%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT171_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:28 AM UTC 2026
% Result : Theorem 22.91s 7.70s
% Output : Refutation 24.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 239
% Syntax : Number of formulae : 480 ( 186 unt; 0 typ; 0 def)
% Number of atoms : 1287 ( 327 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 7576 ( 260 ~; 21 |; 95 &;6509 @)
% ( 50 <=>; 641 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 110 ( 109 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 212 ( 210 usr; 60 con; 0-2 aty)
% Number of variables : 1155 ( 0 ^;1153 !; 2 ?;1155 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_1621810872le_alt_type,type,
arrow_1621810872le_alt: $tType ).
thf(arrow_501706939e_indi_type,type,
arrow_501706939e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(fun_Ar154839667t_bool_type,type,
fun_Ar154839667t_bool: $tType ).
thf(fun_Ar1822233582t_bool_type,type,
fun_Ar1822233582t_bool: $tType ).
thf(fun_Ar1871347069i_bool_type,type,
fun_Ar1871347069i_bool: $tType ).
thf(fun_Ar2035712896di_nat_type,type,
fun_Ar2035712896di_nat: $tType ).
thf(fun_Ar2079322857t_bool_type,type,
fun_Ar2079322857t_bool: $tType ).
thf(fun_Ar1757019876t_bool_type,type,
fun_Ar1757019876t_bool: $tType ).
thf(fun_Ar1200683263t_bool_type,type,
fun_Ar1200683263t_bool: $tType ).
thf(fun_Ar156616864t_bool_type,type,
fun_Ar156616864t_bool: $tType ).
thf(fun_Ar1784032663l_bool_type,type,
fun_Ar1784032663l_bool: $tType ).
thf(fun_Ar1570071899t_bool_type,type,
fun_Ar1570071899t_bool: $tType ).
thf(fun_Ar884201459l_bool_type,type,
fun_Ar884201459l_bool: $tType ).
thf(fun_Ar1821573119l_bool_type,type,
fun_Ar1821573119l_bool: $tType ).
thf(fun_Ar2100459655t_bool_type,type,
fun_Ar2100459655t_bool: $tType ).
thf(fun_Ar2040671475t_bool_type,type,
fun_Ar2040671475t_bool: $tType ).
thf(fun_Ar2047178847t_bool_type,type,
fun_Ar2047178847t_bool: $tType ).
thf(fun_Ar795681735le_alt_type,type,
fun_Ar795681735le_alt: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo676255953i_bool_type,type,
fun_bo676255953i_bool: $tType ).
thf(fun_bo478202017t_bool_type,type,
fun_bo478202017t_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_bo1613497205l_bool_type,type,
fun_bo1613497205l_bool: $tType ).
thf(fun_bo2136393469t_bool_type,type,
fun_bo2136393469t_bool: $tType ).
thf(fun_bo2138151889l_bool_type,type,
fun_bo2138151889l_bool: $tType ).
thf(fun_bo1803678369l_bool_type,type,
fun_bo1803678369l_bool: $tType ).
thf(fun_bo292969573t_bool_type,type,
fun_bo292969573t_bool: $tType ).
thf(fun_bo230129725t_bool_type,type,
fun_bo230129725t_bool: $tType ).
thf(fun_bo1156530537le_alt_type,type,
fun_bo1156530537le_alt: $tType ).
thf(fun_na1602142942e_indi_type,type,
fun_na1602142942e_indi: $tType ).
thf(fun_nat_bool_type,type,
fun_nat_bool: $tType ).
thf(fun_nat_fun_nat_bool_type,type,
fun_nat_fun_nat_bool: $tType ).
thf(fun_fu350122099l_bool_type,type,
fun_fu350122099l_bool: $tType ).
thf(fun_fu892925833l_bool_type,type,
fun_fu892925833l_bool: $tType ).
thf(fun_fu341524965i_bool_type,type,
fun_fu341524965i_bool: $tType ).
thf(fun_fu932525193i_bool_type,type,
fun_fu932525193i_bool: $tType ).
thf(fun_fu1845530641i_bool_type,type,
fun_fu1845530641i_bool: $tType ).
thf(fun_fu1605010205i_bool_type,type,
fun_fu1605010205i_bool: $tType ).
thf(fun_fu1103697397l_bool_type,type,
fun_fu1103697397l_bool: $tType ).
thf(fun_fu682929745l_bool_type,type,
fun_fu682929745l_bool: $tType ).
thf(fun_fu2069019647e_indi_type,type,
fun_fu2069019647e_indi: $tType ).
thf(fun_fu103733537l_bool_type,type,
fun_fu103733537l_bool: $tType ).
thf(fun_fu23838287i_bool_type,type,
fun_fu23838287i_bool: $tType ).
thf(fun_fu658952305l_bool_type,type,
fun_fu658952305l_bool: $tType ).
thf(fun_fu746839971l_bool_type,type,
fun_fu746839971l_bool: $tType ).
thf(fun_fu50365883t_bool_type,type,
fun_fu50365883t_bool: $tType ).
thf(fun_fu2085524157t_bool_type,type,
fun_fu2085524157t_bool: $tType ).
thf(fun_fu1255657237l_bool_type,type,
fun_fu1255657237l_bool: $tType ).
thf(fun_fu1159982633l_bool_type,type,
fun_fu1159982633l_bool: $tType ).
thf(fun_fu797886669l_bool_type,type,
fun_fu797886669l_bool: $tType ).
thf(fun_fu1940222097l_bool_type,type,
fun_fu1940222097l_bool: $tType ).
thf(fun_fu1791463777l_bool_type,type,
fun_fu1791463777l_bool: $tType ).
thf(fun_fu132047767l_bool_type,type,
fun_fu132047767l_bool: $tType ).
thf(fun_fu1655311859l_bool_type,type,
fun_fu1655311859l_bool: $tType ).
thf(fun_fu897278719l_bool_type,type,
fun_fu897278719l_bool: $tType ).
thf(fun_fu2114498143t_bool_type,type,
fun_fu2114498143t_bool: $tType ).
thf(fun_fu243829175l_bool_type,type,
fun_fu243829175l_bool: $tType ).
thf(fun_fu1019918867l_bool_type,type,
fun_fu1019918867l_bool: $tType ).
thf(fun_fu1884117237i_bool_type,type,
fun_fu1884117237i_bool: $tType ).
thf(fun_fu386577431l_bool_type,type,
fun_fu386577431l_bool: $tType ).
thf(fun_fu337461969l_bool_type,type,
fun_fu337461969l_bool: $tType ).
thf(fun_fu123258927l_bool_type,type,
fun_fu123258927l_bool: $tType ).
thf(fun_fu698697681l_bool_type,type,
fun_fu698697681l_bool: $tType ).
thf(fun_fu1743730523e_indi_type,type,
fun_fu1743730523e_indi: $tType ).
thf(fun_fu1251737213l_bool_type,type,
fun_fu1251737213l_bool: $tType ).
thf(fun_fu1950461939i_bool_type,type,
fun_fu1950461939i_bool: $tType ).
thf(fun_fu1734842389l_bool_type,type,
fun_fu1734842389l_bool: $tType ).
thf(fun_fu1904749695l_bool_type,type,
fun_fu1904749695l_bool: $tType ).
thf(fun_fu376055641l_bool_type,type,
fun_fu376055641l_bool: $tType ).
thf(fun_fu1037822389l_bool_type,type,
fun_fu1037822389l_bool: $tType ).
thf(fun_fu664235509l_bool_type,type,
fun_fu664235509l_bool: $tType ).
thf(fun_fu582883361l_bool_type,type,
fun_fu582883361l_bool: $tType ).
thf(fun_fu881806519l_bool_type,type,
fun_fu881806519l_bool: $tType ).
thf(fun_fu288602073l_bool_type,type,
fun_fu288602073l_bool: $tType ).
thf(fun_fu1123909713i_bool_type,type,
fun_fu1123909713i_bool: $tType ).
thf(fun_fu304973171l_bool_type,type,
fun_fu304973171l_bool: $tType ).
thf(fun_fu1740763529l_bool_type,type,
fun_fu1740763529l_bool: $tType ).
thf(fun_fu1786351335l_bool_type,type,
fun_fu1786351335l_bool: $tType ).
thf(fun_fu1536608137l_bool_type,type,
fun_fu1536608137l_bool: $tType ).
thf(fun_fu595758099l_bool_type,type,
fun_fu595758099l_bool: $tType ).
thf(fun_fu2105385269l_bool_type,type,
fun_fu2105385269l_bool: $tType ).
thf(fun_fu1655733109l_bool_type,type,
fun_fu1655733109l_bool: $tType ).
thf(fun_fu1371820951l_bool_type,type,
fun_fu1371820951l_bool: $tType ).
thf(fun_fu278604415l_bool_type,type,
fun_fu278604415l_bool: $tType ).
thf(fun_fu1083074431i_bool_type,type,
fun_fu1083074431i_bool: $tType ).
thf(fun_fu2011759009l_bool_type,type,
fun_fu2011759009l_bool: $tType ).
thf(fun_fu491357777l_bool_type,type,
fun_fu491357777l_bool: $tType ).
thf(fun_fu1479273075l_bool_type,type,
fun_fu1479273075l_bool: $tType ).
thf(fun_fu890127093l_bool_type,type,
fun_fu890127093l_bool: $tType ).
thf(fun_fu66812275l_bool_type,type,
fun_fu66812275l_bool: $tType ).
thf(fun_fu662212797i_bool_type,type,
fun_fu662212797i_bool: $tType ).
thf(fun_fu334384573e_indi_type,type,
fun_fu334384573e_indi: $tType ).
thf(fun_fu383145951l_bool_type,type,
fun_fu383145951l_bool: $tType ).
thf(fun_fu193278215t_bool_type,type,
fun_fu193278215t_bool: $tType ).
thf(fun_fu1760369922t_bool_type,type,
fun_fu1760369922t_bool: $tType ).
thf(fun_fu1867632401i_bool_type,type,
fun_fu1867632401i_bool: $tType ).
thf(fun_fu1917018721t_bool_type,type,
fun_fu1917018721t_bool: $tType ).
thf(fun_fu1903211571l_bool_type,type,
fun_fu1903211571l_bool: $tType ).
thf(fun_fu1008469439t_bool_type,type,
fun_fu1008469439t_bool: $tType ).
thf(fun_fu1157966945l_bool_type,type,
fun_fu1157966945l_bool: $tType ).
thf(fun_fu1965119761t_bool_type,type,
fun_fu1965119761t_bool: $tType ).
thf(fun_fu148272765t_bool_type,type,
fun_fu148272765t_bool: $tType ).
thf(fun_Pr506339783e_indi_type,type,
fun_Pr506339783e_indi: $tType ).
thf(fun_Pr1639951081t_bool_type,type,
fun_Pr1639951081t_bool: $tType ).
thf(fun_Pr123985543i_bool_type,type,
fun_Pr123985543i_bool: $tType ).
thf(fun_Pr534938793l_bool_type,type,
fun_Pr534938793l_bool: $tType ).
thf(produc624534567le_alt_type,type,
produc624534567le_alt: $tType ).
thf(arrow_981905126le_IIA_decl,type,
arrow_981905126le_IIA: fun_fu1251737213l_bool ).
thf(arrow_1008788854le_Lin_decl,type,
arrow_1008788854le_Lin: fun_fu383145951l_bool ).
thf(arrow_1880704820e_Prof_decl,type,
arrow_1880704820e_Prof: fun_fu103733537l_bool ).
thf(arrow_2009189698_above_decl,type,
arrow_2009189698_above: fun_fu193278215t_bool ).
thf(arrow_1322316103ctator_decl,type,
arrow_1322316103ctator: fun_fu1950461939i_bool ).
thf(arrow_1126550734_mkbot_decl,type,
arrow_1126550734_mkbot: fun_fu1760369922t_bool ).
thf(arrow_1275257820_mktop_decl,type,
arrow_1275257820_mktop: fun_fu1760369922t_bool ).
thf(arrow_807483785nimity_decl,type,
arrow_807483785nimity: fun_fu1251737213l_bool ).
thf(cOMBB_124649523e_indi_decl,type,
cOMBB_124649523e_indi: fun_bo292969573t_bool > fun_Ar1871347069i_bool > fun_Ar2100459655t_bool ).
thf(cOMBB_1514803447e_indi_decl,type,
cOMBB_1514803447e_indi: fun_nat_fun_nat_bool > fun_Ar2035712896di_nat > fun_Ar156616864t_bool ).
thf(cOMBB_715840641e_indi_decl,type,
cOMBB_715840641e_indi: fun_fu193278215t_bool > fun_Ar2047178847t_bool > fun_Ar2079322857t_bool ).
thf(cOMBB_1932856316e_indi_decl,type,
cOMBB_1932856316e_indi: fun_fu1760369922t_bool > fun_Ar2047178847t_bool > fun_Ar1757019876t_bool ).
