nres_b > $o ).
thf(member776304031nres_d_type,type,
member776304031nres_d: produc1943257992nres_d > set_Pr1434142398nres_d > $o ).
thf(member318002145nres_a_type,type,
member318002145nres_a: produc1484956106nres_a > set_Pr890971136nres_a > $o ).
thf(member885256801nres_c_type,type,
member885256801nres_c: produc2052210762nres_c > set_Pr1812169344nres_c > $o ).
thf(member994209571nres_b_type,type,
member994209571nres_b: produc13679884nres_b > set_Pr42712642nres_b > $o ).
thf(member1468928819nres_a_type,type,
member1468928819nres_a: produc1609974940nres_a > set_Pr384614482nres_a > $o ).
thf(member1600573749nres_c_type,type,
member1600573749nres_c: produc1741619870nres_c > set_Pr1128439124nres_c > $o ).
thf(member1446466291nres_b_type,type,
member1446466291nres_b: produc1587512412nres_b > set_Pr896671762nres_b > $o ).
thf(member1578111221nres_d_type,type,
member1578111221nres_d: produc1719157342nres_d > set_Pr1640496404nres_d > $o ).
thf(member1292358833nres_a_type,type,
member1292358833nres_a: produc1433404954nres_a > set_Pr664904400nres_a > $o ).
thf(member1424003763nres_c_type,type,
member1424003763nres_c: produc1565049884nres_c > set_Pr1408729042nres_c > $o ).
thf(member1269896305nres_b_type,type,
member1269896305nres_b: produc1410942426nres_b > set_Pr1176961680nres_b > $o ).
thf(member449909584od_a_a_type,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member466432594od_a_c_type,type,
member466432594od_a_c: product_prod_a_c > set_Product_prod_a_c > $o ).
thf(member1302463506od_b_d_type,type,
member1302463506od_b_d: product_prod_b_d > set_Product_prod_b_d > $o ).
thf(r1_type,type,
r1: set_Product_prod_a_c ).
thf(r2_type,type,
r2: set_Product_prod_b_d ).
thf(71,axiom,
! [A: produc1757587562nres_d > $o,B: produc1757587562nres_d] :
( ! [C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc2075136412nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_old_Oprod_Oinducts) ).
thf(2956,plain,
! [A: produc1757587562nres_d > $o,B: produc1757587562nres_d] :
( ! [C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc2075136412nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(89,axiom,
( refine321891363sn_a_c
= ( ^ [A: set_Product_prod_a_c,B: c > $o,C: a] :
? [D: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ C @ D ) @ A )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_lift__assn__def) ).
thf(3021,plain,
( refine321891363sn_a_c
= ( ^ [A: set_Product_prod_a_c,B: c > $o,C: a] :
? [D: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ C @ D ) @ A )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,axiom,
! [A: produc809931564nres_d] :
? [B: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc1910095910nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_surj__pair) ).
thf(2889,plain,
! [A: produc809931564nres_d] :
? [B: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc1910095910nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(61,axiom,
( refine408412177nres_d
= ( ^ [A: set_Pr2080238504nres_d,B: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b] :
? [D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( member189721481nres_d @ ( produc627868012nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_lift__assn__def) ).
thf(2921,plain,
( refine408412177nres_d
= ( ^ [A: set_Pr2080238504nres_d,B: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b] :
? [D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( member189721481nres_d @ ( produc627868012nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(153,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( ( A @ E )
= F )
=> ! [G: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ F @ ( B @ G ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_fun__relD1) ).
thf(3230,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( ( A @ E )
= F )
=> ! [G: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ F @ ( B @ G ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(95,axiom,
! [A: $o,B: $o,C: refine440942639nres_c,D: refine424419629nres_a,E: set_Product_prod_c_a] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1292358833nres_a @ ( produc960353612nres_a @ C @ D ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ E ) ) ) )
=> ( member1292358833nres_a @ ( produc960353612nres_a @ ( refine1437029929_bnd_c @ B @ C ) @ ( refine1437029927_bnd_a @ A @ D ) ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_param__op__nres__ASSERT__bnd) ).
thf(3040,plain,
! [A: $o,B: $o,C: refine440942639nres_c,D: refine424419629nres_a,E: set_Product_prod_c_a] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1292358833nres_a @ ( produc960353612nres_a @ C @ D ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ E ) ) ) )
=> ( member1292358833nres_a @ ( produc960353612nres_a @ ( refine1437029929_bnd_c @ B @ C ) @ ( refine1437029927_bnd_a @ A @ D ) ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(110,axiom,
! [A: set_Product_prod_b_d,B: set_Pr1640496404nres_d] :
( member2139143049nres_d
@ ( produc765243756nres_d
@ ^ [C: b,D: b > refine432681134nres_b] : ( D @ C )
@ ^ [C: d,D: d > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP486948753nres_d @ ( relAPP1996600361nres_d @ fun_re1101734569nres_d @ A ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_autoref__Let) ).
thf(3098,plain,
! [A: set_Product_prod_b_d,B: set_Pr1640496404nres_d] :
( member2139143049nres_d
@ ( produc765243756nres_d
@ ^ [C: b,D: b > refine432681134nres_b] : ( D @ C )
@ ^ [C: d,D: d > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP486948753nres_d @ ( relAPP1996600361nres_d @ fun_re1101734569nres_d @ A ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(40,axiom,
! [A: product_prod_a_c] :
~ ! [B: a,C: c] :
( A
!= ( product_Pair_a_c @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_old_Oprod_Oexhaust) ).
thf(2837,plain,
! [A: product_prod_a_c] :
~ ! [B: a,C: c] :
( A
!= ( product_Pair_a_c @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(136,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: c > refine449204144nres_d,F: refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( ( B @ E )
= F )
=> ! [G: a > refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ G @ E ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ G ) @ F ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_fun__relD2) ).
thf(3185,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: c > refine449204144nres_d,F: refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( ( B @ E )
= F )
=> ! [G: a > refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ G @ E ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ G ) @ F ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(7,axiom,
! [A: ( $o > $o ) > a,B: ( $o > $o ) > c,C: set_Pr934623755_o_o_o,D: set_Product_prod_a_c,E: $o > $o,F: $o > $o] :
( ( member1270020946_o_o_c @ ( produc2068274457_o_o_c @ A @ B ) @ ( relAPP970620078_o_o_c @ ( relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C ) @ D ) )
=> ( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ E @ F ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( autoref_APP_o_o_a @ A @ E ) @ ( autoref_APP_o_o_c @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_autoref__APP) ).
thf(170,plain,
! [A: ( $o > $o ) > a,B: ( $o > $o ) > c,C: set_Pr934623755_o_o_o,D: set_Product_prod_a_c,E: $o > $o,F: $o > $o] :
( ( member1270020946_o_o_c @ ( produc2068274457_o_o_c @ A @ B ) @ ( relAPP970620078_o_o_c @ ( relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C ) @ D ) )
=> ( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ E @ F ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( autoref_APP_o_o_a @ A @ E ) @ ( autoref_APP_o_o_c @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_prod_Oinject) ).
thf(3004,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(121,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_tagged__fun__relD__lhs) ).
thf(3135,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(60,axiom,
! [A: produc1677145714nres_d > $o,B: produc1677145714nres_d] :
( ! [C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc627868012nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_old_Oprod_Oinducts) ).
thf(2918,plain,
! [A: produc1677145714nres_d > $o,B: produc1677145714nres_d] :
( ! [C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc627868012nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(65,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > $o > $o,E: c > $o > $o,F: set_Pr934623755_o_o_o] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ ( D @ H ) @ ( autoref_APP_c_o_o @ E @ G ) ) @ F ) ) )
=> ( member250723412_o_o_o
@ ( product_Pair_o_o_o_o @ ( D @ A )
@ ( autore821920247_o_o_o
@ ( autore1554881264_o_o_o
@ ( autore1757597947_o_o_o
@ ( autore1861331824_o_o_o
@ ^ [G: c,H: c > $o > $o] : ( H @ G ) )
@ ( autore1424734926_o_o_o @ ( relAPP1723270664_o_o_o @ ( relAPP913737114_o_o_o @ fun_re362844942_o_o_o @ C ) @ ( relAPP829628004_o_o_o @ ( relAPP1210499902_o_o_o @ fun_re2021699288_o_o_o @ ( relAPP1525934692_c_o_o @ ( relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_autoref__Let__cong) ).
thf(2933,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > $o > $o,E: c > $o > $o,F: set_Pr934623755_o_o_o] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ ( D @ H ) @ ( autoref_APP_c_o_o @ E @ G ) ) @ F ) ) )
=> ( member250723412_o_o_o
@ ( product_Pair_o_o_o_o @ ( D @ A )
@ ( autore821920247_o_o_o
@ ( autore1554881264_o_o_o
@ ( autore1757597947_o_o_o
@ ( autore1861331824_o_o_o
@ ^ [G: c,H: c > $o > $o] : ( H @ G ) )
@ ( autore1424734926_o_o_o @ ( relAPP1723270664_o_o_o @ ( relAPP913737114_o_o_o @ fun_re362844942_o_o_o @ C ) @ ( relAPP829628004_o_o_o @ ( relAPP1210499902_o_o_o @ fun_re2021699288_o_o_o @ ( relAPP1525934692_c_o_o @ ( relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(28,axiom,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Pair__inject) ).
thf(2712,plain,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(42,axiom,
! [A: produc2103861704nres_d] :
~ ! [B: a > refine432681134nres_b,C: c > refine449204144nres_d] :
( A
!= ( produc210841666nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_old_Oprod_Oexhaust) ).
thf(2844,plain,
! [A: produc2103861704nres_d] :
~ ! [B: a > refine432681134nres_b,C: c > refine449204144nres_d] :
( A
!= ( produc210841666nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(75,axiom,
! [A: product_prod_a_c > $o,B: product_prod_a_c] :
( ! [C: a,D: c] : ( A @ ( product_Pair_a_c @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_old_Oprod_Oinducts) ).
thf(2972,plain,
! [A: product_prod_a_c > $o,B: product_prod_a_c] :
( ! [C: a,D: c] : ( A @ ( product_Pair_a_c @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(52,axiom,
! [A: refine432681134nres_b] :
( ( refine1264602246nd_b_b @ A @ refine2063221605TURN_b )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_nres__monad2) ).
thf(2886,plain,
! [A: refine432681134nres_b] :
( ( refine1264602246nd_b_b @ A @ refine2063221605TURN_b )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
! [A: $o,B: $o,C: refine440942639nres_c,D: refine440942639nres_c,E: set_Product_prod_c_c] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1424003763nres_c @ ( produc976876622nres_c @ C @ D ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ E ) ) ) )
=> ( member1424003763nres_c @ ( produc976876622nres_c @ ( refine1437029929_bnd_c @ B @ C ) @ ( refine1437029929_bnd_c @ A @ D ) ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_param__op__nres__ASSERT__bnd) ).
thf(2819,plain,
! [A: $o,B: $o,C: refine440942639nres_c,D: refine440942639nres_c,E: set_Product_prod_c_c] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1424003763nres_c @ ( produc976876622nres_c @ C @ D ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ E ) ) ) )
=> ( member1424003763nres_c @ ( produc976876622nres_c @ ( refine1437029929_bnd_c @ B @ C ) @ ( refine1437029929_bnd_c @ A @ D ) ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(59,axiom,
! [A: set_Product_prod_c_a] : ( member318002145nres_a @ ( produc1063567300nres_a @ refine2063221606TURN_c @ refine2063221604TURN_a ) @ ( relAPP947801195nres_a @ ( relAPP1825452871nres_a @ fun_re1645900187nres_a @ A ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_autoref__RETURN) ).