thf(cOMBC_1994570734t_bool_decl,type,
cOMBC_1994570734t_bool: fun_Ar2079322857t_bool > arrow_1621810872le_alt > fun_Ar1757019876t_bool ).
thf(cOMBC_377836265t_bool_decl,type,
cOMBC_377836265t_bool: fun_Ar1757019876t_bool > arrow_1621810872le_alt > fun_Ar2047178847t_bool ).
thf(cOMBC_998415407t_bool_decl,type,
cOMBC_998415407t_bool: fun_Ar156616864t_bool > nat > fun_Ar1871347069i_bool ).
thf(cOMBC_64563468t_bool_decl,type,
cOMBC_64563468t_bool: fun_Ar2100459655t_bool > fun_Pr1639951081t_bool > fun_Ar2040671475t_bool ).
thf(cOMBC_1257424504t_bool_decl,type,
cOMBC_1257424504t_bool: fun_Ar2040671475t_bool > fun_Pr1639951081t_bool > fun_Ar2047178847t_bool ).
thf(cOMBK_206372180e_indi_decl,type,
cOMBK_206372180e_indi: fun_bo676255953i_bool ).
thf(cOMBK_70145528t_bool_decl,type,
cOMBK_70145528t_bool: fun_bo1613497205l_bool ).
thf(cOMBK_1362474068t_bool_decl,type,
cOMBK_1362474068t_bool: fun_bo2138151889l_bool ).
thf(cOMBK_1801013008t_bool_decl,type,
cOMBK_1801013008t_bool: fun_bo1803678369l_bool ).
thf(cOMBK_350462144le_alt_decl,type,
cOMBK_350462144le_alt: fun_bo230129725t_bool ).
thf(cOMBK_269839822t_bool_decl,type,
cOMBK_269839822t_bool: fun_fu341524965i_bool ).
thf(cOMBK_519762474t_bool_decl,type,
cOMBK_519762474t_bool: fun_fu932525193i_bool ).
thf(cOMBK_1207925178t_bool_decl,type,
cOMBK_1207925178t_bool: fun_fu1845530641i_bool ).
thf(cOMBK_328807062le_alt_decl,type,
cOMBK_328807062le_alt: fun_fu1605010205i_bool ).
thf(cOMBK_167511280t_bool_decl,type,
cOMBK_167511280t_bool: fun_fu1159982633l_bool ).
thf(cOMBK_1853791052t_bool_decl,type,
cOMBK_1853791052t_bool: fun_fu797886669l_bool ).
thf(cOMBK_1838733848t_bool_decl,type,
cOMBK_1838733848t_bool: fun_fu1940222097l_bool ).
thf(cOMBK_290363320le_alt_decl,type,
cOMBK_290363320le_alt: fun_fu1791463777l_bool ).
thf(cOMBK_30438862e_indi_decl,type,
cOMBK_30438862e_indi: fun_fu337461969l_bool ).
thf(cOMBK_1481288432l_bool_decl,type,
cOMBK_1481288432l_bool: fun_fu123258927l_bool ).
thf(cOMBK_869185066e_indi_decl,type,
cOMBK_869185066e_indi: fun_fu1740763529l_bool ).
thf(cOMBK_343479628l_bool_decl,type,
cOMBK_343479628l_bool: fun_fu1786351335l_bool ).
thf(cOMBK_2098615510e_indi_decl,type,
cOMBK_2098615510e_indi: fun_fu491357777l_bool ).
thf(cOMBK_648664568l_bool_decl,type,
cOMBK_648664568l_bool: fun_fu1479273075l_bool ).
thf(cOMBK_639770490t_bool_decl,type,
cOMBK_639770490t_bool: fun_fu890127093l_bool ).
thf(cOMBK_164791446e_indi_decl,type,
cOMBK_164791446e_indi: fun_fu1917018721t_bool ).
thf(cOMBK_1897375160l_bool_decl,type,
cOMBK_1897375160l_bool: fun_fu1008469439t_bool ).
thf(cOMBS_1833320732t_bool_decl,type,
cOMBS_1833320732t_bool: fun_Ar2100459655t_bool > fun_Ar2047178847t_bool > fun_Ar2040671475t_bool ).
thf(cOMBS_1688227464t_bool_decl,type,
cOMBS_1688227464t_bool: fun_Ar2040671475t_bool > fun_Ar2047178847t_bool > fun_Ar2047178847t_bool ).
thf(finite1317065577e_indi_decl,type,
finite1317065577e_indi: fun_Ar1871347069i_bool > nat ).
thf(inj_on1177549232di_nat_decl,type,
inj_on1177549232di_nat: fun_Ar2035712896di_nat > fun_Ar1871347069i_bool > bool ).
thf(pi_Arr1077238675t_bool_decl,type,
pi_Arr1077238675t_bool: fun_Ar1871347069i_bool > fun_Ar1784032663l_bool > fun_fu1103697397l_bool ).
thf(pi_Arr478149871t_bool_decl,type,
pi_Arr478149871t_bool: fun_Ar1871347069i_bool > fun_Ar884201459l_bool > fun_fu682929745l_bool ).
thf(pi_Arr1358199477t_bool_decl,type,
pi_Arr1358199477t_bool: fun_Ar1871347069i_bool > fun_Ar1821573119l_bool > fun_fu103733537l_bool ).
thf(pi_Arr447918939le_alt_decl,type,
pi_Arr447918939le_alt: fun_Ar1871347069i_bool > fun_Ar2047178847t_bool > fun_fu2085524157t_bool ).
thf(pi_boo2120406325t_bool_decl,type,
pi_boo2120406325t_bool: fun_bool_bool > fun_bo1613497205l_bool > fun_fu132047767l_bool ).
thf(pi_boo853084305t_bool_decl,type,
pi_boo853084305t_bool: fun_bool_bool > fun_bo2138151889l_bool > fun_fu1655311859l_bool ).
thf(pi_boo683563155t_bool_decl,type,
pi_boo683563155t_bool: fun_bool_bool > fun_bo1803678369l_bool > fun_fu897278719l_bool ).
thf(pi_boo158890749le_alt_decl,type,
pi_boo158890749le_alt: fun_bool_bool > fun_bo230129725t_bool > fun_fu2114498143t_bool ).
thf(pi_fun1549517203e_indi_decl,type,
pi_fun1549517203e_indi: fun_fu103733537l_bool > fun_fu23838287i_bool > fun_fu1884117237i_bool ).
thf(pi_fun953636405l_bool_decl,type,
pi_fun953636405l_bool: fun_fu103733537l_bool > fun_fu658952305l_bool > fun_fu386577431l_bool ).
thf(pi_fun456133649t_bool_decl,type,
pi_fun456133649t_bool: fun_fu103733537l_bool > fun_fu746839971l_bool > fun_fu1251737213l_bool ).
thf(pi_fun1545124079e_indi_decl,type,
pi_fun1545124079e_indi: fun_fu1251737213l_bool > fun_fu1950461939i_bool > fun_fu1123909713i_bool ).
thf(pi_fun465500049l_bool_decl,type,
pi_fun465500049l_bool: fun_fu1251737213l_bool > fun_fu1734842389l_bool > fun_fu304973171l_bool ).
thf(pi_fun2132478361e_indi_decl,type,
pi_fun2132478361e_indi: fun_fu383145951l_bool > fun_fu1867632401i_bool > fun_fu1083074431i_bool ).
thf(pi_fun779925307l_bool_decl,type,
pi_fun779925307l_bool: fun_fu383145951l_bool > fun_fu1903211571l_bool > fun_fu2011759009l_bool ).
thf(pi_Pro723839835e_indi_decl,type,
pi_Pro723839835e_indi: fun_Pr1639951081t_bool > fun_Pr123985543i_bool > fun_fu662212797i_bool ).
thf(pi_Pro811330557t_bool_decl,type,
pi_Pro811330557t_bool: fun_Pr1639951081t_bool > fun_Pr534938793l_bool > fun_fu383145951l_bool ).
thf(hilber797233813di_nat_decl,type,
hilber797233813di_nat: fun_Ar1871347069i_bool > fun_Ar2035712896di_nat > fun_na1602142942e_indi ).
thf(if_fun95824985t_bool_decl,type,
if_fun95824985t_bool: fun_bo292969573t_bool ).
thf(ord_less_bool_decl,type,
ord_less_bool: fun_bo1549164019l_bool ).
thf(ord_less_nat_decl,type,
ord_less_nat: fun_nat_fun_nat_bool ).
thf(ord_le287438291i_bool_decl,type,
ord_le287438291i_bool: fun_fu892925833l_bool ).
thf(ord_le2059466615l_bool_decl,type,
ord_le2059466615l_bool: fun_fu698697681l_bool ).
thf(ord_le1419690707l_bool_decl,type,
ord_le1419690707l_bool: fun_fu1536608137l_bool ).
thf(ord_le1472193545l_bool_decl,type,
ord_le1472193545l_bool: fun_fu66812275l_bool ).
thf(ord_le1051050815t_bool_decl,type,
ord_le1051050815t_bool: fun_fu1157966945l_bool ).
thf(top_top_bool_decl,type,
top_top_bool: bool ).
thf(top_to850136695i_bool_decl,type,
top_to850136695i_bool: fun_Ar1871347069i_bool ).
thf(top_to1647826457l_bool_decl,type,
top_to1647826457l_bool: fun_bool_bool ).
thf(top_to653038619l_bool_decl,type,
top_to653038619l_bool: fun_fu103733537l_bool ).
thf(top_to2127553399l_bool_decl,type,
top_to2127553399l_bool: fun_fu1251737213l_bool ).
thf(top_to1057791589l_bool_decl,type,
top_to1057791589l_bool: fun_fu383145951l_bool ).
thf(top_to710777827t_bool_decl,type,
top_to710777827t_bool: fun_Pr1639951081t_bool ).
thf(produc170576535le_alt_decl,type,
produc170576535le_alt: arrow_1621810872le_alt > arrow_1621810872le_alt > produc624534567le_alt ).
thf(collec1241994086e_indi_decl,type,
collec1241994086e_indi: fun_Ar1871347069i_bool > fun_Ar1871347069i_bool ).
thf(collec861220362t_bool_decl,type,
collec861220362t_bool: fun_fu103733537l_bool > fun_fu103733537l_bool ).
thf(collec154865254t_bool_decl,type,
collec154865254t_bool: fun_fu1251737213l_bool > fun_fu1251737213l_bool ).
thf(collec1697917566t_bool_decl,type,
collec1697917566t_bool: fun_fu383145951l_bool > fun_fu383145951l_bool ).
thf(collec2140722898le_alt_decl,type,
collec2140722898le_alt: fun_Pr1639951081t_bool > fun_Pr1639951081t_bool ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fequal_nat_decl,type,
fequal_nat: fun_nat_fun_nat_bool ).
thf(hAPP_A272835723t_bool_decl,type,
hAPP_A272835723t_bool: fun_Ar154839667t_bool > arrow_1621810872le_alt > fun_Ar1822233582t_bool ).
thf(hAPP_A476679046t_bool_decl,type,
hAPP_A476679046t_bool: fun_Ar1822233582t_bool > arrow_1621810872le_alt > fun_Pr1639951081t_bool ).
thf(hAPP_A1059798043i_bool_decl,type,
hAPP_A1059798043i_bool: fun_Ar1871347069i_bool > arrow_501706939e_indi > bool ).
thf(hAPP_A1741215436di_nat_decl,type,
hAPP_A1741215436di_nat: fun_Ar2035712896di_nat > arrow_501706939e_indi > nat ).
thf(hAPP_A784015157t_bool_decl,type,
hAPP_A784015157t_bool: fun_Ar2079322857t_bool > arrow_501706939e_indi > fun_Ar154839667t_bool ).
thf(hAPP_A711829680t_bool_decl,type,
hAPP_A711829680t_bool: fun_Ar1757019876t_bool > arrow_501706939e_indi > fun_Ar1822233582t_bool ).
thf(hAPP_A1159468061t_bool_decl,type,
hAPP_A1159468061t_bool: fun_Ar1200683263t_bool > arrow_501706939e_indi > fun_Ar2047178847t_bool ).
thf(hAPP_A1239621182t_bool_decl,type,
hAPP_A1239621182t_bool: fun_Ar156616864t_bool > arrow_501706939e_indi > fun_nat_bool ).
thf(hAPP_A1790795747l_bool_decl,type,
hAPP_A1790795747l_bool: fun_Ar1784032663l_bool > arrow_501706939e_indi > fun_fu103733537l_bool ).
thf(hAPP_A1168502649t_bool_decl,type,
hAPP_A1168502649t_bool: fun_Ar1570071899t_bool > arrow_501706939e_indi > fun_fu50365883t_bool ).
thf(hAPP_A107624255l_bool_decl,type,
hAPP_A107624255l_bool: fun_Ar884201459l_bool > arrow_501706939e_indi > fun_fu1251737213l_bool ).
thf(hAPP_A1710743709l_bool_decl,type,
hAPP_A1710743709l_bool: fun_Ar1821573119l_bool > arrow_501706939e_indi > fun_fu383145951l_bool ).