thf(2916,plain,
! [A: set_Product_prod_c_a] : ( member318002145nres_a @ ( produc1063567300nres_a @ refine2063221606TURN_c @ refine2063221604TURN_a ) @ ( relAPP947801195nres_a @ ( relAPP1825452871nres_a @ fun_re1645900187nres_a @ A ) @ ( relAPP35306343nres_a @ refine245117724el_c_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(92,axiom,
! [A: produc809931564nres_d > $o,B: produc809931564nres_d] :
( ! [C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc1910095910nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_old_Oprod_Oinducts) ).
thf(3029,plain,
! [A: produc809931564nres_d > $o,B: produc809931564nres_d] :
( ! [C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc1910095910nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(15,axiom,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Product_prod_a_a,D: set_Pr896671762nres_b,E: a,F: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ C ) @ D ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( autore1390664424nres_b @ A @ E ) @ ( autore1390664424nres_b @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_autoref__APP) ).
thf(2667,plain,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Product_prod_a_a,D: set_Pr896671762nres_b,E: a,F: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ C ) @ D ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( autore1390664424nres_b @ A @ E ) @ ( autore1390664424nres_b @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [A: set_Product_prod_a_a,B: set_Pr896671762nres_b] :
( member757031305nres_b
@ ( produc295171948nres_b
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C )
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C ) )
@ ( relAPP91071253nres_b @ ( relAPP1740535279nres_b @ fun_re1165441639nres_b @ A ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_autoref__Let) ).
thf(2682,plain,
! [A: set_Product_prod_a_a,B: set_Pr896671762nres_b] :
( member757031305nres_b
@ ( produc295171948nres_b
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C )
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C ) )
@ ( relAPP91071253nres_b @ ( relAPP1740535279nres_b @ fun_re1165441639nres_b @ A ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [A: produc1677145714nres_d > $o,B: produc1677145714nres_d] :
( ! [C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc627868012nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_prod__cases) ).
thf(2698,plain,
! [A: produc1677145714nres_d > $o,B: produc1677145714nres_d] :
( ! [C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc627868012nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(119,axiom,
( relAPP527276399nres_c
= ( ^ [A: set_Product_prod_a_c > set_Pr1128439124nres_c] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_relAPP__def) ).
thf(3131,plain,
( relAPP527276399nres_c
= ( ^ [A: set_Product_prod_a_c > set_Pr1128439124nres_c] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(63,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_prod_Oinject) ).
thf(2925,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(109,axiom,
! [A: b,B: d,C: set_Product_prod_b_d,D: b > refine424419629nres_a,E: d > refine440942639nres_c,F: set_Pr1128439124nres_c] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ A @ B ) @ C )
=> ( ! [G: d] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: b] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ H @ G ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( D @ H ) @ ( autore113191276nres_c @ E @ G ) ) @ F ) ) )
=> ( member1600573749nres_c
@ ( produc1153446608nres_c @ ( D @ A )
@ ( autore964129529nres_c
@ ( autore1989911767nres_c
@ ( autore73061154nres_c
@ ( autore1836202733nres_c
@ ^ [G: d,H: d > refine440942639nres_c] : ( H @ G ) )
@ ( autore1683160729nres_c @ ( relAPP131141393nres_c @ ( relAPP2017502121nres_c @ fun_re430551721nres_c @ C ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_autoref__Let__cong) ).
thf(3093,plain,
! [A: b,B: d,C: set_Product_prod_b_d,D: b > refine424419629nres_a,E: d > refine440942639nres_c,F: set_Pr1128439124nres_c] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ A @ B ) @ C )
=> ( ! [G: d] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: b] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ H @ G ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( D @ H ) @ ( autore113191276nres_c @ E @ G ) ) @ F ) ) )
=> ( member1600573749nres_c
@ ( produc1153446608nres_c @ ( D @ A )
@ ( autore964129529nres_c
@ ( autore1989911767nres_c
@ ( autore73061154nres_c
@ ( autore1836202733nres_c
@ ^ [G: d,H: d > refine440942639nres_c] : ( H @ G ) )
@ ( autore1683160729nres_c @ ( relAPP131141393nres_c @ ( relAPP2017502121nres_c @ fun_re430551721nres_c @ C ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(126,axiom,
! [A: set_Product_prod_c_c,B: set_Product_prod_d_d] : ( member405013761nres_d @ ( produc1915822052nres_d @ refine2092371655nd_c_d @ refine2092371655nd_c_d ) @ ( relAPP720329701nres_d @ ( relAPP2032940527nres_d @ fun_re1190945563nres_d @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ A ) ) @ ( relAPP1899039865nres_d @ ( relAPP990557099nres_d @ fun_re1740744275nres_d @ ( relAPP941435307nres_d @ ( relAPP508483205nres_d @ fun_re414971739nres_d @ A ) @ ( relAPP1852927595nres_d @ refine1072887134el_d_d @ B ) ) ) @ ( relAPP1852927595nres_d @ refine1072887134el_d_d @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_param__bind) ).
thf(3152,plain,
! [A: set_Product_prod_c_c,B: set_Product_prod_d_d] : ( member405013761nres_d @ ( produc1915822052nres_d @ refine2092371655nd_c_d @ refine2092371655nd_c_d ) @ ( relAPP720329701nres_d @ ( relAPP2032940527nres_d @ fun_re1190945563nres_d @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ A ) ) @ ( relAPP1899039865nres_d @ ( relAPP990557099nres_d @ fun_re1740744275nres_d @ ( relAPP941435307nres_d @ ( relAPP508483205nres_d @ fun_re414971739nres_d @ A ) @ ( relAPP1852927595nres_d @ refine1072887134el_d_d @ B ) ) ) @ ( relAPP1852927595nres_d @ refine1072887134el_d_d @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(33,axiom,
( refine1958703523nres_d
= ( ^ [A: set_Pr797615136nres_d,B: ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: ( a > refine432681134nres_b ) > refine432681134nres_b] :
? [D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_lift__assn__def) ).
thf(2809,plain,
( refine1958703523nres_d
= ( ^ [A: set_Pr797615136nres_d,B: ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: ( a > refine432681134nres_b ) > refine432681134nres_b] :
? [D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(151,axiom,
! [A: set_Pr589481214nres_d,B: set_Pr1640496404nres_d] :
( member660096835nres_d
@ ( produc1910095910nres_d
@ ^ [C: a > refine432681134nres_b,D: ( a > refine432681134nres_b ) > refine432681134nres_b] : ( D @ C )
@ ^ [C: c > refine449204144nres_d,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1388319497nres_d @ ( relAPP1716516381nres_d @ fun_re1306413669nres_d @ A ) @ ( relAPP1552964229nres_d @ ( relAPP1953591565nres_d @ fun_re2071856555nres_d @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_autoref__Let) ).
thf(3226,plain,
! [A: set_Pr589481214nres_d,B: set_Pr1640496404nres_d] :
( member660096835nres_d
@ ( produc1910095910nres_d
@ ^ [C: a > refine432681134nres_b,D: ( a > refine432681134nres_b ) > refine432681134nres_b] : ( D @ C )
@ ^ [C: c > refine449204144nres_d,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1388319497nres_d @ ( relAPP1716516381nres_d @ fun_re1306413669nres_d @ A ) @ ( relAPP1552964229nres_d @ ( relAPP1953591565nres_d @ fun_re2071856555nres_d @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(74,axiom,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Pair__inject) ).
thf(2965,plain,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(70,axiom,
( relAPP1536875909nres_b
= ( ^ [A: set_Product_prod_a_a > set_Pr896671762nres_b > set_Pr1815766654nres_b] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_relAPP__def) ).
thf(2954,plain,
( relAPP1536875909nres_b
= ( ^ [A: set_Product_prod_a_a > set_Pr896671762nres_b > set_Pr1815766654nres_b] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(57,axiom,
! [A: a,B: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_nres__monad1) ).
thf(2910,plain,
! [A: a,B: a > refine424419629nres_a] :
( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(102,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > refine424419629nres_a,E: c > refine440942639nres_c,F: set_Pr1128439124nres_c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( D @ H ) @ ( autore1973425259nres_c @ E @ G ) ) @ F ) ) )
=> ( member1600573749nres_c
@ ( produc1153446608nres_c @ ( D @ A )
@ ( autore2084714426nres_c
@ ( autore224164375nres_c
@ ( autore956520418nres_c
@ ( autore572178349nres_c
@ ^ [G: c,H: c > refine440942639nres_c] : ( H @ G ) )
@ ( autore1545784985nres_c @ ( relAPP998488211nres_c @ ( relAPP1155943915nres_c @ fun_re418666087nres_c @ C ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_autoref__Let__cong) ).
thf(3069,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > refine424419629nres_a,E: c > refine440942639nres_c,F: set_Pr1128439124nres_c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( D @ H ) @ ( autore1973425259nres_c @ E @ G ) ) @ F ) ) )
=> ( member1600573749nres_c
@ ( produc1153446608nres_c @ ( D @ A )
@ ( autore2084714426nres_c
@ ( autore224164375nres_c
@ ( autore956520418nres_c
@ ( autore572178349nres_c
@ ^ [G: c,H: c > refine440942639nres_c] : ( H @ G ) )
@ ( autore1545784985nres_c @ ( relAPP998488211nres_c @ ( relAPP1155943915nres_c @ fun_re418666087nres_c @ C ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(127,axiom,
! [A: set_Product_prod_a_d,B: set_Product_prod_b_c] : ( member1981370113nres_c @ ( produc651225572nres_c @ refine436832839nd_a_b @ refine772657413nd_d_c ) @ ( relAPP745269862nres_c @ ( relAPP1327809903nres_c @ fun_re297775585nres_c @ ( relAPP1043177969nres_d @ refine737062561el_a_d @ A ) ) @ ( relAPP1784890619nres_c @ ( relAPP1763648999nres_c @ fun_re955494798nres_c @ ( relAPP1699156520nres_c @ ( relAPP189920063nres_c @ fun_re631684249nres_c @ A ) @ ( relAPP797192941nres_c @ refine1564831967el_b_c @ B ) ) ) @ ( relAPP797192941nres_c @ refine1564831967el_b_c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_param__bind) ).
thf(3154,plain,
! [A: set_Product_prod_a_d,B: set_Product_prod_b_c] : ( member1981370113nres_c @ ( produc651225572nres_c @ refine436832839nd_a_b @ refine772657413nd_d_c ) @ ( relAPP745269862nres_c @ ( relAPP1327809903nres_c @ fun_re297775585nres_c @ ( relAPP1043177969nres_d @ refine737062561el_a_d @ A ) ) @ ( relAPP1784890619nres_c @ ( relAPP1763648999nres_c @ fun_re955494798nres_c @ ( relAPP1699156520nres_c @ ( relAPP189920063nres_c @ fun_re631684249nres_c @ A ) @ ( relAPP797192941nres_c @ refine1564831967el_b_c @ B ) ) ) @ ( relAPP797192941nres_c @ refine1564831967el_b_c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(143,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_tagged__fun__relD__rhs) ).
thf(3207,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(16,axiom,
! [A: $o,B: $o,C: refine449204144nres_d,D: refine432681134nres_b,E: set_Product_prod_d_b] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1269896305nres_b @ ( produc1954071948nres_b @ C @ D ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ E ) ) ) )
=> ( member1269896305nres_b @ ( produc1954071948nres_b @ ( refine1437029930_bnd_d @ B @ C ) @ ( refine1437029928_bnd_b @ A @ D ) ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_param__op__nres__ASSERT__bnd) ).