thf(hAPP_A1985966547t_bool_decl,type,
hAPP_A1985966547t_bool: fun_Ar2100459655t_bool > arrow_501706939e_indi > fun_fu1965119761t_bool ).
thf(hAPP_A301260095t_bool_decl,type,
hAPP_A301260095t_bool: fun_Ar2040671475t_bool > arrow_501706939e_indi > fun_fu148272765t_bool ).
thf(hAPP_A2044747691t_bool_decl,type,
hAPP_A2044747691t_bool: fun_Ar2047178847t_bool > arrow_501706939e_indi > fun_Pr1639951081t_bool ).
thf(hAPP_A2034733541le_alt_decl,type,
hAPP_A2034733541le_alt: fun_Ar795681735le_alt > arrow_501706939e_indi > produc624534567le_alt ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: fun_bool_bool > bool > bool ).
thf(hAPP_b611520797i_bool_decl,type,
hAPP_b611520797i_bool: fun_bo676255953i_bool > bool > fun_Ar1871347069i_bool ).
thf(hAPP_b114674879t_bool_decl,type,
hAPP_b114674879t_bool: fun_bo478202017t_bool > bool > fun_Ar2047178847t_bool ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).
thf(hAPP_b1178471617l_bool_decl,type,
hAPP_b1178471617l_bool: fun_bo1613497205l_bool > bool > fun_fu103733537l_bool ).
thf(hAPP_b1112685083t_bool_decl,type,
hAPP_b1112685083t_bool: fun_bo2136393469t_bool > bool > fun_fu50365883t_bool ).
thf(hAPP_b930206237l_bool_decl,type,
hAPP_b930206237l_bool: fun_bo2138151889l_bool > bool > fun_fu1251737213l_bool ).
thf(hAPP_b1017527359l_bool_decl,type,
hAPP_b1017527359l_bool: fun_bo1803678369l_bool > bool > fun_fu383145951l_bool ).
thf(hAPP_b1702702257t_bool_decl,type,
hAPP_b1702702257t_bool: fun_bo292969573t_bool > bool > fun_fu1965119761t_bool ).
thf(hAPP_b1848524425t_bool_decl,type,
hAPP_b1848524425t_bool: fun_bo230129725t_bool > bool > fun_Pr1639951081t_bool ).
thf(hAPP_b98736263le_alt_decl,type,
hAPP_b98736263le_alt: fun_bo1156530537le_alt > bool > produc624534567le_alt ).
thf(hAPP_n1582158000e_indi_decl,type,
hAPP_n1582158000e_indi: fun_na1602142942e_indi > nat > arrow_501706939e_indi ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: fun_nat_bool > nat > bool ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).
thf(hAPP_f90330565l_bool_decl,type,
hAPP_f90330565l_bool: fun_fu350122099l_bool > fun_Ar1871347069i_bool > bool ).
thf(hAPP_f1993665755l_bool_decl,type,
hAPP_f1993665755l_bool: fun_fu892925833l_bool > fun_Ar1871347069i_bool > fun_fu350122099l_bool ).
thf(hAPP_f823592631i_bool_decl,type,
hAPP_f823592631i_bool: fun_fu341524965i_bool > fun_Ar1871347069i_bool > fun_fu23838287i_bool ).
thf(hAPP_f1224613979i_bool_decl,type,
hAPP_f1224613979i_bool: fun_fu932525193i_bool > fun_Ar1871347069i_bool > fun_fu1950461939i_bool ).
thf(hAPP_f1364159657i_bool_decl,type,
hAPP_f1364159657i_bool: fun_fu1845530641i_bool > fun_Ar1871347069i_bool > fun_fu1867632401i_bool ).
thf(hAPP_f1561296623i_bool_decl,type,
hAPP_f1561296623i_bool: fun_fu1605010205i_bool > fun_Ar1871347069i_bool > fun_Pr123985543i_bool ).
thf(hAPP_f1631746589e_indi_decl,type,
hAPP_f1631746589e_indi: fun_fu2069019647e_indi > fun_Ar2047178847t_bool > arrow_501706939e_indi ).
thf(hAPP_f1095388607l_bool_decl,type,
hAPP_f1095388607l_bool: fun_fu103733537l_bool > fun_Ar2047178847t_bool > bool ).
thf(hAPP_f1511451035i_bool_decl,type,
hAPP_f1511451035i_bool: fun_fu23838287i_bool > fun_Ar2047178847t_bool > fun_Ar1871347069i_bool ).
thf(hAPP_f1418708797l_bool_decl,type,
hAPP_f1418708797l_bool: fun_fu658952305l_bool > fun_Ar2047178847t_bool > fun_bool_bool ).
thf(hAPP_f1265202753l_bool_decl,type,
hAPP_f1265202753l_bool: fun_fu746839971l_bool > fun_Ar2047178847t_bool > fun_fu383145951l_bool ).
thf(hAPP_f718157575t_bool_decl,type,
hAPP_f718157575t_bool: fun_fu50365883t_bool > fun_Ar2047178847t_bool > fun_Pr1639951081t_bool ).
thf(hAPP_f387058535l_bool_decl,type,
hAPP_f387058535l_bool: fun_fu1255657237l_bool > fun_bool_bool > bool ).
thf(hAPP_f1325493883l_bool_decl,type,
hAPP_f1325493883l_bool: fun_fu1159982633l_bool > fun_bool_bool > fun_fu658952305l_bool ).
thf(hAPP_f1364914207l_bool_decl,type,
hAPP_f1364914207l_bool: fun_fu797886669l_bool > fun_bool_bool > fun_fu1734842389l_bool ).
thf(hAPP_f1230984105l_bool_decl,type,
hAPP_f1230984105l_bool: fun_fu1940222097l_bool > fun_bool_bool > fun_fu1903211571l_bool ).
thf(hAPP_f1601816755l_bool_decl,type,
hAPP_f1601816755l_bool: fun_fu1791463777l_bool > fun_bool_bool > fun_Pr534938793l_bool ).
thf(hAPP_f1753158741l_bool_decl,type,
hAPP_f1753158741l_bool: fun_fu243829175l_bool > fun_fu1103697397l_bool > bool ).
thf(hAPP_f598211249l_bool_decl,type,
hAPP_f598211249l_bool: fun_fu1019918867l_bool > fun_fu682929745l_bool > bool ).
thf(hAPP_f1237345129l_bool_decl,type,
hAPP_f1237345129l_bool: fun_fu386577431l_bool > fun_fu103733537l_bool > bool ).
thf(hAPP_f466810275l_bool_decl,type,
hAPP_f466810275l_bool: fun_fu337461969l_bool > fun_fu103733537l_bool > fun_Ar1784032663l_bool ).
thf(hAPP_f2013855105l_bool_decl,type,
hAPP_f2013855105l_bool: fun_fu123258927l_bool > fun_fu103733537l_bool > fun_bo1613497205l_bool ).
thf(hAPP_f786935331l_bool_decl,type,
hAPP_f786935331l_bool: fun_fu698697681l_bool > fun_fu103733537l_bool > fun_fu386577431l_bool ).
thf(hAPP_f87993209e_indi_decl,type,
hAPP_f87993209e_indi: fun_fu1743730523e_indi > fun_fu50365883t_bool > arrow_501706939e_indi ).
thf(hAPP_f725100827l_bool_decl,type,
hAPP_f725100827l_bool: fun_fu1251737213l_bool > fun_fu50365883t_bool > bool ).
thf(hAPP_f1559864639i_bool_decl,type,
hAPP_f1559864639i_bool: fun_fu1950461939i_bool > fun_fu50365883t_bool > fun_Ar1871347069i_bool ).
thf(hAPP_f626809057l_bool_decl,type,
hAPP_f626809057l_bool: fun_fu1734842389l_bool > fun_fu50365883t_bool > fun_bool_bool ).
thf(hAPP_f748921117l_bool_decl,type,
hAPP_f748921117l_bool: fun_fu1904749695l_bool > fun_fu2085524157t_bool > bool ).
thf(hAPP_f1481710327l_bool_decl,type,
hAPP_f1481710327l_bool: fun_fu376055641l_bool > fun_fu132047767l_bool > bool ).
thf(hAPP_f759862099l_bool_decl,type,
hAPP_f759862099l_bool: fun_fu1037822389l_bool > fun_fu1655311859l_bool > bool ).
thf(hAPP_f639792199l_bool_decl,type,
hAPP_f639792199l_bool: fun_fu664235509l_bool > fun_fu897278719l_bool > bool ).
thf(hAPP_f899216831l_bool_decl,type,
hAPP_f899216831l_bool: fun_fu582883361l_bool > fun_fu2114498143t_bool > bool ).
thf(hAPP_f243652437l_bool_decl,type,
hAPP_f243652437l_bool: fun_fu881806519l_bool > fun_fu1884117237i_bool > bool ).
thf(hAPP_f1394256759l_bool_decl,type,
hAPP_f1394256759l_bool: fun_fu288602073l_bool > fun_fu386577431l_bool > bool ).
thf(hAPP_f1435434693l_bool_decl,type,
hAPP_f1435434693l_bool: fun_fu304973171l_bool > fun_fu1251737213l_bool > bool ).
thf(hAPP_f544895323l_bool_decl,type,
hAPP_f544895323l_bool: fun_fu1740763529l_bool > fun_fu1251737213l_bool > fun_Ar884201459l_bool ).
thf(hAPP_f989466937l_bool_decl,type,
hAPP_f989466937l_bool: fun_fu1786351335l_bool > fun_fu1251737213l_bool > fun_bo2138151889l_bool ).
thf(hAPP_f1303771867l_bool_decl,type,
hAPP_f1303771867l_bool: fun_fu1536608137l_bool > fun_fu1251737213l_bool > fun_fu304973171l_bool ).
thf(hAPP_f174050481l_bool_decl,type,
hAPP_f174050481l_bool: fun_fu595758099l_bool > fun_fu1123909713i_bool > bool ).
thf(hAPP_f1827424979l_bool_decl,type,
hAPP_f1827424979l_bool: fun_fu2105385269l_bool > fun_fu304973171l_bool > bool ).
thf(hAPP_f359017159l_bool_decl,type,
hAPP_f359017159l_bool: fun_fu1655733109l_bool > fun_fu1083074431i_bool > bool ).
thf(hAPP_f1347377641l_bool_decl,type,
hAPP_f1347377641l_bool: fun_fu1371820951l_bool > fun_fu2011759009l_bool > bool ).
thf(hAPP_f1270259485l_bool_decl,type,
hAPP_f1270259485l_bool: fun_fu278604415l_bool > fun_fu662212797i_bool > bool ).
thf(hAPP_f180608831l_bool_decl,type,
hAPP_f180608831l_bool: fun_fu2011759009l_bool > fun_fu383145951l_bool > bool ).
thf(hAPP_f1651042461l_bool_decl,type,
hAPP_f1651042461l_bool: fun_fu491357777l_bool > fun_fu383145951l_bool > fun_Ar1821573119l_bool ).
thf(hAPP_f71505983l_bool_decl,type,
hAPP_f71505983l_bool: fun_fu1479273075l_bool > fun_fu383145951l_bool > fun_bo1803678369l_bool ).
thf(hAPP_f459175489l_bool_decl,type,
hAPP_f459175489l_bool: fun_fu890127093l_bool > fun_fu383145951l_bool > fun_fu746839971l_bool ).
thf(hAPP_f279586623l_bool_decl,type,
hAPP_f279586623l_bool: fun_fu66812275l_bool > fun_fu383145951l_bool > fun_fu2011759009l_bool ).
thf(hAPP_f671542927e_indi_decl,type,
hAPP_f671542927e_indi: fun_fu334384573e_indi > fun_Pr1639951081t_bool > arrow_501706939e_indi ).
thf(hAPP_f1944886577l_bool_decl,type,
hAPP_f1944886577l_bool: fun_fu383145951l_bool > fun_Pr1639951081t_bool > bool ).
thf(hAPP_f1560118175t_bool_decl,type,
hAPP_f1560118175t_bool: fun_fu193278215t_bool > fun_Pr1639951081t_bool > fun_Ar154839667t_bool ).
thf(hAPP_f1699392794t_bool_decl,type,
hAPP_f1699392794t_bool: fun_fu1760369922t_bool > fun_Pr1639951081t_bool > fun_Ar1822233582t_bool ).
thf(hAPP_f906860201i_bool_decl,type,
hAPP_f906860201i_bool: fun_fu1867632401i_bool > fun_Pr1639951081t_bool > fun_Ar1871347069i_bool ).
thf(hAPP_f1172974131t_bool_decl,type,
hAPP_f1172974131t_bool: fun_fu1917018721t_bool > fun_Pr1639951081t_bool > fun_Ar2047178847t_bool ).
thf(hAPP_f2128533835l_bool_decl,type,
hAPP_f2128533835l_bool: fun_fu1903211571l_bool > fun_Pr1639951081t_bool > fun_bool_bool ).
thf(hAPP_f1758973969t_bool_decl,type,
hAPP_f1758973969t_bool: fun_fu1008469439t_bool > fun_Pr1639951081t_bool > fun_bo230129725t_bool ).
thf(hAPP_f1911990195l_bool_decl,type,
hAPP_f1911990195l_bool: fun_fu1157966945l_bool > fun_Pr1639951081t_bool > fun_fu383145951l_bool ).
thf(hAPP_f910728105t_bool_decl,type,
hAPP_f910728105t_bool: fun_fu1965119761t_bool > fun_Pr1639951081t_bool > fun_fu148272765t_bool ).
thf(hAPP_f727188501t_bool_decl,type,
hAPP_f727188501t_bool: fun_fu148272765t_bool > fun_Pr1639951081t_bool > fun_Pr1639951081t_bool ).
thf(hAPP_P163170789e_indi_decl,type,
hAPP_P163170789e_indi: fun_Pr506339783e_indi > produc624534567le_alt > arrow_501706939e_indi ).
thf(hAPP_P751176071t_bool_decl,type,
hAPP_P751176071t_bool: fun_Pr1639951081t_bool > produc624534567le_alt > bool ).
thf(hAPP_P259956691i_bool_decl,type,
hAPP_P259956691i_bool: fun_Pr123985543i_bool > produc624534567le_alt > fun_Ar1871347069i_bool ).
thf(hAPP_P2005668213l_bool_decl,type,
hAPP_P2005668213l_bool: fun_Pr534938793l_bool > produc624534567le_alt > fun_bool_bool ).
thf(hBOOL_decl,type,
hBOOL: bool > $o ).
thf(member1124131880e_indi_decl,type,
member1124131880e_indi: arrow_501706939e_indi > fun_fu350122099l_bool ).
thf(member_bool_decl,type,
member_bool: bool > fun_fu1255657237l_bool ).
thf(member1701178322t_bool_decl,type,
member1701178322t_bool: fun_Ar1200683263t_bool > fun_fu243829175l_bool ).
thf(member2069173038t_bool_decl,type,
member2069173038t_bool: fun_Ar1570071899t_bool > fun_fu1019918867l_bool ).
thf(member558395596t_bool_decl,type,
member558395596t_bool: fun_Ar2047178847t_bool > fun_fu386577431l_bool ).
thf(member844573594le_alt_decl,type,
member844573594le_alt: fun_Ar795681735le_alt > fun_fu1904749695l_bool ).
thf(member1494646772t_bool_decl,type,
member1494646772t_bool: fun_bo478202017t_bool > fun_fu376055641l_bool ).
thf(member1211611472t_bool_decl,type,
member1211611472t_bool: fun_bo2136393469t_bool > fun_fu1037822389l_bool ).
thf(member2079888426t_bool_decl,type,
member2079888426t_bool: fun_bo230129725t_bool > fun_fu664235509l_bool ).
thf(member158436796le_alt_decl,type,
member158436796le_alt: fun_bo1156530537le_alt > fun_fu582883361l_bool ).
thf(member422031058e_indi_decl,type,
member422031058e_indi: fun_fu2069019647e_indi > fun_fu881806519l_bool ).
thf(member1120178292l_bool_decl,type,
member1120178292l_bool: fun_fu103733537l_bool > fun_fu288602073l_bool ).
thf(member256508712t_bool_decl,type,
member256508712t_bool: fun_fu50365883t_bool > fun_fu304973171l_bool ).
thf(member95348014e_indi_decl,type,
member95348014e_indi: fun_fu1743730523e_indi > fun_fu595758099l_bool ).
thf(member326955216l_bool_decl,type,
member326955216l_bool: fun_fu1251737213l_bool > fun_fu2105385269l_bool ).
thf(member993084970e_indi_decl,type,
member993084970e_indi: fun_fu334384573e_indi > fun_fu1655733109l_bool ).
thf(member85421004l_bool_decl,type,
member85421004l_bool: fun_fu383145951l_bool > fun_fu1371820951l_bool ).
thf(member555231642e_indi_decl,type,
member555231642e_indi: fun_Pr506339783e_indi > fun_fu278604415l_bool ).
thf(member641857340t_bool_decl,type,
member641857340t_bool: fun_Pr1639951081t_bool > fun_fu2011759009l_bool ).
thf(member1484933012le_alt_decl,type,
member1484933012le_alt: produc624534567le_alt > fun_fu383145951l_bool ).
thf(f_decl,type,
f: fun_fu50365883t_bool ).
thf(lab_decl,type,
lab: fun_Pr1639951081t_bool ).
thf(lba_decl,type,
lba: fun_Pr1639951081t_bool ).
thf(p_decl,type,
p: fun_Ar2047178847t_bool ).
thf(a_decl,type,
a: arrow_1621810872le_alt ).
thf(b_decl,type,
b: arrow_1621810872le_alt ).
thf(c_decl,type,
c: arrow_1621810872le_alt ).
thf(d_decl,type,
d: arrow_1621810872le_alt ).
thf(e_decl,type,
e: arrow_1621810872le_alt ).
thf(h_decl,type,
h: fun_Ar2035712896di_nat ).
thf(n_decl,type,
n: nat ).
thf(196,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_fu1950461939i_bool] :
( ( D @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1559864639i_bool ) @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pi__mem) ).
thf(1036,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_fu1950461939i_bool] :
( ( D @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1559864639i_bool ) @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(105,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar2035712896di_nat,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A1741215436di_nat ) @ ( B @ ( C @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_inv__into__f__f) ).
thf(628,plain,
! [A: arrow_501706939e_indi,B: fun_Ar2035712896di_nat,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A1741215436di_nat ) @ ( B @ ( C @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(146,axiom,
! [A: fun_fu383145951l_bool] :
( ( A != top_to1057791589l_bool )
<=> ( top_to1057791589l_bool @ ( A @ ( ord_le1472193545l_bool @ hAPP_f279586623l_bool ) @ hAPP_f180608831l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_less__top) ).
thf(777,plain,
! [A: fun_fu383145951l_bool] :
( ( ( top_to1057791589l_bool @ ( A @ ( ord_le1472193545l_bool @ hAPP_f279586623l_bool ) @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A != top_to1057791589l_bool ) )
& ( ( A != top_to1057791589l_bool )
=> ( top_to1057791589l_bool @ ( A @ ( ord_le1472193545l_bool @ hAPP_f279586623l_bool ) @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(220,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_269839822t_bool @ hAPP_f823592631i_bool ) @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_funcset__mem) ).
thf(1110,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_269839822t_bool @ hAPP_f823592631i_bool ) @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(75,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).
thf(479,plain,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(218,axiom,
! [A: fun_Ar1871347069i_bool] :
~ ( A @ ( top_to850136695i_bool @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_not__top__less) ).
thf(1105,plain,
! [A: fun_Ar1871347069i_bool] :
~ ( A @ ( top_to850136695i_bool @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(210,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_fu23838287i_bool] :
( ( D @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1511451035i_bool ) @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_PiE) ).
thf(1083,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_fu23838287i_bool] :
( ( D @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1511451035i_bool ) @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(71,axiom,
top_to850136695i_bool @ ( h @ inj_on1177549232di_nat ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).
thf(468,plain,
top_to850136695i_bool @ ( h @ inj_on1177549232di_nat ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(232,axiom,
! [A: fun_Ar2047178847t_bool] : ( top_to653038619l_bool @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_iso__tuple__UNIV__I) ).
thf(1158,plain,
! [A: fun_Ar2047178847t_bool] : ( top_to653038619l_bool @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(193,axiom,
! [A: fun_fu50365883t_bool] :
( ( A @ ( arrow_981905126le_IIA @ hAPP_f725100827l_bool ) @ hBOOL )
<=> ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ! [F: arrow_501706939e_indi] :
( ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( F @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( C @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).
thf(1005,plain,
! [A: fun_fu50365883t_bool] :
( ( ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ! [F: arrow_501706939e_indi] :
( ( ( F @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) )
=> ( A @ ( arrow_981905126le_IIA @ hAPP_f725100827l_bool ) @ hBOOL ) )
& ( ( A @ ( arrow_981905126le_IIA @ hAPP_f725100827l_bool ) @ hBOOL )
=> ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ! [F: arrow_501706939e_indi] :
( ( ( F @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(120,axiom,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Pr123985543i_bool] :
( ( D @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P259956691i_bool ) @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Pi__mem) ).
thf(683,plain,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Pr123985543i_bool] :
( ( D @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P259956691i_bool ) @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ord__eq__less__trans) ).
thf(1068,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(26,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_269839822t_bool @ hAPP_f823592631i_bool ) @ hAPP_f1511451035i_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___165) ).
thf(308,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_269839822t_bool @ hAPP_f823592631i_bool ) @ hAPP_f1511451035i_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(236,axiom,
! [A: fun_Pr1639951081t_bool] :
( ( A != top_to710777827t_bool )
<=> ( top_to710777827t_bool @ ( A @ ( ord_le1051050815t_bool @ hAPP_f1911990195l_bool ) @ hAPP_f1944886577l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_less__top) ).
thf(1173,plain,
! [A: fun_Pr1639951081t_bool] :
( ( ( top_to710777827t_bool @ ( A @ ( ord_le1051050815t_bool @ hAPP_f1911990195l_bool ) @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A != top_to710777827t_bool ) )
& ( ( A != top_to710777827t_bool )
=> ( top_to710777827t_bool @ ( A @ ( ord_le1051050815t_bool @ hAPP_f1911990195l_bool ) @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(12,axiom,
! [A: fun_fu1251737213l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_343479628l_bool @ hAPP_f989466937l_bool ) @ hAPP_b930206237l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).
thf(269,plain,
! [A: fun_fu1251737213l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_343479628l_bool @ hAPP_f989466937l_bool ) @ hAPP_b930206237l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(117,axiom,
! [A: fun_Ar2047178847t_bool] : ( top_to653038619l_bool @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_UNIV__I) ).
thf(677,plain,
! [A: fun_Ar2047178847t_bool] : ( top_to653038619l_bool @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(37,axiom,
( top_to850136695i_bool
= ( fTrue @ ( cOMBK_206372180e_indi @ hAPP_b611520797i_bool ) @ collec1241994086e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_UNIV__def) ).
thf(340,plain,
( top_to850136695i_bool
= ( fTrue @ ( cOMBK_206372180e_indi @ hAPP_b611520797i_bool ) @ collec1241994086e_indi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(171,axiom,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( e @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(930,plain,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( e @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(58,axiom,
! [A: fun_fu1251737213l_bool] :
( ( A != top_to2127553399l_bool )
<=> ( top_to2127553399l_bool @ ( A @ ( ord_le1419690707l_bool @ hAPP_f1303771867l_bool ) @ hAPP_f1435434693l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_less__top) ).
thf(404,plain,
! [A: fun_fu1251737213l_bool] :
( ( ( top_to2127553399l_bool @ ( A @ ( ord_le1419690707l_bool @ hAPP_f1303771867l_bool ) @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A != top_to2127553399l_bool ) )
& ( ( A != top_to2127553399l_bool )
=> ( top_to2127553399l_bool @ ( A @ ( ord_le1419690707l_bool @ hAPP_f1303771867l_bool ) @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(192,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_order__less__imp__not__eq) ).
thf(1001,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(228,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__imp__neq) ).
thf(1127,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(156,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu746839971l_bool] :
( ( D @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1265202753l_bool ) @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Pi__mem) ).
thf(841,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu746839971l_bool] :
( ( D @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1265202753l_bool ) @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(200,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_fu1867632401i_bool] :
( ( D @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f906860201i_bool ) @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Pi__mem) ).
thf(1046,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_fu1867632401i_bool] :
( ( D @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f906860201i_bool ) @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(19,axiom,
! [A: fun_fu103733537l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_30438862e_indi @ hAPP_f466810275l_bool ) @ hAPP_A1790795747l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_166) ).
thf(288,plain,
! [A: fun_fu103733537l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_30438862e_indi @ hAPP_f466810275l_bool ) @ hAPP_A1790795747l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: fun_Pr1639951081t_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ hAPP_A2044747691t_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_160) ).
thf(320,plain,
! [A: fun_Pr1639951081t_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ hAPP_A2044747691t_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(68,axiom,
! [A: produc624534567le_alt] :
( ( A @ ( top_to710777827t_bool @ hAPP_P751176071t_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_top__apply) ).
thf(436,plain,
! [A: produc624534567le_alt] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to710777827t_bool @ hAPP_P751176071t_bool ) @ hBOOL ) )
& ( ( A @ ( top_to710777827t_bool @ hAPP_P751176071t_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(8,axiom,
! [A: fun_Pr1639951081t_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_1897375160l_bool @ hAPP_f1758973969t_bool ) @ hAPP_b1848524425t_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf) ).