thf(2670,plain,
! [A: $o,B: $o,C: refine449204144nres_d,D: refine432681134nres_b,E: set_Product_prod_d_b] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1269896305nres_b @ ( produc1954071948nres_b @ C @ D ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ E ) ) ) )
=> ( member1269896305nres_b @ ( produc1954071948nres_b @ ( refine1437029930_bnd_d @ B @ C ) @ ( refine1437029928_bnd_b @ A @ D ) ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(124,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_tagged__fun__relD__none) ).
thf(3144,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(108,axiom,
! [A: refine424419629nres_a] :
( ( refine436832838nd_a_a @ A @ refine2063221604TURN_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_nres__monad2) ).
thf(3090,plain,
! [A: refine424419629nres_a] :
( ( refine436832838nd_a_a @ A @ refine2063221604TURN_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(139,axiom,
! [A: set_Product_prod_c_a,B: set_Product_prod_d_b] : ( member2039405057nres_b @ ( produc183923940nres_b @ refine2092371655nd_c_d @ refine436832839nd_a_b ) @ ( relAPP1077394663nres_b @ ( relAPP1747515631nres_b @ fun_re650017687nres_b @ ( relAPP35306343nres_a @ refine245117724el_c_a @ A ) ) @ ( relAPP1033339257nres_b @ ( relAPP38185259nres_b @ fun_re1925572817nres_b @ ( relAPP1977623725nres_b @ ( relAPP774904585nres_b @ fun_re492134875nres_b @ A ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ B ) ) ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_param__bind) ).
thf(3198,plain,
! [A: set_Product_prod_c_a,B: set_Product_prod_d_b] : ( member2039405057nres_b @ ( produc183923940nres_b @ refine2092371655nd_c_d @ refine436832839nd_a_b ) @ ( relAPP1077394663nres_b @ ( relAPP1747515631nres_b @ fun_re650017687nres_b @ ( relAPP35306343nres_a @ refine245117724el_c_a @ A ) ) @ ( relAPP1033339257nres_b @ ( relAPP38185259nres_b @ fun_re1925572817nres_b @ ( relAPP1977623725nres_b @ ( relAPP774904585nres_b @ fun_re492134875nres_b @ A ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ B ) ) ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(3,axiom,
! [A: product_prod_o_o_o_o] :
? [B: $o > $o,C: $o > $o] :
( A
= ( product_Pair_o_o_o_o @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_surj__pair) ).
thf(156,plain,
! [A: product_prod_o_o_o_o] :
? [B: $o > $o,C: $o > $o] :
( A
= ( product_Pair_o_o_o_o @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,axiom,
! [A: set_Pr2080238504nres_d] :
( ( collec554837959nres_d
@ ^ [B: produc1677145714nres_d] : ( member189721481nres_d @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Collect__mem__eq) ).
thf(2841,plain,
! [A: set_Pr2080238504nres_d] :
( ( collec554837959nres_d
@ ^ [B: produc1677145714nres_d] : ( member189721481nres_d @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [A: set_Pr589481214nres_d] :
( ( collec1639315997nres_d
@ ^ [B: produc2103861704nres_d] : ( member936907743nres_d @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Collect__mem__eq) ).
thf(2709,plain,
! [A: set_Pr589481214nres_d] :
( ( collec1639315997nres_d
@ ^ [B: produc2103861704nres_d] : ( member936907743nres_d @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(147,axiom,
! [A: set_Pr1128439124nres_c,B: set_Pr797615136nres_d] :
( member508530605nres_d
@ ( produc912866704nres_d
@ ^ [C: refine424419629nres_a,D: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b] : ( D @ C )
@ ^ [C: refine440942639nres_c,D: refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1095654971nres_d @ ( relAPP422583323nres_d @ fun_re1190106143nres_d @ A ) @ ( relAPP1659518317nres_d @ ( relAPP759382665nres_d @ fun_re692194867nres_d @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_autoref__Let) ).
thf(3218,plain,
! [A: set_Pr1128439124nres_c,B: set_Pr797615136nres_d] :
( member508530605nres_d
@ ( produc912866704nres_d
@ ^ [C: refine424419629nres_a,D: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b] : ( D @ C )
@ ^ [C: refine440942639nres_c,D: refine440942639nres_c > ( c > refine449204144nres_d ) > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1095654971nres_d @ ( relAPP422583323nres_d @ fun_re1190106143nres_d @ A ) @ ( relAPP1659518317nres_d @ ( relAPP759382665nres_d @ fun_re692194867nres_d @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(21,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr797615136nres_d,D: ( a > refine432681134nres_b ) > refine432681134nres_b] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ C )
=> ( ( autore1360171649nres_b @ A @ D )
=> ( member461830657nres_d @ ( produc2075136412nres_d @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_autoref__REMOVE__INTERNAL__EQ) ).
thf(2692,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr797615136nres_d,D: ( a > refine432681134nres_b ) > refine432681134nres_b] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ C )
=> ( ( autore1360171649nres_b @ A @ D )
=> ( member461830657nres_d @ ( produc2075136412nres_d @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(112,axiom,
( relAPP173519167nres_c
= ( ^ [A: set_Product_prod_a_c > set_Pr1128439124nres_c > set_Pr134917244nres_c] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_relAPP__def) ).
thf(3102,plain,
( relAPP173519167nres_c
= ( ^ [A: set_Product_prod_a_c > set_Pr1128439124nres_c > set_Pr134917244nres_c] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(118,axiom,
! [A: $o,B: $o,C: refine432681134nres_b,D: refine449204144nres_d,E: set_Product_prod_b_d] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ C @ D ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ E ) ) ) )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( refine1437029928_bnd_b @ B @ C ) @ ( refine1437029930_bnd_d @ A @ D ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_param__op__nres__ASSERT__bnd) ).
thf(3119,plain,
! [A: $o,B: $o,C: refine432681134nres_b,D: refine449204144nres_d,E: set_Product_prod_b_d] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ C @ D ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ E ) ) ) )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( refine1437029928_bnd_b @ B @ C ) @ ( refine1437029930_bnd_d @ A @ D ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(142,axiom,
! [A: set_Product_prod_a_c,B: set_Product_prod_b_d] : ( member65788417nres_d @ ( produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d ) @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_param__bind) ).
thf(3205,plain,
! [A: set_Product_prod_a_c,B: set_Product_prod_b_d] : ( member65788417nres_d @ ( produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d ) @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(83,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Pr589481214nres_d,D: ( c > refine449204144nres_d ) > $o] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine746536475nres_d @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_lift__assnI) ).
thf(3001,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Pr589481214nres_d,D: ( c > refine449204144nres_d ) > $o] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine746536475nres_d @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(99,axiom,
! [A: produc1677145714nres_d] :
? [B: a > ( a > refine432681134nres_b ) > refine432681134nres_b,C: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc627868012nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_surj__pair) ).
thf(3060,plain,
! [A: produc1677145714nres_d] :
? [B: a > ( a > refine432681134nres_b ) > refine432681134nres_b,C: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc627868012nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(107,axiom,
! [A: produc2103861704nres_d > $o,B: produc2103861704nres_d] :
( ! [C: a > refine432681134nres_b,D: c > refine449204144nres_d] : ( A @ ( produc210841666nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_old_Oprod_Oinducts) ).
thf(3087,plain,
! [A: produc2103861704nres_d > $o,B: produc2103861704nres_d] :
( ! [C: a > refine432681134nres_b,D: c > refine449204144nres_d] : ( A @ ( produc210841666nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(88,axiom,
! [A: produc1757587562nres_d > $o,B: produc1757587562nres_d] :
( ! [C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc2075136412nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_prod__cases) ).
thf(3018,plain,
! [A: produc1757587562nres_d > $o,B: produc1757587562nres_d] :
( ! [C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc2075136412nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(123,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_tagged__fun__relD__both) ).
thf(3141,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(144,axiom,
! [A: c,B: c > refine449204144nres_d] :
( ( refine2092371655nd_c_d @ ( refine2063221606TURN_c @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_nres__monad1) ).
thf(3210,plain,
! [A: c,B: c > refine449204144nres_d] :
( ( refine2092371655nd_c_d @ ( refine2063221606TURN_c @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(49,axiom,
! [A: c,B: c > refine440942639nres_c] :
( ( refine2092371654nd_c_c @ ( refine2063221606TURN_c @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_nres__monad1) ).
thf(2868,plain,
! [A: c,B: c > refine440942639nres_c] :
( ( refine2092371654nd_c_c @ ( refine2063221606TURN_c @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(93,axiom,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr613277282nres_d,D: ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine1711024813nres_d @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_lift__assnI) ).
thf(3032,plain,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr613277282nres_d,D: ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine1711024813nres_d @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(77,axiom,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_prod_Oinject) ).
thf(2978,plain,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(12,axiom,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Pair__inject) ).
thf(1424,plain,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(86,axiom,
! [A: b > refine432681134nres_b,B: d > refine449204144nres_d,C: set_Product_prod_b_d,D: set_Pr1640496404nres_d,E: b,F: d] :
( ( member776304031nres_d @ ( produc847298946nres_d @ A @ B ) @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ C ) @ D ) )
=> ( ( member1302463506od_b_d @ ( product_Pair_b_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( autore1677914089nres_b @ A @ E ) @ ( autore121452781nres_d @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_autoref__APP) ).
thf(3010,plain,
! [A: b > refine432681134nres_b,B: d > refine449204144nres_d,C: set_Product_prod_b_d,D: set_Pr1640496404nres_d,E: b,F: d] :
( ( member776304031nres_d @ ( produc847298946nres_d @ A @ B ) @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ C ) @ D ) )
=> ( ( member1302463506od_b_d @ ( product_Pair_b_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( autore1677914089nres_b @ A @ E ) @ ( autore121452781nres_d @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(8,axiom,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Pr896671762nres_b,D: refine432681134nres_b,E: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ C ) )
=> ( ( D
= ( A @ E ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ D @ ( B @ E ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_fun__relE2) ).
thf(173,plain,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Pr896671762nres_b,D: refine432681134nres_b,E: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ C ) )
=> ( ( D
= ( A @ E ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ D @ ( B @ E ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(149,axiom,
! [A: set_Product_prod_a_b,B: set_Product_prod_b_a] : ( member1468277761nres_a @ ( produc1066811108nres_a @ refine436832839nd_a_b @ refine1264602245nd_b_a ) @ ( relAPP1102334824nres_a @ ( relAPP1042385007nres_a @ fun_re1904331357nres_a @ ( relAPP11374829nres_b @ refine737062559el_a_b @ A ) ) @ ( relAPP919190011nres_a @ ( relAPP811277159nres_a @ fun_re1140323340nres_a @ ( relAPP587861290nres_a @ ( relAPP456341443nres_a @ fun_re708847385nres_a @ A ) @ ( relAPP1912873449nres_a @ refine1564831965el_b_a @ B ) ) ) @ ( relAPP1912873449nres_a @ refine1564831965el_b_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_param__bind) ).