thf(257,plain,
! [A: fun_Pr1639951081t_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_1897375160l_bool @ hAPP_f1758973969t_bool ) @ hAPP_b1848524425t_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(89,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1784032663l_bool] :
( ( D @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1790795747l_bool ) @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Pi__mem) ).
thf(570,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1784032663l_bool] :
( ( D @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1790795747l_bool ) @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(147,axiom,
! [A: fun_Pr1639951081t_bool] : ( top_to1057791589l_bool @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).
thf(785,plain,
! [A: fun_Pr1639951081t_bool] : ( top_to1057791589l_bool @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(48,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_Ar2035712896di_nat,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_1514803447e_indi ) @ hAPP_A1239621182t_bool ) )
= ( C @ ( B @ hAPP_A1741215436di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(372,plain,
! [A: fun_nat_fun_nat_bool,B: fun_Ar2035712896di_nat,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_1514803447e_indi ) @ hAPP_A1239621182t_bool ) )
= ( C @ ( B @ hAPP_A1741215436di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_linorder__less__linear) ).
thf(587,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(43,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_519762474t_bool @ hAPP_f1224613979i_bool ) @ hAPP_f1559864639i_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___171) ).
thf(357,plain,
! [A: fun_Ar1871347069i_bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_519762474t_bool @ hAPP_f1224613979i_bool ) @ hAPP_f1559864639i_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(212,axiom,
! [A: bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__less__imp__triv) ).
thf(1087,plain,
! [A: bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(182,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_fu1903211571l_bool] :
( ( D @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f2128533835l_bool ) @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_PiE) ).
thf(969,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_fu1903211571l_bool] :
( ( D @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f2128533835l_bool ) @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(61,axiom,
! [A: nat,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A1741215436di_nat ) )
= A )
=> ( ( A @ ( C @ ( D @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_inv__into__f__eq) ).
thf(416,plain,
! [A: nat,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A1741215436di_nat ) )
= A )
=> ( ( A @ ( C @ ( D @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,axiom,
! [A: fun_Pr1639951081t_bool] :
( ( A @ ( top_to1057791589l_bool @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_top__apply) ).
thf(492,plain,
! [A: fun_Pr1639951081t_bool] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to1057791589l_bool @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to1057791589l_bool @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(138,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Pr1639951081t_bool] :
( ( D @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_funcset__mem) ).
thf(756,plain,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Pr1639951081t_bool] :
( ( D @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(149,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_in__above) ).
thf(789,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( A != B ) )
=> ( E @ ( D @ ( C @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( E @ ( D @ ( C @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( A != B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(198,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_xt1_I1_J) ).
thf(1040,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(107,axiom,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_bo1803678369l_bool] :
( ( D @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1017527359l_bool ) @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_PiE) ).
thf(646,plain,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_bo1803678369l_bool] :
( ( D @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1017527359l_bool ) @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(154,axiom,
top_to850136695i_bool @ finite1317065577e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).
thf(834,plain,
top_to850136695i_bool @ finite1317065577e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(40,axiom,
! [A: fun_fu103733537l_bool] :
( ( top_to1057791589l_bool @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( A @ pi_fun456133649t_bool ) )
= top_to2127553399l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Pi__UNIV) ).
thf(348,plain,
! [A: fun_fu103733537l_bool] :
( ( top_to1057791589l_bool @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( A @ pi_fun456133649t_bool ) )
= top_to2127553399l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(202,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [F: arrow_501706939e_indi] :
( ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( F @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).
thf(1051,plain,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [F: arrow_501706939e_indi] :
( ( ( F @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( F @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(122,axiom,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Pr123985543i_bool] :
( ( D @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P259956691i_bool ) @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_PiE) ).
thf(687,plain,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Pr123985543i_bool] :
( ( D @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P259956691i_bool ) @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(125,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_fu1251737213l_bool] :
( ( D @ ( cOMBK_869185066e_indi @ hAPP_f544895323l_bool ) @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_funcset__mem) ).
thf(692,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_fu1251737213l_bool] :
( ( D @ ( cOMBK_869185066e_indi @ hAPP_f544895323l_bool ) @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(176,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__less__not__sym) ).
thf(956,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(205,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_funcset__mem) ).
thf(1072,plain,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(224,axiom,
! [A: fun_na1602142942e_indi,B: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( A @ hAPP_n1582158000e_indi ) @ ( B @ hAPP_A1741215436di_nat ) )
= C )
=> ( ( B @ ( top_to850136695i_bool @ hilber797233813di_nat ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_inj__imp__inv__eq) ).
thf(1119,plain,
! [A: fun_na1602142942e_indi,B: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( A @ hAPP_n1582158000e_indi ) @ ( B @ hAPP_A1741215436di_nat ) )
= C )
=> ( ( B @ ( top_to850136695i_bool @ hilber797233813di_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(54,axiom,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_fu103733537l_bool] :
( ( D @ ( cOMBK_1481288432l_bool @ hAPP_f2013855105l_bool ) @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_funcset__mem) ).
thf(396,plain,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_fu103733537l_bool] :
( ( D @ ( cOMBK_1481288432l_bool @ hAPP_f2013855105l_bool ) @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(190,axiom,
f @ ( arrow_981905126le_IIA @ hAPP_f725100827l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(998,plain,
f @ ( arrow_981905126le_IIA @ hAPP_f725100827l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(189,axiom,
! [A: fun_fu50365883t_bool] :
( ( A @ ( arrow_807483785nimity @ hAPP_f725100827l_bool ) @ hBOOL )
<=> ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ! [E: arrow_501706939e_indi] : ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).
thf(988,plain,
! [A: fun_fu50365883t_bool] :
( ( ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ! [E: arrow_501706939e_indi] : ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( A @ ( arrow_807483785nimity @ hAPP_f725100827l_bool ) @ hBOOL ) )
& ( ( A @ ( arrow_807483785nimity @ hAPP_f725100827l_bool ) @ hBOOL )
=> ! [B: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ! [E: arrow_501706939e_indi] : ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(66,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1821573119l_bool] :
( ( D @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1710743709l_bool ) @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Pi__mem) ).
thf(428,plain,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1821573119l_bool] :
( ( D @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1710743709l_bool ) @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(206,axiom,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_inj__onD) ).
thf(1074,plain,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(239,axiom,
! [A: bool] :
~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_not__top__less) ).
thf(1206,plain,
! [A: bool] :
~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(5,axiom,
! [A: fun_Ar2100459655t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBS_1833320732t_bool ) @ hAPP_A301260095t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( C @ ( A @ hAPP_A1985966547t_bool ) @ hAPP_f910728105t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_175) ).
thf(248,plain,
! [A: fun_Ar2100459655t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBS_1833320732t_bool ) @ hAPP_A301260095t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( C @ ( A @ hAPP_A1985966547t_bool ) @ hAPP_f910728105t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(112,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_order__less__asym) ).
thf(661,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(141,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool] :
( ( B @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f1095388607l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_mem__def) ).
thf(761,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool] :
( ( ( A @ ( B @ hAPP_f1095388607l_bool ) @ hBOOL )
=> ( B @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f1095388607l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(46,axiom,
! [A: fun_Ar1871347069i_bool] :
( ( top_to1057791589l_bool @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( A @ pi_Arr1358199477t_bool ) )
= top_to653038619l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Pi__UNIV) ).
thf(366,plain,
! [A: fun_Ar1871347069i_bool] :
( ( top_to1057791589l_bool @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( A @ pi_Arr1358199477t_bool ) )
= top_to653038619l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(35,axiom,
! [A: fun_bool_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_167511280t_bool @ hAPP_f1325493883l_bool ) @ hAPP_f1418708797l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_163) ).
thf(334,plain,
! [A: fun_bool_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_167511280t_bool @ hAPP_f1325493883l_bool ) @ hAPP_f1418708797l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(168,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( B @ ( A @ produc170576535le_alt ) )
= ( D @ ( C @ produc170576535le_alt ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).
thf(894,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( B @ ( A @ produc170576535le_alt ) )
= ( D @ ( C @ produc170576535le_alt ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(214,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_1838733848t_bool @ hAPP_f1230984105l_bool ) @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_funcset__mem) ).
thf(1091,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_1838733848t_bool @ hAPP_f1230984105l_bool ) @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(150,axiom,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_bo230129725t_bool] :
( ( D @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1848524425t_bool ) @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Pi__mem) ).
thf(825,plain,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_bo230129725t_bool] :
( ( D @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1848524425t_bool ) @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(174,axiom,
! [A: produc624534567le_alt] : ( A @ ( top_to710777827t_bool @ hAPP_P751176071t_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top1I) ).
thf(952,plain,
! [A: produc624534567le_alt] : ( A @ ( top_to710777827t_bool @ hAPP_P751176071t_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(24,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1207925178t_bool @ hAPP_f1364159657i_bool ) @ hAPP_f906860201i_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___161) ).
thf(302,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1207925178t_bool @ hAPP_f1364159657i_bool ) @ hAPP_f906860201i_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,axiom,
( top_to653038619l_bool
= ( fTrue @ ( cOMBK_70145528t_bool @ hAPP_b1178471617l_bool ) @ collec861220362t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_UNIV__def) ).
thf(297,plain,
( top_to653038619l_bool
= ( fTrue @ ( cOMBK_70145528t_bool @ hAPP_b1178471617l_bool ) @ collec861220362t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: arrow_501706939e_indi] : ( A @ ( top_to850136695i_bool @ hAPP_A1059798043i_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top1I) ).
thf(424,plain,
! [A: arrow_501706939e_indi] : ( A @ ( top_to850136695i_bool @ hAPP_A1059798043i_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(14,axiom,
( top_to1057791589l_bool
= ( fTrue @ ( cOMBK_1801013008t_bool @ hAPP_b1017527359l_bool ) @ collec1697917566t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_UNIV__def) ).
thf(275,plain,
( top_to1057791589l_bool
= ( fTrue @ ( cOMBK_1801013008t_bool @ hAPP_b1017527359l_bool ) @ collec1697917566t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: fun_fu383145951l_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ hAPP_f1265202753l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_169) ).
thf(260,plain,
! [A: fun_fu383145951l_bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ hAPP_f1265202753l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(226,axiom,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_bo1613497205l_bool] :
( ( D @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1178471617l_bool ) @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Pi__mem) ).
thf(1123,plain,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_bo1613497205l_bool] :
( ( D @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1178471617l_bool ) @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(162,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool] :
( ( B @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f725100827l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__def) ).
thf(862,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool] :
( ( ( A @ ( B @ hAPP_f725100827l_bool ) @ hBOOL )
=> ( B @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f725100827l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(70,axiom,
arrow_1880704820e_Prof @ ( p @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
thf(467,plain,
arrow_1880704820e_Prof @ ( p @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(33,axiom,
( top_to2127553399l_bool
= ( fTrue @ ( cOMBK_1362474068t_bool @ hAPP_b930206237l_bool ) @ collec154865254t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_UNIV__def) ).
thf(329,plain,
( top_to2127553399l_bool
= ( fTrue @ ( cOMBK_1362474068t_bool @ hAPP_b930206237l_bool ) @ collec154865254t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(114,axiom,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A1741215436di_nat ) )
= ( A @ ( C @ hAPP_A1741215436di_nat ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_inj__on__iff) ).
thf(665,plain,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP_A1741215436di_nat ) )
= ( A @ ( C @ hAPP_A1741215436di_nat ) ) ) )
& ( ( ( B @ ( C @ hAPP_A1741215436di_nat ) )
= ( A @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(208,axiom,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_Pr1639951081t_bool] :
( ( D @ ( cOMBK_1897375160l_bool @ hAPP_f1758973969t_bool ) @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_funcset__mem) ).
thf(1079,plain,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_Pr1639951081t_bool] :
( ( D @ ( cOMBK_1897375160l_bool @ hAPP_f1758973969t_bool ) @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(131,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).
thf(710,plain,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(185,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_fu23838287i_bool] :
( ( D @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1511451035i_bool ) @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Pi__mem) ).
thf(974,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu2069019647e_indi,C: fun_fu103733537l_bool,D: fun_fu23838287i_bool] :
( ( D @ ( C @ pi_fun1549517203e_indi ) @ ( B @ member422031058e_indi @ hAPP_f243652437l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1511451035i_bool ) @ ( A @ ( B @ hAPP_f1631746589e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(18,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp) ).
thf(285,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(83,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_1207925178t_bool @ hAPP_f1364159657i_bool ) @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_funcset__mem) ).
thf(522,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_1207925178t_bool @ hAPP_f1364159657i_bool ) @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(152,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1784032663l_bool] :
( ( D @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1790795747l_bool ) @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_PiE) ).
thf(830,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1784032663l_bool] :
( ( D @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1790795747l_bool ) @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(213,axiom,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_fu1251737213l_bool] :
( ( D @ ( cOMBK_343479628l_bool @ hAPP_f989466937l_bool ) @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_funcset__mem) ).
thf(1089,plain,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_fu1251737213l_bool] :
( ( D @ ( cOMBK_343479628l_bool @ hAPP_f989466937l_bool ) @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(29,axiom,
! [A: fun_fu1760369922t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_1932856316e_indi ) @ hAPP_A711829680t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( A @ hAPP_f1699392794t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf) ).
thf(317,plain,
! [A: fun_fu1760369922t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_1932856316e_indi ) @ hAPP_A711829680t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( A @ hAPP_f1699392794t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(109,axiom,
! [A: fun_Ar2047178847t_bool] :
( ( A @ ( top_to653038619l_bool @ hAPP_f1095388607l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_top__apply) ).
thf(650,plain,
! [A: fun_Ar2047178847t_bool] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to653038619l_bool @ hAPP_f1095388607l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to653038619l_bool @ hAPP_f1095388607l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(99,axiom,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(615,plain,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(57,axiom,
lba @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(403,plain,
lba @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(62,axiom,
! [A: arrow_501706939e_indi] : ( top_to850136695i_bool @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_UNIV__I) ).
thf(420,plain,
! [A: arrow_501706939e_indi] : ( top_to850136695i_bool @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(223,axiom,
lab @ ( b @ ( a @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(1118,plain,
lab @ ( b @ ( a @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(233,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Ar2047178847t_bool] :
( ( D @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A2044747691t_bool ) @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Pi__mem) ).
thf(1160,plain,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Ar2047178847t_bool] :
( ( D @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A2044747691t_bool ) @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(73,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_1853791052t_bool @ hAPP_f1364914207l_bool ) @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_funcset__mem) ).
thf(476,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_1853791052t_bool @ hAPP_f1364914207l_bool ) @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(85,axiom,
! [A: fun_Ar2035712896di_nat] :
( ! [B: arrow_501706939e_indi,C: arrow_501706939e_indi] :
( ( ( B @ ( A @ hAPP_A1741215436di_nat ) )
= ( C @ ( A @ hAPP_A1741215436di_nat ) ) )
=> ( B = C ) )
=> ( top_to850136695i_bool @ ( A @ inj_on1177549232di_nat ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_injI) ).
thf(526,plain,
! [A: fun_Ar2035712896di_nat] :
( ! [B: arrow_501706939e_indi,C: arrow_501706939e_indi] :
( ( ( B @ ( A @ hAPP_A1741215436di_nat ) )
= ( C @ ( A @ hAPP_A1741215436di_nat ) ) )
=> ( B = C ) )
=> ( top_to850136695i_bool @ ( A @ inj_on1177549232di_nat ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(92,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt] :
( ( A != B )
=> ? [C: fun_Pr1639951081t_bool] :
( ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
& ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_complete__Lin) ).
thf(590,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt] :
( ( A != B )
=> ? [C: fun_Pr1639951081t_bool] :
( ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
& ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(118,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_order__less__asym_H) ).
thf(679,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(129,axiom,
! [A: bool] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_iso__tuple__UNIV__I) ).
thf(706,plain,
! [A: bool] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(102,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar884201459l_bool] :
( ( D @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A107624255l_bool ) @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Pi__mem) ).
thf(622,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar884201459l_bool] :
( ( D @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A107624255l_bool ) @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order__less__trans) ).
thf(393,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_linorder__cases) ).
thf(1099,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(127,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_funcset__mem) ).
thf(701,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(229,axiom,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_Pr534938793l_bool] :
( ( D @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P2005668213l_bool ) @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_PiE) ).
thf(1131,plain,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_Pr534938793l_bool] :
( ( D @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P2005668213l_bool ) @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(238,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( B @ ( A @ produc170576535le_alt ) )
= ( D @ ( C @ produc170576535le_alt ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).
thf(1192,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ produc170576535le_alt ) )
= ( D @ ( C @ produc170576535le_alt ) ) ) )
& ( ( ( B @ ( A @ produc170576535le_alt ) )
= ( D @ ( C @ produc170576535le_alt ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(188,axiom,
! [A: arrow_501706939e_indi,B: nat,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= B )
=> ( ( B @ ( C @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_inv__f__eq) ).
thf(984,plain,
! [A: arrow_501706939e_indi,B: nat,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= B )
=> ( ( B @ ( C @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(132,axiom,
! [A: fun_fu50365883t_bool] : ( top_to2127553399l_bool @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).
thf(721,plain,
! [A: fun_fu50365883t_bool] : ( top_to2127553399l_bool @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(96,axiom,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_Pr534938793l_bool] :
( ( D @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P2005668213l_bool ) @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Pi__mem) ).
thf(605,plain,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_Pr534938793l_bool] :
( ( D @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P2005668213l_bool ) @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(11,axiom,
! [A: fun_fu193278215t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_715840641e_indi ) @ hAPP_A784015157t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( A @ hAPP_f1560118175t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_173) ).
thf(266,plain,
! [A: fun_fu193278215t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_715840641e_indi ) @ hAPP_A784015157t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( A @ hAPP_f1560118175t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,axiom,
! [A: bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_70145528t_bool @ hAPP_b1178471617l_bool ) @ hAPP_f1095388607l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).
thf(360,plain,
! [A: bool,B: fun_Ar2047178847t_bool] :
( ( B @ ( A @ ( cOMBK_70145528t_bool @ hAPP_b1178471617l_bool ) @ hAPP_f1095388607l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(80,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_fu1867632401i_bool] :
( ( D @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f906860201i_bool ) @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_PiE) ).
thf(508,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu334384573e_indi,C: fun_fu383145951l_bool,D: fun_fu1867632401i_bool] :
( ( D @ ( C @ pi_fun2132478361e_indi ) @ ( B @ member993084970e_indi @ hAPP_f359017159l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f906860201i_bool ) @ ( A @ ( B @ hAPP_f671542927e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(27,axiom,
! [A: fun_Ar1871347069i_bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_328807062le_alt @ hAPP_f1561296623i_bool ) @ hAPP_P259956691i_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__) ).
thf(311,plain,
! [A: fun_Ar1871347069i_bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_328807062le_alt @ hAPP_f1561296623i_bool ) @ hAPP_P259956691i_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(55,axiom,
! [A: fun_Ar2047178847t_bool] : ( A @ ( top_to653038619l_bool @ hAPP_f1095388607l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top1I) ).
thf(398,plain,
! [A: fun_Ar2047178847t_bool] : ( A @ ( top_to653038619l_bool @ hAPP_f1095388607l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(167,axiom,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_P751176071t_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_mem__def) ).
thf(888,plain,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool] :
( ( ( A @ ( B @ hAPP_P751176071t_bool ) @ hBOOL )
=> ( B @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P751176071t_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(137,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool] :
( ( B @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f1944886577l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mem__def) ).
thf(750,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool] :
( ( ( A @ ( B @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(101,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ord__eq__less__trans) ).
thf(618,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(67,axiom,
! [A: fun_Pr1639951081t_bool] :
( ! [B: produc624534567le_alt] : ( B @ ( A @ hAPP_P751176071t_bool ) @ hBOOL )
<=> ! [B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] : ( C @ ( B @ produc170576535le_alt ) @ ( A @ hAPP_P751176071t_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).
thf(430,plain,
! [A: fun_Pr1639951081t_bool] :
( ( ! [B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] : ( C @ ( B @ produc170576535le_alt ) @ ( A @ hAPP_P751176071t_bool ) @ hBOOL )
=> ! [B: produc624534567le_alt] : ( B @ ( A @ hAPP_P751176071t_bool ) @ hBOOL ) )
& ( ! [B: produc624534567le_alt] : ( B @ ( A @ hAPP_P751176071t_bool ) @ hBOOL )
=> ! [B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] : ( C @ ( B @ produc170576535le_alt ) @ ( A @ hAPP_P751176071t_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,axiom,
! [A: fun_Ar156616864t_bool,B: nat,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_998415407t_bool ) @ hAPP_A1059798043i_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1239621182t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000) ).
thf(279,plain,
! [A: fun_Ar156616864t_bool,B: nat,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_998415407t_bool ) @ hAPP_A1059798043i_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1239621182t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(123,axiom,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_bo2138151889l_bool] :
( ( D @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b930206237l_bool ) @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_PiE) ).
thf(689,plain,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_bo2138151889l_bool] :
( ( D @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b930206237l_bool ) @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(49,axiom,
( top_to710777827t_bool
= ( fTrue @ ( cOMBK_350462144le_alt @ hAPP_b1848524425t_bool ) @ collec2140722898le_alt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_UNIV__def) ).
thf(375,plain,
( top_to710777827t_bool
= ( fTrue @ ( cOMBK_350462144le_alt @ hAPP_b1848524425t_bool ) @ collec2140722898le_alt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(231,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt] :
( ( D @ ( C @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).
thf(1135,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt] :
( ( ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) )
=> ( D @ ( C @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(59,axiom,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_328807062le_alt @ hAPP_f1561296623i_bool ) @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_funcset__mem) ).
thf(412,plain,
! [A: produc624534567le_alt,B: fun_Pr506339783e_indi,C: fun_Pr1639951081t_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_328807062le_alt @ hAPP_f1561296623i_bool ) @ ( C @ pi_Pro723839835e_indi ) @ ( B @ member555231642e_indi @ hAPP_f1270259485l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P163170789e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(169,axiom,
! [A: bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1801013008t_bool @ hAPP_b1017527359l_bool ) @ hAPP_f1944886577l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).
thf(904,plain,
! [A: bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1801013008t_bool @ hAPP_b1017527359l_bool ) @ hAPP_f1944886577l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_linorder__antisym__conv3) ).
thf(694,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(20,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193__096a_A_126_061_Ab_096) ).
thf(291,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(177,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Ar2047178847t_bool] :
( ( D @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A2044747691t_bool ) @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_PiE) ).
thf(958,plain,
! [A: arrow_501706939e_indi,B: fun_Ar795681735le_alt,C: fun_Ar1871347069i_bool,D: fun_Ar2047178847t_bool] :
( ( D @ ( C @ pi_Arr447918939le_alt ) @ ( B @ member844573594le_alt @ hAPP_f748921117l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A2044747691t_bool ) @ ( A @ ( B @ hAPP_A2034733541le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(157,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_fu103733537l_bool] :
( ( D @ ( cOMBK_30438862e_indi @ hAPP_f466810275l_bool ) @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_funcset__mem) ).
thf(843,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1200683263t_bool,C: fun_Ar1871347069i_bool,D: fun_fu103733537l_bool] :
( ( D @ ( cOMBK_30438862e_indi @ hAPP_f466810275l_bool ) @ ( C @ pi_Arr1077238675t_bool ) @ ( B @ member1701178322t_bool @ hAPP_f1753158741l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1159468061t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(227,axiom,
! [A: produc624534567le_alt] : ( top_to710777827t_bool @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_UNIV__I) ).
thf(1125,plain,
! [A: produc624534567le_alt] : ( top_to710777827t_bool @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(90,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( C != D )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [E: arrow_501706939e_indi] :
( ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( E @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).
thf(572,plain,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( C != D )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [E: arrow_501706939e_indi] :
( ( ( E @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( E @ ( B @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( E @ ( A @ hAPP_A2044747691t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( C @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(148,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_xt1_I10_J) ).
thf(787,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(78,axiom,
! [A: fun_fu103733537l_bool] :
( ( A != top_to653038619l_bool )
<=> ( top_to653038619l_bool @ ( A @ ( ord_le2059466615l_bool @ hAPP_f786935331l_bool ) @ hAPP_f1237345129l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_less__top) ).
thf(498,plain,
! [A: fun_fu103733537l_bool] :
( ( ( top_to653038619l_bool @ ( A @ ( ord_le2059466615l_bool @ hAPP_f786935331l_bool ) @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A != top_to653038619l_bool ) )
& ( ( A != top_to653038619l_bool )
=> ( top_to653038619l_bool @ ( A @ ( ord_le2059466615l_bool @ hAPP_f786935331l_bool ) @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(115,axiom,
! [A: fun_fu1251737213l_bool] :
~ ( A @ ( top_to2127553399l_bool @ ( ord_le1419690707l_bool @ hAPP_f1303771867l_bool ) @ hAPP_f1435434693l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_not__top__less) ).
thf(672,plain,
! [A: fun_fu1251737213l_bool] :
~ ( A @ ( top_to2127553399l_bool @ ( ord_le1419690707l_bool @ hAPP_f1303771867l_bool ) @ hAPP_f1435434693l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(240,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_order__less__irrefl) ).
thf(1209,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(119,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_519762474t_bool @ hAPP_f1224613979i_bool ) @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_funcset__mem) ).
thf(681,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_Ar1871347069i_bool] :
( ( D @ ( cOMBK_519762474t_bool @ hAPP_f1224613979i_bool ) @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(201,axiom,
! [A: fun_fu103733537l_bool] :
~ ( A @ ( top_to653038619l_bool @ ( ord_le2059466615l_bool @ hAPP_f786935331l_bool ) @ hAPP_f1237345129l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_not__top__less) ).