thf(3222,plain,
! [A: set_Product_prod_a_b,B: set_Product_prod_b_a] : ( member1468277761nres_a @ ( produc1066811108nres_a @ refine436832839nd_a_b @ refine1264602245nd_b_a ) @ ( relAPP1102334824nres_a @ ( relAPP1042385007nres_a @ fun_re1904331357nres_a @ ( relAPP11374829nres_b @ refine737062559el_a_b @ A ) ) @ ( relAPP919190011nres_a @ ( relAPP811277159nres_a @ fun_re1140323340nres_a @ ( relAPP587861290nres_a @ ( relAPP456341443nres_a @ fun_re708847385nres_a @ A ) @ ( relAPP1912873449nres_a @ refine1564831965el_b_a @ B ) ) ) @ ( relAPP1912873449nres_a @ refine1564831965el_b_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(35,axiom,
! [A: a > refine424419629nres_a,B: c > refine440942639nres_c,C: set_Product_prod_a_c,D: set_Pr1128439124nres_c,E: a,F: c] :
( ( member100096605nres_c @ ( produc1827604032nres_c @ A @ B ) @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( autore1382402919nres_a @ A @ E ) @ ( autore1973425259nres_c @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_autoref__APP) ).
thf(2813,plain,
! [A: a > refine424419629nres_a,B: c > refine440942639nres_c,C: set_Product_prod_a_c,D: set_Pr1128439124nres_c,E: a,F: c] :
( ( member100096605nres_c @ ( produc1827604032nres_c @ A @ B ) @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( autore1382402919nres_a @ A @ E ) @ ( autore1973425259nres_c @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(131,axiom,
! [A: set_Pr589481214nres_d,B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d,D: set_Pr1640496404nres_d] :
( ! [E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ A )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( B @ E ) @ ( C @ F ) ) @ D ) )
=> ( member461830657nres_d @ ( produc2075136412nres_d @ B @ C ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_fun__relI) ).
thf(3162,plain,
! [A: set_Pr589481214nres_d,B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d,D: set_Pr1640496404nres_d] :
( ! [E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ A )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( B @ E ) @ ( C @ F ) ) @ D ) )
=> ( member461830657nres_d @ ( produc2075136412nres_d @ B @ C ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(146,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_tagged__fun__relD__rhs) ).
thf(3215,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(115,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_tagged__fun__relD__lhs) ).
thf(3109,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(103,axiom,
! [A: set_Pr797615136nres_d] :
( ( collec1671161663nres_d
@ ^ [B: produc1757587562nres_d] : ( member461830657nres_d @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Collect__mem__eq) ).
thf(3074,plain,
! [A: set_Pr797615136nres_d] :
( ( collec1671161663nres_d
@ ^ [B: produc1757587562nres_d] : ( member461830657nres_d @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(125,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: refine432681134nres_b] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( ( A @ E )
= F )
=> ! [G: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ E @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ F @ ( B @ G ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_fun__relD1) ).
thf(3147,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: refine432681134nres_b] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( ( A @ E )
= F )
=> ! [G: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ E @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ F @ ( B @ G ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(51,axiom,
! [A: b,B: b > refine424419629nres_a] :
( ( refine1264602245nd_b_a @ ( refine2063221605TURN_b @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_nres__monad1) ).
thf(2883,plain,
! [A: b,B: b > refine424419629nres_a] :
( ( refine1264602245nd_b_a @ ( refine2063221605TURN_b @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(137,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_tagged__fun__relD__none) ).
thf(3190,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr589481214nres_d,D: set_Pr1640496404nres_d,E: a > refine432681134nres_b,F: c > refine449204144nres_d] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ C ) @ D ) )
=> ( ( member936907743nres_d @ ( produc210841666nres_d @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(81,axiom,
! [A: set_Product_prod_a_c] :
( ( collec662378644od_a_c
@ ^ [B: product_prod_a_c] : ( member466432594od_a_c @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__mem__eq) ).
thf(2995,plain,
! [A: set_Product_prod_a_c] :
( ( collec662378644od_a_c
@ ^ [B: product_prod_a_c] : ( member466432594od_a_c @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(55,axiom,
! [A: d,B: d > refine440942639nres_c] :
( ( refine772657413nd_d_c @ ( refine2063221607TURN_d @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_nres__monad1) ).
thf(2904,plain,
! [A: d,B: d > refine440942639nres_c] :
( ( refine772657413nd_d_c @ ( refine2063221607TURN_d @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(105,axiom,
! [A: product_prod_a_c] :
? [B: a,C: c] :
( A
= ( product_Pair_a_c @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_surj__pair) ).
thf(3079,plain,
! [A: product_prod_a_c] :
? [B: a,C: c] :
( A
= ( product_Pair_a_c @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(129,axiom,
! [A: set_Pr589481214nres_d,B: set_Product_prod_b_d] : ( member449974729nres_d @ ( produc973126316nres_d @ refine1985319227es_b_b @ refine1129534141es_d_d ) @ ( relAPP745136137nres_d @ ( relAPP1787540131nres_d @ fun_re1732033515nres_d @ ( relAPP1482036727nres_d @ refine1535302424nres_d @ A ) ) @ ( relAPP1552964229nres_d @ ( relAPP1953591565nres_d @ fun_re2071856555nres_d @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_param__bind) ).
thf(3158,plain,
! [A: set_Pr589481214nres_d,B: set_Product_prod_b_d] : ( member449974729nres_d @ ( produc973126316nres_d @ refine1985319227es_b_b @ refine1129534141es_d_d ) @ ( relAPP745136137nres_d @ ( relAPP1787540131nres_d @ fun_re1732033515nres_d @ ( relAPP1482036727nres_d @ refine1535302424nres_d @ A ) ) @ ( relAPP1552964229nres_d @ ( relAPP1953591565nres_d @ fun_re2071856555nres_d @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(66,axiom,
! [A: produc1757587562nres_d] :
~ ! [B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc2075136412nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_old_Oprod_Oexhaust) ).
thf(2938,plain,
! [A: produc1757587562nres_d] :
~ ! [B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc2075136412nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(78,axiom,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Oprod_Oinject) ).
thf(2981,plain,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: a > ( a > refine432681134nres_b ) > refine432681134nres_b,D: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc627868012nres_d @ A @ B )
= ( produc627868012nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(22,axiom,
! [A: produc2103861704nres_d > $o,B: produc2103861704nres_d] :
( ! [C: a > refine432681134nres_b,D: c > refine449204144nres_d] : ( A @ ( produc210841666nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_prod__cases) ).
thf(2695,plain,
! [A: produc2103861704nres_d > $o,B: produc2103861704nres_d] :
( ! [C: a > refine432681134nres_b,D: c > refine449204144nres_d] : ( A @ ( produc210841666nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(72,axiom,
! [A: set_Product_prod_a_c,B: set_Pr1128439124nres_c] :
( member427035401nres_c
@ ( produc1824358636nres_c
@ ^ [C: a,D: a > refine424419629nres_a] : ( D @ C )
@ ^ [C: c,D: c > refine440942639nres_c] : ( D @ C ) )
@ ( relAPP998488211nres_c @ ( relAPP1155943915nres_c @ fun_re418666087nres_c @ A ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_autoref__Let) ).
thf(2959,plain,
! [A: set_Product_prod_a_c,B: set_Pr1128439124nres_c] :
( member427035401nres_c
@ ( produc1824358636nres_c
@ ^ [C: a,D: a > refine424419629nres_a] : ( D @ C )
@ ^ [C: c,D: c > refine440942639nres_c] : ( D @ C ) )
@ ( relAPP998488211nres_c @ ( relAPP1155943915nres_c @ fun_re418666087nres_c @ A ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(145,axiom,
( relAPP1313094511nres_d
= ( ^ [A: set_Product_prod_b_d > set_Pr1640496404nres_d] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_relAPP__def) ).
thf(3213,plain,
( relAPP1313094511nres_d
= ( ^ [A: set_Product_prod_b_d > set_Pr1640496404nres_d] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(90,axiom,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oinject) ).
thf(3023,plain,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(104,axiom,
( relAPP1642956907nres_a
= ( ^ [A: set_Product_prod_a_a > set_Pr384614482nres_a] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_relAPP__def) ).
thf(3077,plain,
( relAPP1642956907nres_a
= ( ^ [A: set_Product_prod_a_a > set_Pr384614482nres_a] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(134,axiom,
! [A: $o,B: $o,C: refine424419629nres_a,D: refine440942639nres_c,E: set_Product_prod_a_c] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ C @ D ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ E ) ) ) )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( refine1437029927_bnd_a @ B @ C ) @ ( refine1437029929_bnd_c @ A @ D ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_param__op__nres__ASSERT__bnd) ).
thf(3170,plain,
! [A: $o,B: $o,C: refine424419629nres_a,D: refine440942639nres_c,E: set_Product_prod_a_c] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ C @ D ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ E ) ) ) )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( refine1437029927_bnd_a @ B @ C ) @ ( refine1437029929_bnd_c @ A @ D ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(4,axiom,
! [A: a > $o > $o,B: c > $o > $o,C: set_Product_prod_a_c,D: set_Pr934623755_o_o_o,E: a,F: c] :
( ( member1051493202_c_o_o @ ( produc1393542937_c_o_o @ A @ B ) @ ( relAPP1525934692_c_o_o @ ( relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ ( autoref_APP_a_o_o @ A @ E ) @ ( autoref_APP_c_o_o @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_autoref__APP) ).
thf(159,plain,
! [A: a > $o > $o,B: c > $o > $o,C: set_Product_prod_a_c,D: set_Pr934623755_o_o_o,E: a,F: c] :
( ( member1051493202_c_o_o @ ( produc1393542937_c_o_o @ A @ B ) @ ( relAPP1525934692_c_o_o @ ( relAPP589338430_c_o_o @ fun_rel_a_c_o_o_o_o @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ ( autoref_APP_a_o_o @ A @ E ) @ ( autoref_APP_c_o_o @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(114,axiom,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr2080238504nres_d,D: a > ( a > refine432681134nres_b ) > refine432681134nres_b] :
( ( member189721481nres_d @ ( produc627868012nres_d @ A @ B ) @ C )
=> ( ( autore1318775848nres_b @ A @ D )
=> ( member189721481nres_d @ ( produc627868012nres_d @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_autoref__REMOVE__INTERNAL__EQ) ).
thf(3106,plain,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr2080238504nres_d,D: a > ( a > refine432681134nres_b ) > refine432681134nres_b] :
( ( member189721481nres_d @ ( produc627868012nres_d @ A @ B ) @ C )
=> ( ( autore1318775848nres_b @ A @ D )
=> ( member189721481nres_d @ ( produc627868012nres_d @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(68,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Pair__inject) ).
thf(2945,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(122,axiom,
! [A: a,B: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_nres__monad1) ).
thf(3138,plain,
! [A: a,B: a > refine432681134nres_b] :
( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(50,axiom,
! [A: $o,B: $o,C: refine424419629nres_a,D: refine424419629nres_a,E: set_Product_prod_a_a] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1468928819nres_a @ ( produc1136923598nres_a @ C @ D ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ E ) ) ) )
=> ( member1468928819nres_a @ ( produc1136923598nres_a @ ( refine1437029927_bnd_a @ B @ C ) @ ( refine1437029927_bnd_a @ A @ D ) ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_param__op__nres__ASSERT__bnd) ).
thf(2871,plain,
! [A: $o,B: $o,C: refine424419629nres_a,D: refine424419629nres_a,E: set_Product_prod_a_a] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1468928819nres_a @ ( produc1136923598nres_a @ C @ D ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ E ) ) ) )
=> ( member1468928819nres_a @ ( produc1136923598nres_a @ ( refine1437029927_bnd_a @ B @ C ) @ ( refine1437029927_bnd_a @ A @ D ) ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(130,axiom,
( relAPP1270454529nres_d
= ( ^ [A: set_Product_prod_a_c > set_Pr1640496404nres_d > set_Pr589481214nres_d] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_relAPP__def) ).