thf(1048,plain,
! [A: fun_fu103733537l_bool] :
~ ( A @ ( top_to653038619l_bool @ ( ord_le2059466615l_bool @ hAPP_f786935331l_bool ) @ hAPP_f1237345129l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(50,axiom,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(377,plain,
e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(4,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( fTrue @ ( if_fun95824985t_bool @ hAPP_b1702702257t_bool ) @ hAPP_f910728105t_bool ) @ hAPP_f727188501t_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp) ).
thf(245,plain,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( fTrue @ ( if_fun95824985t_bool @ hAPP_b1702702257t_bool ) @ hAPP_f910728105t_bool ) @ hAPP_f727188501t_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(94,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ord__less__eq__trans) ).
thf(599,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(100,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_fu658952305l_bool] :
( ( D @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1418708797l_bool ) @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_PiE) ).
thf(616,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_fu658952305l_bool] :
( ( D @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1418708797l_bool ) @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(225,axiom,
arrow_1008788854le_Lin @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( arrow_1880704820e_Prof @ pi_fun456133649t_bool ) @ ( f @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_assms_I1_J) ).
thf(1122,plain,
arrow_1008788854le_Lin @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( arrow_1880704820e_Prof @ pi_fun456133649t_bool ) @ ( f @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(106,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
=> ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).
thf(631,plain,
! [A: fun_Ar2047178847t_bool,B: fun_Ar2047178847t_bool,C: arrow_1621810872le_alt,D: arrow_1621810872le_alt,E: arrow_1621810872le_alt,F: arrow_1621810872le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_1880704820e_Prof @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( arrow_1880704820e_Prof @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ! [G: arrow_501706939e_indi] :
( ( ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A2044747691t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A2044747691t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f718157575t_bool ) @ ( F @ ( E @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f718157575t_bool ) @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(139,axiom,
arrow_1880704820e_Prof @ ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).
thf(758,plain,
arrow_1880704820e_Prof @ ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(39,axiom,
! [A: bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_206372180e_indi @ hAPP_b611520797i_bool ) @ hAPP_A1059798043i_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____yfv) ).
thf(345,plain,
! [A: bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_206372180e_indi @ hAPP_b611520797i_bool ) @ hAPP_A1059798043i_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__less__imp__not__eq2) ).
thf(535,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,axiom,
! [A: fun_fu50365883t_bool] :
( ( A @ ( top_to2127553399l_bool @ hAPP_f725100827l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_top__apply) ).
thf(609,plain,
! [A: fun_fu50365883t_bool] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to2127553399l_bool @ hAPP_f725100827l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to2127553399l_bool @ hAPP_f725100827l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(31,axiom,
! [A: bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_1362474068t_bool @ hAPP_b930206237l_bool ) @ hAPP_f725100827l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).
thf(323,plain,
! [A: bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_1362474068t_bool @ hAPP_b930206237l_bool ) @ hAPP_f725100827l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(234,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_order__less__imp__not__eq) ).
thf(1162,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(82,axiom,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_648664568l_bool @ hAPP_f71505983l_bool ) @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_funcset__mem) ).
thf(520,plain,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_fu383145951l_bool] :
( ( D @ ( cOMBK_648664568l_bool @ hAPP_f71505983l_bool ) @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(6,axiom,
! [A: fun_Ar2100459655t_bool,B: fun_Pr1639951081t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_64563468t_bool ) @ hAPP_A301260095t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1985966547t_bool ) @ hAPP_f910728105t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_174) ).
thf(251,plain,
! [A: fun_Ar2100459655t_bool,B: fun_Pr1639951081t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_64563468t_bool ) @ hAPP_A301260095t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1985966547t_bool ) @ hAPP_f910728105t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(104,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_167511280t_bool @ hAPP_f1325493883l_bool ) @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_funcset__mem) ).
thf(626,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_167511280t_bool @ hAPP_f1325493883l_bool ) @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(143,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Lin__irrefl) ).
thf(769,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(221,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_xt1_I2_J) ).
thf(1112,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(121,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1821573119l_bool] :
( ( D @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1710743709l_bool ) @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_PiE) ).
thf(685,plain,
! [A: arrow_501706939e_indi,B: fun_Ar2047178847t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar1821573119l_bool] :
( ( D @ ( C @ pi_Arr1358199477t_bool ) @ ( B @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1710743709l_bool ) @ ( A @ ( B @ hAPP_A2044747691t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_linorder__neqE) ).
thf(827,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(199,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_order__less__trans) ).
thf(1044,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool,C: fun_Ar1871347069i_bool] :
( ( C @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(23,axiom,
! [A: fun_bool_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1838733848t_bool @ hAPP_f1230984105l_bool ) @ hAPP_f2128533835l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).
thf(299,plain,
! [A: fun_bool_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( cOMBK_1838733848t_bool @ hAPP_f1230984105l_bool ) @ hAPP_f2128533835l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(241,plain,
~ ( p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(111,axiom,
! [A: fun_fu383145951l_bool] :
~ ( A @ ( top_to1057791589l_bool @ ( ord_le1472193545l_bool @ hAPP_f279586623l_bool ) @ hAPP_f180608831l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_not__top__less) ).
thf(658,plain,
! [A: fun_fu383145951l_bool] :
~ ( A @ ( top_to1057791589l_bool @ ( ord_le1472193545l_bool @ hAPP_f279586623l_bool ) @ hAPP_f180608831l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(203,axiom,
! [A: fun_Pr1639951081t_bool] : ( A @ ( top_to1057791589l_bool @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).
thf(1066,plain,
! [A: fun_Pr1639951081t_bool] : ( A @ ( top_to1057791589l_bool @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(868,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(159,axiom,
( ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBC_64563468t_bool ) @ cOMBC_1257424504t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).
thf(851,plain,
( ( ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBC_64563468t_bool ) @ cOMBC_1257424504t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBC_64563468t_bool ) @ cOMBC_1257424504t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(217,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A1741215436di_nat ) @ ( B @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_inv__f__f) ).
thf(1102,plain,
! [A: arrow_501706939e_indi,B: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( B @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A1741215436di_nat ) @ ( B @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(113,axiom,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_bo2138151889l_bool] :
( ( D @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b930206237l_bool ) @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Pi__mem) ).
thf(663,plain,
! [A: bool,B: fun_bo2136393469t_bool,C: fun_bool_bool,D: fun_bo2138151889l_bool] :
( ( D @ ( C @ pi_boo853084305t_bool ) @ ( B @ member1211611472t_bool @ hAPP_f759862099l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b930206237l_bool ) @ ( A @ ( B @ hAPP_b1112685083t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(108,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_fu1734842389l_bool] :
( ( D @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f626809057l_bool ) @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Pi__mem) ).
thf(648,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_fu1734842389l_bool] :
( ( D @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f626809057l_bool ) @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(209,axiom,
! [A: arrow_501706939e_indi] : ( top_to850136695i_bool @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_iso__tuple__UNIV__I) ).
thf(1081,plain,
! [A: arrow_501706939e_indi] : ( top_to850136695i_bool @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(38,axiom,
! [A: fun_fu1251737213l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_869185066e_indi @ hAPP_f544895323l_bool ) @ hAPP_A107624255l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_172) ).
thf(342,plain,
! [A: fun_fu1251737213l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_869185066e_indi @ hAPP_f544895323l_bool ) @ hAPP_A107624255l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_linorder__neq__iff) ).
thf(1181,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(76,axiom,
! [A: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1880704820e_Prof @ ( A @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_const__Lin__Prof) ).
thf(490,plain,
! [A: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1880704820e_Prof @ ( A @ ( cOMBK_164791446e_indi @ hAPP_f1172974131t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(116,axiom,
! [A: fun_fu50365883t_bool] : ( top_to2127553399l_bool @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).
thf(675,plain,
! [A: fun_fu50365883t_bool] : ( top_to2127553399l_bool @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(65,axiom,
~ ( lab @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(426,plain,
~ ( lab @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(235,axiom,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_inj__eq) ).
thf(1166,plain,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A = B )
=> ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) ) )
& ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__less__eq__trans) ).
thf(855,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(164,axiom,
( ( p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
thf(872,plain,
( ( ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( p @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( e @ ( p @ ( arrow_1126550734_mkbot @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( e @ ( c @ ( p @ ( arrow_2009189698_above @ cOMBB_715840641e_indi ) @ cOMBC_1994570734t_bool ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( e @ ( p @ ( arrow_1275257820_mktop @ cOMBB_1932856316e_indi ) @ cOMBC_377836265t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBS_1833320732t_bool ) @ cOMBS_1688227464t_bool ) @ ( f @ hAPP_f718157575t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(17,axiom,
! [A: fun_Ar2079322857t_bool,B: arrow_1621810872le_alt,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_1994570734t_bool ) @ hAPP_A711829680t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A784015157t_bool ) @ hAPP_A272835723t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_167) ).
thf(282,plain,
! [A: fun_Ar2079322857t_bool,B: arrow_1621810872le_alt,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_1994570734t_bool ) @ hAPP_A711829680t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A784015157t_bool ) @ hAPP_A272835723t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(175,axiom,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_funcset__mem) ).
thf(954,plain,
! [A: produc624534567le_alt,B: fun_Pr1639951081t_bool,C: fun_Pr1639951081t_bool,D: fun_bool_bool] :
( ( D @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ ( C @ pi_Pro811330557t_bool ) @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P751176071t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(10,axiom,
! [A: fun_Pr1639951081t_bool] :
( ( top_to1647826457l_bool @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ ( A @ pi_Pro811330557t_bool ) )
= top_to1057791589l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Pi__UNIV) ).
thf(263,plain,
! [A: fun_Pr1639951081t_bool] :
( ( top_to1647826457l_bool @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ ( A @ pi_Pro811330557t_bool ) )
= top_to1057791589l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [A: bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order__less__imp__triv) ).
thf(414,plain,
! [A: bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(183,axiom,
arrow_1008788854le_Lin @ ( lba @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116__096Lba_A_058_ALin_096) ).
thf(971,plain,
arrow_1008788854le_Lin @ ( lba @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(34,axiom,
! [A: fun_bo292969573t_bool,B: fun_Ar1871347069i_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_124649523e_indi ) @ hAPP_A1985966547t_bool ) )
= ( C @ ( B @ hAPP_A1059798043i_bool ) @ ( A @ hAPP_b1702702257t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).
thf(331,plain,
! [A: fun_bo292969573t_bool,B: fun_Ar1871347069i_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBB_124649523e_indi ) @ hAPP_A1985966547t_bool ) )
= ( C @ ( B @ hAPP_A1059798043i_bool ) @ ( A @ hAPP_b1702702257t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(197,axiom,
! [A: arrow_1621810872le_alt,B: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( A @ ( B @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_mkbot__Lin) ).
thf(1038,plain,
! [A: arrow_1621810872le_alt,B: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( A @ ( B @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(211,axiom,
! [A: fun_Pr1639951081t_bool] : ( top_to1057791589l_bool @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_UNIV__I) ).
thf(1085,plain,
! [A: fun_Pr1639951081t_bool] : ( top_to1057791589l_bool @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(170,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt] :
( ( D @ ( C @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).
thf(907,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool,D: arrow_1621810872le_alt] :
( ( ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) )
=> ( D @ ( C @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(128,axiom,
! [A: fun_Ar1871347069i_bool] :
~ ( A @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__less__irrefl) ).
thf(703,plain,
! [A: fun_Ar1871347069i_bool] :
~ ( A @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(110,axiom,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_bo230129725t_bool] :
( ( D @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1848524425t_bool ) @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_PiE) ).
thf(656,plain,
! [A: bool,B: fun_bo1156530537le_alt,C: fun_bool_bool,D: fun_bo230129725t_bool] :
( ( D @ ( C @ pi_boo158890749le_alt ) @ ( B @ member158436796le_alt @ hAPP_f899216831l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1848524425t_bool ) @ ( A @ ( B @ hAPP_b98736263le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(28,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(314,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_not__less__iff__gr__or__eq) ).
thf(876,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(859,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(158,axiom,
! [A: arrow_501706939e_indi] :
( ( A @ ( top_to850136695i_bool @ hAPP_A1059798043i_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_top__apply) ).
thf(845,plain,
! [A: arrow_501706939e_indi] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to850136695i_bool @ hAPP_A1059798043i_bool ) @ hBOOL ) )
& ( ( A @ ( top_to850136695i_bool @ hAPP_A1059798043i_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(45,axiom,
! [A: fun_bool_bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ hAPP_P2005668213l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).
thf(363,plain,
! [A: fun_bool_bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_290363320le_alt @ hAPP_f1601816755l_bool ) @ hAPP_P2005668213l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(186,axiom,
! [A: bool,B: fun_bool_bool] :
( ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_mem__def) ).
thf(976,plain,
! [A: bool,B: fun_bool_bool] :
( ( ( A @ ( B @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_xt1_I9_J) ).
thf(524,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(140,axiom,
! [A: arrow_1621810872le_alt,B: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( A @ ( B @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mktop__Lin) ).