thf(3160,plain,
( relAPP1270454529nres_d
= ( ^ [A: set_Product_prod_a_c > set_Pr1640496404nres_d > set_Pr589481214nres_d] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(135,axiom,
! [A: set_Product_prod_a_c,B: a > refine432681134nres_b,C: c > refine449204144nres_d,D: set_Pr1640496404nres_d] :
( ! [E: a,F: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ A )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( B @ E ) @ ( C @ F ) ) @ D ) )
=> ( member936907743nres_d @ ( produc210841666nres_d @ B @ C ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fun__relI) ).
thf(3182,plain,
! [A: set_Product_prod_a_c,B: a > refine432681134nres_b,C: c > refine449204144nres_d,D: set_Pr1640496404nres_d] :
( ! [E: a,F: c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ A )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( B @ E ) @ ( C @ F ) ) @ D ) )
=> ( member936907743nres_d @ ( produc210841666nres_d @ B @ C ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(101,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_old_Oprod_Oinject) ).
thf(3066,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc2075136412nres_d @ A @ B )
= ( produc2075136412nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(132,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( autore1390664424nres_b @ A @ E ) @ ( autore1981686764nres_d @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_autoref__APP) ).
thf(3165,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( autore1390664424nres_b @ A @ E ) @ ( autore1981686764nres_d @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(62,axiom,
! [A: set_Product_prod_c_c] : ( member885256801nres_c @ ( produc465280580nres_c @ refine2063221606TURN_c @ refine2063221606TURN_c ) @ ( relAPP2059096425nres_c @ ( relAPP1559031491nres_c @ fun_re1568737051nres_c @ A ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_autoref__RETURN) ).
thf(2923,plain,
! [A: set_Product_prod_c_c] : ( member885256801nres_c @ ( produc465280580nres_c @ refine2063221606TURN_c @ refine2063221606TURN_c ) @ ( relAPP2059096425nres_c @ ( relAPP1559031491nres_c @ fun_re1568737051nres_c @ A ) @ ( relAPP1067109483nres_c @ refine245117726el_c_c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr797615136nres_d,D: ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine1958703523nres_d @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_lift__assnI) ).
thf(2664,plain,
! [A: ( a > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr797615136nres_d,D: ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member461830657nres_d @ ( produc2075136412nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine1958703523nres_d @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
member65788417nres_d @ ( produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d ) @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ ( relAPP527276399nres_c @ refine737062560el_a_c @ r1 ) ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1 ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member65788417nres_d @ ( produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d ) @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ ( relAPP527276399nres_c @ refine737062560el_a_c @ r1 ) ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1 ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(155,plain,
~ ( member65788417nres_d @ ( produc1576596708nres_d @ refine436832839nd_a_b @ refine2092371655nd_c_d ) @ ( relAPP511982311nres_d @ ( relAPP1396672239nres_d @ fun_re439246495nres_d @ ( relAPP527276399nres_c @ refine737062560el_a_c @ r1 ) ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ r1 ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ r2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(64,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > a,E: c > c,F: set_Product_prod_a_c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( D @ H ) @ ( autoref_APP_c_c @ E @ G ) ) @ F ) ) )
=> ( member466432594od_a_c
@ ( product_Pair_a_c @ ( D @ A )
@ ( autoref_APP_c_c_c
@ ( autoref_APP_c_c_c_c
@ ( autore1422848225_c_c_c
@ ( autoref_OP_c_c_c_c
@ ^ [G: c,H: c > c] : ( H @ G ) )
@ ( autore464253722_c_c_c @ ( relAPP1804623572_c_c_c @ ( relAPP1889825126_c_c_c @ fun_re836380558_c_c_c @ C ) @ ( relAPP1311785006_c_c_c @ ( relAPP981449866_c_c_c @ fun_rel_a_a_c_c_a_c @ ( relAPP237429680_a_c_c @ ( relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_autoref__Let__cong) ).
thf(2928,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > a,E: c > c,F: set_Product_prod_a_c] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( D @ H ) @ ( autoref_APP_c_c @ E @ G ) ) @ F ) ) )
=> ( member466432594od_a_c
@ ( product_Pair_a_c @ ( D @ A )
@ ( autoref_APP_c_c_c
@ ( autoref_APP_c_c_c_c
@ ( autore1422848225_c_c_c
@ ( autoref_OP_c_c_c_c
@ ^ [G: c,H: c > c] : ( H @ G ) )
@ ( autore464253722_c_c_c @ ( relAPP1804623572_c_c_c @ ( relAPP1889825126_c_c_c @ fun_re836380558_c_c_c @ C ) @ ( relAPP1311785006_c_c_c @ ( relAPP981449866_c_c_c @ fun_rel_a_a_c_c_a_c @ ( relAPP237429680_a_c_c @ ( relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(120,axiom,
! [A: set_Product_prod_b_d,B: set_Product_prod_a_c] : ( member1715717121nres_c @ ( produc385572580nres_c @ refine1264602245nd_b_a @ refine772657413nd_d_c ) @ ( relAPP944912869nres_c @ ( relAPP492592111nres_c @ fun_re816936095nres_c @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_param__bind) ).
thf(3133,plain,
! [A: set_Product_prod_b_d,B: set_Product_prod_a_c] : ( member1715717121nres_c @ ( produc385572580nres_c @ refine1264602245nd_b_a @ refine772657413nd_d_c ) @ ( relAPP944912869nres_c @ ( relAPP492592111nres_c @ fun_re816936095nres_c @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(97,axiom,
( relAPP1135042155nres_d
= ( ^ [A: set_Product_prod_a_c > set_Pr797615136nres_d > set_Pr2080238504nres_d] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_relAPP__def) ).
thf(3055,plain,
( relAPP1135042155nres_d
= ( ^ [A: set_Product_prod_a_c > set_Pr797615136nres_d > set_Pr2080238504nres_d] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(31,axiom,
! [A: a > a,B: c > c,C: set_Product_prod_a_c,D: set_Product_prod_a_c,E: a,F: c] :
( ( member1010099668_a_c_c @ ( product_Pair_a_a_c_c @ A @ B ) @ ( relAPP237429680_a_c_c @ ( relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( autoref_APP_a_a @ A @ E ) @ ( autoref_APP_c_c @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_autoref__APP) ).
thf(2725,plain,
! [A: a > a,B: c > c,C: set_Product_prod_a_c,D: set_Product_prod_a_c,E: a,F: c] :
( ( member1010099668_a_c_c @ ( product_Pair_a_a_c_c @ A @ B ) @ ( relAPP237429680_a_c_c @ ( relAPP887115074_a_c_c @ fun_rel_a_c_a_c @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( autoref_APP_a_a @ A @ E ) @ ( autoref_APP_c_c @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [A: product_prod_o_o_o_o > $o,B: product_prod_o_o_o_o] :
( ! [C: $o > $o,D: $o > $o] : ( A @ ( product_Pair_o_o_o_o @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_old_Oprod_Oinducts) ).
thf(167,plain,
! [A: product_prod_o_o_o_o > $o,B: product_prod_o_o_o_o] :
( ! [C: $o > $o,D: $o > $o] : ( A @ ( product_Pair_o_o_o_o @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,axiom,
! [A: produc809931564nres_d] :
~ ! [B: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc1910095910nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_old_Oprod_Oexhaust) ).
thf(2984,plain,
! [A: produc809931564nres_d] :
~ ! [B: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc1910095910nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(36,axiom,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr613277282nres_d,D: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ A @ B ) @ C )
=> ( ( autore233619284nres_b @ A @ D )
=> ( member660096835nres_d @ ( produc1910095910nres_d @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_autoref__REMOVE__INTERNAL__EQ) ).
thf(2816,plain,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr613277282nres_d,D: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ A @ B ) @ C )
=> ( ( autore233619284nres_b @ A @ D )
=> ( member660096835nres_d @ ( produc1910095910nres_d @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(69,axiom,
! [A: set_Product_prod_d_b] : ( member994209571nres_b @ ( produc83262214nres_b @ refine2063221607TURN_d @ refine2063221605TURN_b ) @ ( relAPP1523780267nres_b @ ( relAPP1311256519nres_b @ fun_re934539163nres_b @ A ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_autoref__RETURN) ).
thf(2952,plain,
! [A: set_Product_prod_d_b] : ( member994209571nres_b @ ( produc83262214nres_b @ refine2063221607TURN_d @ refine2063221605TURN_b ) @ ( relAPP1523780267nres_b @ ( relAPP1311256519nres_b @ fun_re934539163nres_b @ A ) @ ( relAPP821124455nres_b @ refine1072887132el_d_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(138,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > refine432681134nres_b,E: c > refine449204144nres_d,F: set_Pr1640496404nres_d] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( D @ H ) @ ( autore1981686764nres_d @ E @ G ) ) @ F ) ) )
=> ( member1578111221nres_d
@ ( produc2147164944nres_d @ ( D @ A )
@ ( autore1159379066nres_d
@ ( autore430131799nres_d
@ ( autore241567778nres_d
@ ( autore2004709357nres_d
@ ^ [G: c,H: c > refine449204144nres_d] : ( H @ G ) )
@ ( autore349294361nres_d @ ( relAPP1354295571nres_d @ ( relAPP1135042155nres_d @ fun_re1089848935nres_d @ C ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_autoref__Let__cong) ).
thf(3193,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: a > refine432681134nres_b,E: c > refine449204144nres_d,F: set_Pr1640496404nres_d] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ! [G: c] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ H @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( D @ H ) @ ( autore1981686764nres_d @ E @ G ) ) @ F ) ) )
=> ( member1578111221nres_d
@ ( produc2147164944nres_d @ ( D @ A )
@ ( autore1159379066nres_d
@ ( autore430131799nres_d
@ ( autore241567778nres_d
@ ( autore2004709357nres_d
@ ^ [G: c,H: c > refine449204144nres_d] : ( H @ G ) )
@ ( autore349294361nres_d @ ( relAPP1354295571nres_d @ ( relAPP1135042155nres_d @ fun_re1089848935nres_d @ C ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(5,axiom,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Pr896671762nres_b,D: refine432681134nres_b,E: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ C ) )
=> ( ( D
= ( B @ E ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( A @ E ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_fun__relE1) ).
thf(162,plain,
! [A: a > refine432681134nres_b,B: a > refine432681134nres_b,C: set_Pr896671762nres_b,D: refine432681134nres_b,E: a] :
( ( member369653087nres_b @ ( produc809128386nres_b @ A @ B ) @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ C ) )
=> ( ( D
= ( B @ E ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( A @ E ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: produc809931564nres_d,B: produc809931564nres_d > $o] :
( ( member660096835nres_d @ A @ ( collec1321668993nres_d @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_mem__Collect__eq) ).
thf(2684,plain,
! [A: produc809931564nres_d,B: produc809931564nres_d > $o] :
( ( member660096835nres_d @ A @ ( collec1321668993nres_d @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(67,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Oprod_Oinject) ).
thf(2942,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(47,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Pr589481214nres_d,D: a > refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ C )
=> ( ( autore519998265nres_b @ A @ D )
=> ( member936907743nres_d @ ( produc210841666nres_d @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_autoref__REMOVE__INTERNAL__EQ) ).
thf(2863,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Pr589481214nres_d,D: a > refine432681134nres_b] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ C )
=> ( ( autore519998265nres_b @ A @ D )
=> ( member936907743nres_d @ ( produc210841666nres_d @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(116,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: c,F: refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( ( B @ E )
= F )
=> ! [G: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ G @ E ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ G ) @ F ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_fun__relD2) ).
thf(3112,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: c,F: refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( ( B @ E )
= F )
=> ! [G: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ G @ E ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ G ) @ F ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(13,axiom,
! [A: product_prod_o_o_o_o > $o,B: product_prod_o_o_o_o] :
( ! [C: $o > $o,D: $o > $o] : ( A @ ( product_Pair_o_o_o_o @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_prod__cases) ).
thf(2661,plain,
! [A: product_prod_o_o_o_o > $o,B: product_prod_o_o_o_o] :
( ! [C: $o > $o,D: $o > $o] : ( A @ ( product_Pair_o_o_o_o @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(106,axiom,
! [A: b,B: d,C: set_Product_prod_b_d,D: b > refine432681134nres_b,E: d > refine449204144nres_d,F: set_Pr1640496404nres_d] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ A @ B ) @ C )
=> ( ! [G: d] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: b] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ H @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( D @ H ) @ ( autore121452781nres_d @ E @ G ) ) @ F ) ) )
=> ( member1578111221nres_d
@ ( produc2147164944nres_d @ ( D @ A )
@ ( autore38794169nres_d
@ ( autore48395543nres_d
@ ( autore1505592162nres_d
@ ( autore1121250093nres_d
@ ^ [G: d,H: d > refine449204144nres_d] : ( H @ G ) )
@ ( autore486670105nres_d @ ( relAPP486948753nres_d @ ( relAPP1996600361nres_d @ fun_re1101734569nres_d @ C ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_autoref__Let__cong) ).
thf(3082,plain,
! [A: b,B: d,C: set_Product_prod_b_d,D: b > refine432681134nres_b,E: d > refine449204144nres_d,F: set_Pr1640496404nres_d] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ A @ B ) @ C )
=> ( ! [G: d] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: b] :
( ( member1302463506od_b_d @ ( product_Pair_b_d @ H @ G ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( D @ H ) @ ( autore121452781nres_d @ E @ G ) ) @ F ) ) )
=> ( member1578111221nres_d
@ ( produc2147164944nres_d @ ( D @ A )
@ ( autore38794169nres_d
@ ( autore48395543nres_d
@ ( autore1505592162nres_d
@ ( autore1121250093nres_d
@ ^ [G: d,H: d > refine449204144nres_d] : ( H @ G ) )
@ ( autore486670105nres_d @ ( relAPP486948753nres_d @ ( relAPP1996600361nres_d @ fun_re1101734569nres_d @ C ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(152,axiom,
! [A: set_Product_prod_a_c,B: set_Pr1640496404nres_d] :
( member189721481nres_d
@ ( produc627868012nres_d
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C )
@ ^ [C: c,D: c > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1354295571nres_d @ ( relAPP1135042155nres_d @ fun_re1089848935nres_d @ A ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_autoref__Let) ).
thf(3228,plain,
! [A: set_Product_prod_a_c,B: set_Pr1640496404nres_d] :
( member189721481nres_d
@ ( produc627868012nres_d
@ ^ [C: a,D: a > refine432681134nres_b] : ( D @ C )
@ ^ [C: c,D: c > refine449204144nres_d] : ( D @ C ) )
@ ( relAPP1354295571nres_d @ ( relAPP1135042155nres_d @ fun_re1089848935nres_d @ A ) @ ( relAPP813854073nres_d @ ( relAPP98076839nres_d @ fun_re1394577105nres_d @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(44,axiom,
! [A: produc2103861704nres_d] :
? [B: a > refine432681134nres_b,C: c > refine449204144nres_d] :
( A
= ( produc210841666nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_surj__pair) ).
thf(2850,plain,
! [A: produc2103861704nres_d] :
? [B: a > refine432681134nres_b,C: c > refine449204144nres_d] :
( A
= ( produc210841666nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [A: produc809931564nres_d > $o,B: produc809931564nres_d] :
( ! [C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc1910095910nres_d @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_prod__cases) ).
thf(2831,plain,
! [A: produc809931564nres_d > $o,B: produc809931564nres_d] :
( ! [C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] : ( A @ ( produc1910095910nres_d @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(20,axiom,
! [A: produc2103861704nres_d,B: produc2103861704nres_d > $o] :
( ( member936907743nres_d @ A @ ( collec1639315997nres_d @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_mem__Collect__eq) ).
thf(2689,plain,
! [A: produc2103861704nres_d,B: produc2103861704nres_d > $o] :
( ( member936907743nres_d @ A @ ( collec1639315997nres_d @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(141,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_tagged__fun__relD__both) ).
thf(3202,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: set_Product_prod_a_c,D: set_Pr1640496404nres_d,E: a,F: c] :
( ( member936907743nres_d @ ( produc210841666nres_d @ A @ B ) @ ( relAPP900772393nres_d @ ( relAPP1270454529nres_d @ fun_re1760530651nres_d @ C ) @ D ) )
=> ( ( member466432594od_a_c @ ( product_Pair_a_c @ E @ F ) @ C )
=> ( member1578111221nres_d @ ( produc2147164944nres_d @ ( A @ E ) @ ( B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(91,axiom,
! [A: produc1677145714nres_d,B: produc1677145714nres_d > $o] :
( ( member189721481nres_d @ A @ ( collec554837959nres_d @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_mem__Collect__eq) ).
thf(3026,plain,
! [A: produc1677145714nres_d,B: produc1677145714nres_d > $o] :
( ( member189721481nres_d @ A @ ( collec554837959nres_d @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24,axiom,
! [A: product_prod_a_c > $o,B: product_prod_a_c] :
( ! [C: a,D: c] : ( A @ ( product_Pair_a_c @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_prod__cases) ).
thf(2701,plain,
! [A: product_prod_a_c > $o,B: product_prod_a_c] :
( ! [C: a,D: c] : ( A @ ( product_Pair_a_c @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(100,axiom,
! [A: product_prod_a_c,B: product_prod_a_c > $o] :
( ( member466432594od_a_c @ A @ ( collec662378644od_a_c @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_mem__Collect__eq) ).
thf(3063,plain,
! [A: product_prod_a_c,B: product_prod_a_c > $o] :
( ( member466432594od_a_c @ A @ ( collec662378644od_a_c @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_old_Oprod_Oinject) ).
thf(182,plain,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
! [A: b,B: b > refine432681134nres_b] :
( ( refine1264602246nd_b_b @ ( refine2063221605TURN_b @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_nres__monad1) ).
thf(2975,plain,
! [A: b,B: b > refine432681134nres_b] :
( ( refine1264602246nd_b_b @ ( refine2063221605TURN_b @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(150,axiom,
! [A: set_Product_prod_b_d,B: set_Product_prod_b_d] : ( member30090369nres_d @ ( produc2035736420nres_d @ refine1264602246nd_b_b @ refine772657414nd_d_d ) @ ( relAPP691268197nres_d @ ( relAPP1711926383nres_d @ fun_re1488118943nres_d @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_param__bind) ).
thf(3224,plain,
! [A: set_Product_prod_b_d,B: set_Product_prod_b_d] : ( member30090369nres_d @ ( produc2035736420nres_d @ refine1264602246nd_b_b @ refine772657414nd_d_d ) @ ( relAPP691268197nres_d @ ( relAPP1711926383nres_d @ fun_re1488118943nres_d @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) @ ( relAPP1676317369nres_d @ ( relAPP1405476647nres_d @ fun_re884113425nres_d @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(32,axiom,
! [A: $o > $o,B: $o > $o,C: set_Pr934623755_o_o_o,D: ( $o > $o ) > a,E: ( $o > $o ) > c,F: set_Product_prod_a_c] :
( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ A @ B ) @ C )
=> ( ! [G: $o > $o] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: $o > $o] :
( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ H @ G ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( D @ H ) @ ( autoref_APP_o_o_c @ E @ G ) ) @ F ) ) )
=> ( member466432594od_a_c
@ ( product_Pair_a_c @ ( D @ A )
@ ( autoref_APP_o_o_c_c
@ ( autore1733926270_o_c_c
@ ( autore867490625_o_c_c
@ ( autore971224502_o_c_c
@ ^ [G: $o > $o,H: ( $o > $o ) > c] : ( H @ G ) )
@ ( autore821969498_o_c_c @ ( relAPP1562327022_o_c_c @ ( relAPP2129980178_o_c_c @ fun_re1144975870_o_c_c @ C ) @ ( relAPP1774770060_o_c_c @ ( relAPP412764446_o_c_c @ fun_re1859931662_c_a_c @ ( relAPP970620078_o_o_c @ ( relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_autoref__Let__cong) ).
thf(2728,plain,
! [A: $o > $o,B: $o > $o,C: set_Pr934623755_o_o_o,D: ( $o > $o ) > a,E: ( $o > $o ) > c,F: set_Product_prod_a_c] :
( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ A @ B ) @ C )
=> ( ! [G: $o > $o] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: $o > $o] :
( ( member250723412_o_o_o @ ( product_Pair_o_o_o_o @ H @ G ) @ C )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ ( D @ H ) @ ( autoref_APP_o_o_c @ E @ G ) ) @ F ) ) )
=> ( member466432594od_a_c
@ ( product_Pair_a_c @ ( D @ A )
@ ( autoref_APP_o_o_c_c
@ ( autore1733926270_o_c_c
@ ( autore867490625_o_c_c
@ ( autore971224502_o_c_c
@ ^ [G: $o > $o,H: ( $o > $o ) > c] : ( H @ G ) )
@ ( autore821969498_o_c_c @ ( relAPP1562327022_o_c_c @ ( relAPP2129980178_o_c_c @ fun_re1144975870_o_c_c @ C ) @ ( relAPP1774770060_o_c_c @ ( relAPP412764446_o_c_c @ fun_re1859931662_c_a_c @ ( relAPP970620078_o_o_c @ ( relAPP1750172554_o_o_c @ fun_rel_o_o_o_o_a_c @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(54,axiom,
! [A: $o,B: $o,C: refine432681134nres_b,D: refine432681134nres_b,E: set_Product_prod_b_b] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ C @ D ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ E ) ) ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( refine1437029928_bnd_b @ B @ C ) @ ( refine1437029928_bnd_b @ A @ D ) ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_param__op__nres__ASSERT__bnd) ).
thf(2892,plain,
! [A: $o,B: $o,C: refine432681134nres_b,D: refine432681134nres_b,E: set_Product_prod_b_b] :
( ( A
=> B )
=> ( ( A
=> ( B
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ C @ D ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ E ) ) ) )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( refine1437029928_bnd_b @ B @ C ) @ ( refine1437029928_bnd_b @ A @ D ) ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(128,axiom,
( relAPP511982311nres_d
= ( ^ [A: set_Pr797615136nres_d > set_Pr24800800nres_d] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_relAPP__def) ).
thf(3156,plain,
( relAPP511982311nres_d
= ( ^ [A: set_Pr797615136nres_d > set_Pr24800800nres_d] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(43,axiom,
! [A: set_Product_prod_a_a] : ( member1680325597nres_a @ ( produc278407104nres_a @ refine2063221604TURN_a @ refine2063221604TURN_a ) @ ( relAPP907138281nres_a @ ( relAPP439940547nres_a @ fun_re843975451nres_a @ A ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_autoref__RETURN) ).
thf(2848,plain,
! [A: set_Product_prod_a_a] : ( member1680325597nres_a @ ( produc278407104nres_a @ refine2063221604TURN_a @ refine2063221604TURN_a ) @ ( relAPP907138281nres_a @ ( relAPP439940547nres_a @ fun_re843975451nres_a @ A ) @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,axiom,
! [A: b > refine424419629nres_a,B: d > refine440942639nres_c,C: set_Product_prod_b_d,D: set_Pr1128439124nres_c,E: b,F: d] :
( ( member2086976541nres_c @ ( produc316577664nres_c @ A @ B ) @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ C ) @ D ) )
=> ( ( member1302463506od_b_d @ ( product_Pair_b_d @ E @ F ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( autore1669652584nres_a @ A @ E ) @ ( autore113191276nres_c @ B @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_autoref__APP) ).
thf(3007,plain,
! [A: b > refine424419629nres_a,B: d > refine440942639nres_c,C: set_Product_prod_b_d,D: set_Pr1128439124nres_c,E: b,F: d] :
( ( member2086976541nres_c @ ( produc316577664nres_c @ A @ B ) @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ C ) @ D ) )
=> ( ( member1302463506od_b_d @ ( product_Pair_b_d @ E @ F ) @ C )
=> ( member1600573749nres_c @ ( produc1153446608nres_c @ ( autore1669652584nres_a @ A @ E ) @ ( autore113191276nres_c @ B @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(117,axiom,
( relAPP98076839nres_d
= ( ^ [A: set_Pr589481214nres_d > set_Pr1640496404nres_d > set_Pr797615136nres_d] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_relAPP__def) ).
thf(3117,plain,
( relAPP98076839nres_d
= ( ^ [A: set_Pr589481214nres_d > set_Pr1640496404nres_d > set_Pr797615136nres_d] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(46,axiom,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Oinject) ).
thf(2860,plain,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: produc1757587562nres_d] :
? [B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc2075136412nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_surj__pair) ).
thf(2722,plain,
! [A: produc1757587562nres_d] :
? [B: ( a > refine432681134nres_b ) > refine432681134nres_b,C: ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
= ( produc2075136412nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(133,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_b_b] : ( member1700179713nres_b @ ( produc1992182244nres_b @ refine436832839nd_a_b @ refine436832839nd_a_b ) @ ( relAPP869047273nres_b @ ( relAPP1111247343nres_b @ fun_re2045802267nres_b @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ A ) ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ B ) ) ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_param__bind) ).
thf(3168,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_b_b] : ( member1700179713nres_b @ ( produc1992182244nres_b @ refine436832839nd_a_b @ refine436832839nd_a_b ) @ ( relAPP869047273nres_b @ ( relAPP1111247343nres_b @ fun_re2045802267nres_b @ ( relAPP1642956907nres_a @ refine737062558el_a_a @ A ) ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ B ) ) ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(56,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ( autore1904863386L_EQ_a @ A @ D )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_autoref__REMOVE__INTERNAL__EQ) ).
thf(2907,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: a] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ( autore1904863386L_EQ_a @ A @ D )
=> ( member466432594od_a_c @ ( product_Pair_a_c @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(26,axiom,
( relAPP281291371nres_b
= ( ^ [A: set_Product_prod_b_b > set_Pr896671762nres_b] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_relAPP__def) ).
thf(2707,plain,
( relAPP281291371nres_b
= ( ^ [A: set_Product_prod_b_b > set_Pr896671762nres_b] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(80,axiom,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pair__inject) ).
thf(2988,plain,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(45,axiom,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Pair__inject) ).
thf(2853,plain,
! [A: a > refine432681134nres_b,B: c > refine449204144nres_d,C: a > refine432681134nres_b,D: c > refine449204144nres_d] :
( ( ( produc210841666nres_d @ A @ B )
= ( produc210841666nres_d @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(148,axiom,
! [A: set_Product_prod_a_c] : ( member100096605nres_c @ ( produc1827604032nres_c @ refine2063221604TURN_a @ refine2063221606TURN_c ) @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_autoref__RETURN) ).
thf(3220,plain,
! [A: set_Product_prod_a_c] : ( member100096605nres_c @ ( produc1827604032nres_c @ refine2063221604TURN_a @ refine2063221606TURN_c ) @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(154,axiom,
! [A: set_Product_prod_b_d] : ( member776304031nres_d @ ( produc847298946nres_d @ refine2063221605TURN_b @ refine2063221607TURN_d ) @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_autoref__RETURN) ).
thf(3235,plain,
! [A: set_Product_prod_b_d] : ( member776304031nres_d @ ( produc847298946nres_d @ refine2063221605TURN_b @ refine2063221607TURN_d ) @ ( relAPP446928935nres_d @ ( relAPP1806806463nres_d @ fun_re55451291nres_d @ A ) @ ( relAPP1313094511nres_d @ refine1564831968el_b_d @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(34,axiom,
! [A: set_Product_prod_b_d,B: set_Pr1128439124nres_c] :
( member228973321nres_c
@ ( produc1961734380nres_c
@ ^ [C: b,D: b > refine424419629nres_a] : ( D @ C )
@ ^ [C: d,D: d > refine440942639nres_c] : ( D @ C ) )
@ ( relAPP131141393nres_c @ ( relAPP2017502121nres_c @ fun_re430551721nres_c @ A ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ A ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_autoref__Let) ).
thf(2811,plain,
! [A: set_Product_prod_b_d,B: set_Pr1128439124nres_c] :
( member228973321nres_c
@ ( produc1961734380nres_c
@ ^ [C: b,D: b > refine424419629nres_a] : ( D @ C )
@ ^ [C: d,D: d > refine440942639nres_c] : ( D @ C ) )
@ ( relAPP131141393nres_c @ ( relAPP2017502121nres_c @ fun_re430551721nres_c @ A ) @ ( relAPP489595641nres_c @ ( relAPP1790450405nres_c @ fun_re1366722255nres_c @ ( relAPP1564590053nres_c @ ( relAPP709871101nres_c @ fun_re1209216603nres_c @ A ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(113,axiom,
( refine746536475nres_d
= ( ^ [A: set_Pr589481214nres_d,B: ( c > refine449204144nres_d ) > $o,C: a > refine432681134nres_b] :
? [D: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_lift__assn__def) ).
thf(3104,plain,
( refine746536475nres_d
= ( ^ [A: set_Pr589481214nres_d,B: ( c > refine449204144nres_d ) > $o,C: a > refine432681134nres_b] :
? [D: c > refine449204144nres_d] :
( ( member936907743nres_d @ ( produc210841666nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(29,axiom,
! [A: refine440942639nres_c] :
( ( refine2092371654nd_c_c @ A @ refine2063221606TURN_c )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_nres__monad2) ).
thf(2719,plain,
! [A: refine440942639nres_c] :
( ( refine2092371654nd_c_c @ A @ refine2063221606TURN_c )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(111,axiom,
( ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ id_Ref1256934482nres_b )
= id_a_R351071993nres_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_fun__rel__id__simp) ).
thf(3100,plain,
( ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ id_a ) @ id_Ref1256934482nres_b )
= id_a_R351071993nres_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(25,axiom,
! [A: produc1757587562nres_d,B: produc1757587562nres_d > $o] :
( ( member461830657nres_d @ A @ ( collec1671161663nres_d @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_mem__Collect__eq) ).
thf(2704,plain,
! [A: produc1757587562nres_d,B: produc1757587562nres_d > $o] :
( ( member461830657nres_d @ A @ ( collec1671161663nres_d @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(73,axiom,
! [A: produc1677145714nres_d] :
~ ! [B: a > ( a > refine432681134nres_b ) > refine432681134nres_b,C: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc627868012nres_d @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_old_Oprod_Oexhaust) ).
thf(2961,plain,
! [A: produc1677145714nres_d] :
~ ! [B: a > ( a > refine432681134nres_b ) > refine432681134nres_b,C: c > ( c > refine449204144nres_d ) > refine449204144nres_d] :
( A
!= ( produc627868012nres_d @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(58,axiom,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_prod_Oinject) ).
thf(2913,plain,
! [A: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,B: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b,D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( ( produc1910095910nres_d @ A @ B )
= ( produc1910095910nres_d @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(98,axiom,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_prod_Oinject) ).
thf(3057,plain,
! [A: a,B: c,C: a,D: c] :
( ( ( product_Pair_a_c @ A @ B )
= ( product_Pair_a_c @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(19,axiom,
( refine1711024813nres_d
= ( ^ [A: set_Pr613277282nres_d,B: ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b] :
? [D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_lift__assn__def) ).
thf(2687,plain,
( refine1711024813nres_d
= ( ^ [A: set_Pr613277282nres_d,B: ( ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d ) > $o,C: ( a > refine432681134nres_b ) > ( ( a > refine432681134nres_b ) > refine432681134nres_b ) > refine432681134nres_b] :
? [D: ( c > refine449204144nres_d ) > ( ( c > refine449204144nres_d ) > refine449204144nres_d ) > refine449204144nres_d] :
( ( member660096835nres_d @ ( produc1910095910nres_d @ C @ D ) @ A )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [A: product_prod_o_o_o_o] :
~ ! [B: $o > $o,C: $o > $o] :
( A
!= ( product_Pair_o_o_o_o @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_old_Oprod_Oexhaust) ).
thf(178,plain,
! [A: product_prod_o_o_o_o] :
~ ! [B: $o > $o,C: $o > $o] :
( A
!= ( product_Pair_o_o_o_o @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(87,axiom,
! [A: set_Product_prod_a_a,B: set_Pr896671762nres_b] :
( ( A = id_a )
=> ( ( B = id_Ref1256934482nres_b )
=> ( ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ B )
= id_a_R351071993nres_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_fun__rel__id) ).
thf(3013,plain,
! [A: set_Product_prod_a_a,B: set_Pr896671762nres_b] :
( ( A = id_a )
=> ( ( B = id_Ref1256934482nres_b )
=> ( ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ A ) @ B )
= id_a_R351071993nres_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(11,axiom,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_prod_Oinject) ).
thf(803,plain,
! [A: $o > $o,B: $o > $o,C: $o > $o,D: $o > $o] :
( ( ( product_Pair_o_o_o_o @ A @ B )
= ( product_Pair_o_o_o_o @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(82,axiom,
! [A: set_Pr613277282nres_d] :
( ( collec1321668993nres_d
@ ^ [B: produc809931564nres_d] : ( member660096835nres_d @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__mem__eq) ).
thf(2998,plain,
! [A: set_Pr613277282nres_d] :
( ( collec1321668993nres_d
@ ^ [B: produc809931564nres_d] : ( member660096835nres_d @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(48,axiom,
! [A: set_Product_prod_b_b] : ( member209049375nres_b @ ( produc1445585666nres_b @ refine2063221605TURN_b @ refine2063221605TURN_b ) @ ( relAPP1483117353nres_b @ ( relAPP2073227843nres_b @ fun_re132614427nres_b @ A ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_autoref__RETURN) ).
thf(2866,plain,
! [A: set_Product_prod_b_b] : ( member209049375nres_b @ ( produc1445585666nres_b @ refine2063221605TURN_b @ refine2063221605TURN_b ) @ ( relAPP1483117353nres_b @ ( relAPP2073227843nres_b @ fun_re132614427nres_b @ A ) @ ( relAPP281291371nres_b @ refine1564831966el_b_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(96,axiom,
! [A: a,B: c,C: set_Product_prod_a_c,D: c > $o] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine321891363sn_a_c @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_lift__assnI) ).
thf(3052,plain,
! [A: a,B: c,C: set_Product_prod_a_c,D: c > $o] :
( ( member466432594od_a_c @ ( product_Pair_a_c @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine321891363sn_a_c @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(39,axiom,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr2080238504nres_d,D: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member189721481nres_d @ ( produc627868012nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine408412177nres_d @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_lift__assnI) ).
thf(2834,plain,
! [A: a > ( a > refine432681134nres_b ) > refine432681134nres_b,B: c > ( c > refine449204144nres_d ) > refine449204144nres_d,C: set_Pr2080238504nres_d,D: ( c > ( c > refine449204144nres_d ) > refine449204144nres_d ) > $o] :
( ( member189721481nres_d @ ( produc627868012nres_d @ A @ B ) @ C )
=> ( ( D @ B )
=> ( refine408412177nres_d @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(140,axiom,
! [A: set_Product_prod_a_c,B: set_Product_prod_a_c] : ( member1751415169nres_c @ ( produc2073916516nres_c @ refine436832838nd_a_a @ refine2092371654nd_c_c ) @ ( relAPP765626983nres_c @ ( relAPP177337967nres_c @ fun_re1915547295nres_c @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_param__bind) ).
thf(3200,plain,
! [A: set_Product_prod_a_c,B: set_Product_prod_a_c] : ( member1751415169nres_c @ ( produc2073916516nres_c @ refine436832838nd_a_a @ refine2092371654nd_c_c ) @ ( relAPP765626983nres_c @ ( relAPP177337967nres_c @ fun_re1915547295nres_c @ ( relAPP527276399nres_c @ refine737062560el_a_c @ A ) ) @ ( relAPP1774615993nres_c @ ( relAPP483050597nres_c @ fun_re1877185935nres_c @ ( relAPP2018433511nres_c @ ( relAPP173519167nres_c @ fun_re766812315nres_c @ A ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) @ ( relAPP527276399nres_c @ refine737062560el_a_c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(94,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > refine432681134nres_b,E: a > refine432681134nres_b,F: set_Pr896671762nres_b] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ! [G: a] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ H @ G ) @ C )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( D @ H ) @ ( autore1390664424nres_b @ E @ G ) ) @ F ) ) )
=> ( member1446466291nres_b
@ ( produc2130641934nres_b @ ( D @ A )
@ ( autore956252284nres_b
@ ( autore781669463nres_b
@ ( autore1290907938nres_b
@ ( autore906565869nres_b
@ ^ [G: a,H: a > refine432681134nres_b] : ( H @ G ) )
@ ( autore16598297nres_b @ ( relAPP91071253nres_b @ ( relAPP1740535279nres_b @ fun_re1165441639nres_b @ C ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_autoref__Let__cong) ).
thf(3035,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > refine432681134nres_b,E: a > refine432681134nres_b,F: set_Pr896671762nres_b] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ! [G: a] :
( ( autore1113312320RNAL_o @ ( B = G ) )
=> ! [H: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ H @ G ) @ C )
=> ( member1446466291nres_b @ ( produc2130641934nres_b @ ( D @ H ) @ ( autore1390664424nres_b @ E @ G ) ) @ F ) ) )
=> ( member1446466291nres_b
@ ( produc2130641934nres_b @ ( D @ A )
@ ( autore956252284nres_b
@ ( autore781669463nres_b
@ ( autore1290907938nres_b
@ ( autore906565869nres_b
@ ^ [G: a,H: a > refine432681134nres_b] : ( H @ G ) )
@ ( autore16598297nres_b @ ( relAPP91071253nres_b @ ( relAPP1740535279nres_b @ fun_re1165441639nres_b @ C ) @ ( relAPP2095637113nres_b @ ( relAPP1293188647nres_b @ fun_re1579405647nres_b @ ( relAPP1936960811nres_b @ ( relAPP1536875909nres_b @ fun_re1837693787nres_b @ C ) @ F ) ) @ F ) ) ) )
@ B )
@ E ) )
@ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(3239,plain,
$false,
inference(e,[status(thm)],[2956,3021,2889,2921,3230,3040,3098,2837,3185,170,3004,3135,2918,2933,2712,2844,2972,2886,2819,2916,3029,2667,2682,2698,3131,2925,3093,3152,2809,3226,2965,2954,2910,3069,3154,3207,2670,3144,3090,3198,156,2841,2709,3218,2692,3102,3119,3205,3001,3060,3087,3018,3141,3210,2868,3032,2978,1424,3010,173,3222,2813,3162,3215,3109,3074,3147,2883,3190,2995,2904,3079,3158,2938,2981,2695,2959,3213,3023,3077,3170,159,3106,2945,3138,2871,3160,3182,3066,3165,2923,2664,155,2928,3133,3055,2725,167,2984,2816,2952,3193,162,2684,2942,2863,3112,2661,3082,3228,2850,2831,2689,3202,3026,2701,3063,182,2975,3224,2728,2892,3156,2848,3007,3117,2860,2722,3168,2907,2707,2988,2853,3220,3235,2811,3104,2719,3100,2704,2961,2913,3057,2687,178,3013,803,2998,2866,3052,2834,3200,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP160^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 15:27:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.04/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.50/1.33 % [INFO] Parsing done (387ms).
% 2.50/1.34 % [INFO] Running in sequential loop mode.
% 3.17/1.61 % [INFO] eprover registered as external prover.
% 3.17/1.62 % [INFO] cvc4 registered as external prover.
% 3.17/1.62 % [INFO] Scanning for conjecture ...
% 3.70/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ...
% 4.44/2.00 % [INFO] Axiom selection finished. Selected 152 axioms (removed 198 axioms).
% 5.20/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 5.20/2.20 % [INFO] Type checking passed.
% 5.20/2.21 % [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 ...
% 29.65/8.96 % External prover 'e' found a proof!
% 29.65/8.96 % [INFO] Killing All external provers ...
% 29.65/8.96 % Time passed: 8446ms (effective reasoning time: 7615ms)
% 29.65/8.96 % 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)>
% 29.65/8.97 % Axioms used in derivation (152): fact_139_old_Oprod_Oinducts, fact_127_lift__assnI, fact_187_relAPP__def, fact_56_tagged__fun__relD__lhs, fact_209_param__op__nres__ASSERT__bnd, fact_338_fun__rel__id, fact_236_autoref__Let__cong, fact_0_param__bind, fact_29_autoref__Let, fact_168_prod__cases, fact_185_relAPP__def, fact_114_autoref__APP, fact_46_fun__relD2, fact_212_param__op__nres__ASSERT__bnd, fact_182_relAPP__def, fact_205_autoref__RETURN, fact_160_prod__cases, fact_186_relAPP__def, fact_175_surj__pair, fact_26_autoref__Let, fact_294_fun__rel__id__simp, fact_254_autoref__REMOVE__INTERNAL__EQ, fact_159_Pair__inject, fact_157_Pair__inject, fact_25_autoref__Let, fact_95_prod_Oinject, fact_66_tagged__fun__relD__rhs, fact_109_old_Oprod_Oinject, fact_111_autoref__APP, fact_203_autoref__RETURN, fact_195_lift__assn__def, fact_108_old_Oprod_Oinject, fact_206_autoref__RETURN, fact_106_old_Oprod_Oinject, fact_273_Collect__mem__eq, fact_21_autoref__Let, fact_130_old_Oprod_Oinducts, fact_3_param__bind, fact_72_tagged__fun__relD__both, fact_210_param__op__nres__ASSERT__bnd, fact_2_param__bind, fact_263_mem__Collect__eq, fact_272_Collect__mem__eq, fact_219_fun__relE2, fact_12_fun__relI, fact_7_param__bind, fact_107_old_Oprod_Oinject, fact_156_Pair__inject, fact_150_Pair__inject, fact_155_Pair__inject, fact_284_nres__monad2, fact_235_autoref__Let__cong, fact_52_tagged__fun__relD__lhs, fact_264_mem__Collect__eq, fact_261_mem__Collect__eq, fact_169_prod__cases, fact_181_relAPP__def, fact_198_lift__assn__def, fact_275_nres__monad1, fact_118_autoref__APP, fact_105_old_Oprod_Oinject, fact_100_old_Oprod_Oinject, fact_145_old_Oprod_Oexhaust, fact_1_param__bind, fact_242_autoref__Let__cong, fact_28_autoref__Let, fact_115_autoref__APP, fact_250_autoref__REMOVE__INTERNAL__EQ, fact_5_param__bind, fact_117_autoref__APP, fact_148_old_Oprod_Oexhaust, fact_253_autoref__REMOVE__INTERNAL__EQ, fact_91_prod_Oinject, fact_149_old_Oprod_Oexhaust, fact_276_nres__monad1, fact_196_lift__assn__def, fact_126_lift__assnI, fact_8_param__bind, fact_178_surj__pair, fact_86_tagged__fun__relD__none, fact_92_prod_Oinject, fact_207_param__op__nres__ASSERT__bnd, fact_23_autoref__Let, fact_176_surj__pair, fact_280_nres__monad1, fact_136_old_Oprod_Oinducts, fact_274_Collect__mem__eq, fact_283_nres__monad2, fact_6_param__bind, fact_282_nres__monad2, fact_262_mem__Collect__eq, fact_279_nres__monad1, fact_202_autoref__RETURN, fact_113_autoref__APP, fact_116_autoref__APP, fact_270_Collect__mem__eq, fact_188_relAPP__def, fact_281_nres__monad1, fact_82_tagged__fun__relD__none, fact_128_lift__assnI, fact_201_autoref__RETURN, fact_42_fun__relD2, fact_243_autoref__Let__cong, fact_9_param__bind, fact_179_surj__pair, fact_146_old_Oprod_Oexhaust, fact_158_Pair__inject, fact_137_old_Oprod_Oinducts, fact_278_nres__monad1, fact_16_fun__relI, fact_166_prod__cases, fact_147_old_Oprod_Oexhaust, fact_211_param__op__nres__ASSERT__bnd, fact_237_autoref__Let__cong, fact_238_autoref__Let__cong, fact_229_fun__relE1, fact_93_prod_Oinject, fact_125_lift__assnI, fact_170_surj__pair, fact_140_old_Oprod_Oexhaust, fact_32_fun__relD1, fact_177_surj__pair, fact_135_old_Oprod_Oinducts, fact_76_tagged__fun__relD__both, fact_277_nres__monad1, fact_183_relAPP__def, fact_138_old_Oprod_Oinducts, fact_119_autoref__APP, fact_260_mem__Collect__eq, fact_240_autoref__Let__cong, fact_90_prod_Oinject, fact_199_lift__assn__def, fact_129_lift__assnI, fact_251_autoref__REMOVE__INTERNAL__EQ, fact_208_param__op__nres__ASSERT__bnd, fact_184_relAPP__def, fact_271_Collect__mem__eq, fact_197_lift__assn__def, fact_180_relAPP__def, fact_27_autoref__Let, fact_213_param__op__nres__ASSERT__bnd, fact_167_prod__cases, fact_94_prod_Oinject, fact_252_autoref__REMOVE__INTERNAL__EQ, fact_200_autoref__RETURN, fact_189_relAPP__def, fact_204_autoref__RETURN, fact_4_param__bind, fact_36_fun__relD1, fact_62_tagged__fun__relD__rhs, fact_165_prod__cases, fact_239_autoref__Let__cong
% 29.65/8.97 % No. of inferences in proof: 308
% 29.65/8.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8446 ms resp. 7615 ms w/o parsing
% 30.53/9.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.53/9.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------