thf(759,plain,
! [A: arrow_1621810872le_alt,B: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( B @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( A @ ( B @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_xt1_I1_J) ).
thf(771,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(219,axiom,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_bo1803678369l_bool] :
( ( D @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1017527359l_bool ) @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Pi__mem) ).
thf(1108,plain,
! [A: bool,B: fun_bo230129725t_bool,C: fun_bool_bool,D: fun_bo1803678369l_bool] :
( ( D @ ( C @ pi_boo683563155t_bool ) @ ( B @ member2079888426t_bool @ hAPP_f639792199l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1017527359l_bool ) @ ( A @ ( B @ hAPP_b1848524425t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__imp__neq) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(88,axiom,
! [A: arrow_501706939e_indi] :
( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
<=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).
thf(539,plain,
! [A: arrow_501706939e_indi] :
( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( e @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_order__less__asym_H) ).
thf(961,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__less__imp__not__eq2) ).
thf(963,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(136,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_fu1950461939i_bool] :
( ( D @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1559864639i_bool ) @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_PiE) ).
thf(748,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1743730523e_indi,C: fun_fu1251737213l_bool,D: fun_fu1950461939i_bool] :
( ( D @ ( C @ pi_fun1545124079e_indi ) @ ( B @ member95348014e_indi @ hAPP_f174050481l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1559864639i_bool ) @ ( A @ ( B @ hAPP_f87993209e_indi ) @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(41,axiom,
! [A: fun_Ar2040671475t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBS_1688227464t_bool ) @ hAPP_A2044747691t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( C @ ( A @ hAPP_A301260095t_bool ) @ hAPP_f727188501t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000) ).
thf(351,plain,
! [A: fun_Ar2040671475t_bool,B: fun_Ar2047178847t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBS_1688227464t_bool ) @ hAPP_A2044747691t_bool ) )
= ( C @ ( B @ hAPP_A2044747691t_bool ) @ ( C @ ( A @ hAPP_A301260095t_bool ) @ hAPP_f727188501t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_xt1_I2_J) ).
thf(731,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(194,axiom,
! [A: fun_Pr1639951081t_bool] :
~ ( A @ ( top_to710777827t_bool @ ( ord_le1051050815t_bool @ hAPP_f1911990195l_bool ) @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_not__top__less) ).
thf(1030,plain,
! [A: fun_Pr1639951081t_bool] :
~ ( A @ ( top_to710777827t_bool @ ( ord_le1051050815t_bool @ hAPP_f1911990195l_bool ) @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(51,axiom,
! [A: fun_Ar2035712896di_nat,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ inj_on1177549232di_nat ) @ hBOOL )
<=> ! [C: arrow_501706939e_indi] :
( ( B @ ( C @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ! [D: arrow_501706939e_indi] :
( ( B @ ( D @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A1741215436di_nat ) )
= ( D @ ( A @ hAPP_A1741215436di_nat ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_inj__on__def) ).
thf(378,plain,
! [A: fun_Ar2035712896di_nat,B: fun_Ar1871347069i_bool] :
( ( ! [C: arrow_501706939e_indi] :
( ( B @ ( C @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ! [D: arrow_501706939e_indi] :
( ( B @ ( D @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A1741215436di_nat ) )
= ( D @ ( A @ hAPP_A1741215436di_nat ) ) )
=> ( C = D ) ) ) )
=> ( B @ ( A @ inj_on1177549232di_nat ) @ hBOOL ) )
& ( ( B @ ( A @ inj_on1177549232di_nat ) @ hBOOL )
=> ! [C: arrow_501706939e_indi] :
( ( B @ ( C @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ! [D: arrow_501706939e_indi] :
( ( B @ ( D @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A1741215436di_nat ) )
= ( D @ ( A @ hAPP_A1741215436di_nat ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(81,axiom,
! [A: fun_fu50365883t_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( arrow_1322316103ctator @ hAPP_f1559864639i_bool ) @ hAPP_A1059798043i_bool ) @ hBOOL )
<=> ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f718157575t_bool ) )
= ( B @ ( C @ hAPP_A2044747691t_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_dictator__def) ).
thf(510,plain,
! [A: fun_fu50365883t_bool,B: arrow_501706939e_indi] :
( ( ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f718157575t_bool ) )
= ( B @ ( C @ hAPP_A2044747691t_bool ) ) ) )
=> ( B @ ( A @ ( arrow_1322316103ctator @ hAPP_f1559864639i_bool ) @ hAPP_A1059798043i_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( arrow_1322316103ctator @ hAPP_f1559864639i_bool ) @ hAPP_A1059798043i_bool ) @ hBOOL )
=> ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f718157575t_bool ) )
= ( B @ ( C @ hAPP_A2044747691t_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(13,axiom,
! [A: fun_fu383145951l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_648664568l_bool @ hAPP_f71505983l_bool ) @ hAPP_b1017527359l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).
thf(272,plain,
! [A: fun_fu383145951l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_648664568l_bool @ hAPP_f71505983l_bool ) @ hAPP_b1017527359l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(153,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_xt1_I9_J) ).
thf(832,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(207,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu746839971l_bool] :
( ( D @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1265202753l_bool ) @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_PiE) ).
thf(1077,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu50365883t_bool,C: fun_fu103733537l_bool,D: fun_fu746839971l_bool] :
( ( D @ ( C @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f1265202753l_bool ) @ ( A @ ( B @ hAPP_f718157575t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(74,axiom,
fTrue @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(478,plain,
fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(222,axiom,
! [A: produc624534567le_alt] : ( top_to710777827t_bool @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_iso__tuple__UNIV__I) ).
thf(1116,plain,
! [A: produc624534567le_alt] : ( top_to710777827t_bool @ ( A @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(230,axiom,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_bo1613497205l_bool] :
( ( D @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1178471617l_bool ) @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_PiE) ).
thf(1133,plain,
! [A: bool,B: fun_bo478202017t_bool,C: fun_bool_bool,D: fun_bo1613497205l_bool] :
( ( D @ ( C @ pi_boo2120406325t_bool ) @ ( B @ member1494646772t_bool @ hAPP_f1481710327l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1178471617l_bool ) @ ( A @ ( B @ hAPP_b114674879t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(191,axiom,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_order__less__imp__not__less) ).
thf(999,plain,
! [A: fun_Ar1871347069i_bool,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(181,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar884201459l_bool] :
( ( D @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A107624255l_bool ) @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_PiE) ).
thf(967,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1570071899t_bool,C: fun_Ar1871347069i_bool,D: fun_Ar884201459l_bool] :
( ( D @ ( C @ pi_Arr478149871t_bool ) @ ( B @ member2069173038t_bool @ hAPP_f598211249l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A107624255l_bool ) @ ( A @ ( B @ hAPP_A1168502649t_bool ) @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(155,axiom,
! [A: arrow_501706939e_indi,B: fun_Ar1871347069i_bool] :
( ( B @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_A1059798043i_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_mem__def) ).
thf(835,plain,
! [A: arrow_501706939e_indi,B: fun_Ar1871347069i_bool] :
( ( ( A @ ( B @ hAPP_A1059798043i_bool ) @ hBOOL )
=> ( B @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_A1059798043i_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__less__not__sym) ).
thf(422,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(95,axiom,
! [A: bool] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_UNIV__I) ).
thf(603,plain,
! [A: bool] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(135,axiom,
! [A: bool] :
( ~ ( ( A @ hBOOL )
<=> ( top_top_bool @ hBOOL ) )
<=> ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__top) ).
thf(735,plain,
! [A: bool] :
( ( ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ~ ( ( ( top_top_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ) )
& ( ~ ( ( ( top_top_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) )
=> ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(25,axiom,
! [A: fun_Ar1757019876t_bool,B: arrow_1621810872le_alt,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_377836265t_bool ) @ hAPP_A2044747691t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A711829680t_bool ) @ hAPP_A476679046t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_164) ).
thf(305,plain,
! [A: fun_Ar1757019876t_bool,B: arrow_1621810872le_alt,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_377836265t_bool ) @ hAPP_A2044747691t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A711829680t_bool ) @ hAPP_A476679046t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [A: fun_Ar2040671475t_bool,B: fun_Pr1639951081t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_1257424504t_bool ) @ hAPP_A2044747691t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A301260095t_bool ) @ hAPP_f727188501t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_168) ).
thf(326,plain,
! [A: fun_Ar2040671475t_bool,B: fun_Pr1639951081t_bool,C: arrow_501706939e_indi] :
( ( C @ ( B @ ( A @ cOMBC_1257424504t_bool ) @ hAPP_A2044747691t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A301260095t_bool ) @ hAPP_f727188501t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [A: fun_Ar1871347069i_bool] :
( ( A @ collec1241994086e_indi )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Collect__def) ).
thf(242,plain,
! [A: fun_Ar1871347069i_bool] :
( ( A @ collec1241994086e_indi )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: fun_fu103733537l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_1481288432l_bool @ hAPP_f2013855105l_bool ) @ hAPP_b1178471617l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv) ).
thf(294,plain,
! [A: fun_fu103733537l_bool,B: bool] :
( ( B @ ( A @ ( cOMBK_1481288432l_bool @ hAPP_f2013855105l_bool ) @ hAPP_b1178471617l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_order__less__asym) ).
thf(506,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(142,axiom,
! [A: nat] : ( arrow_1880704820e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBC_64563468t_bool ) @ cOMBC_1257424504t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_PiProf) ).
thf(767,plain,
! [A: nat] : ( arrow_1880704820e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1514803447e_indi ) @ cOMBC_998415407t_bool ) @ ( if_fun95824985t_bool @ cOMBB_124649523e_indi ) @ cOMBC_64563468t_bool ) @ cOMBC_1257424504t_bool ) @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(178,axiom,
n @ ( h @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) @ ( p @ hAPP_A2044747691t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).
thf(960,plain,
n @ ( h @ ( top_to850136695i_bool @ hilber797233813di_nat ) @ hAPP_n1582158000e_indi ) @ ( p @ hAPP_A2044747691t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(86,axiom,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( A != B )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
!= ( B @ ( C @ hAPP_A1741215436di_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inj__on__contraD) ).
thf(532,plain,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat,D: fun_Ar1871347069i_bool] :
( ( D @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( A != B )
=> ( ( D @ ( A @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member1124131880e_indi @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
!= ( B @ ( C @ hAPP_A1741215436di_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(166,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_fu1903211571l_bool] :
( ( D @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f2128533835l_bool ) @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Pi__mem) ).
thf(886,plain,
! [A: fun_Pr1639951081t_bool,B: fun_fu383145951l_bool,C: fun_fu383145951l_bool,D: fun_fu1903211571l_bool] :
( ( D @ ( C @ pi_fun779925307l_bool ) @ ( B @ member85421004l_bool @ hAPP_f1347377641l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f2128533835l_bool ) @ ( A @ ( B @ hAPP_f1944886577l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(195,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).
thf(1033,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(56,axiom,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_injD) ).
thf(400,plain,
! [A: arrow_501706939e_indi,B: arrow_501706939e_indi,C: fun_Ar2035712896di_nat] :
( ( top_to850136695i_bool @ ( C @ inj_on1177549232di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A1741215436di_nat ) )
= ( B @ ( C @ hAPP_A1741215436di_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(93,axiom,
! [A: fun_Pr1639951081t_bool,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] :
( ( B != C )
=> ( ( arrow_1008788854le_Lin @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( C @ ( B @ ( A @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_above__Lin) ).
thf(596,plain,
! [A: fun_Pr1639951081t_bool,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] :
( ( B != C )
=> ( ( arrow_1008788854le_Lin @ ( A @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( arrow_1008788854le_Lin @ ( C @ ( B @ ( A @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(133,axiom,
! [A: fun_Ar1871347069i_bool] :
( ( A != top_to850136695i_bool )
<=> ( top_to850136695i_bool @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__top) ).
thf(723,plain,
! [A: fun_Ar1871347069i_bool] :
( ( ( top_to850136695i_bool @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL )
=> ( A != top_to850136695i_bool ) )
& ( ( A != top_to850136695i_bool )
=> ( top_to850136695i_bool @ ( A @ ( ord_le287438291i_bool @ hAPP_f1993665755l_bool ) @ hAPP_f90330565l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(187,axiom,
~ ( lba @ ( b @ ( a @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(982,plain,
~ ( lba @ ( b @ ( a @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(69,axiom,
! [A: arrow_501706939e_indi] :
( ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).
thf(442,plain,
! [A: arrow_501706939e_indi] :
( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1126550734_mkbot @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A1741215436di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_2009189698_above @ hAPP_f1560118175t_bool ) @ hAPP_A272835723t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A1741215436di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A2044747691t_bool ) @ ( arrow_1275257820_mktop @ hAPP_f1699392794t_bool ) @ hAPP_A476679046t_bool ) @ ( d @ ( c @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(215,axiom,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( ~ ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( B @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_notin__Lin__iff) ).
thf(1093,plain,
! [A: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: fun_Pr1639951081t_bool] :
( ( arrow_1008788854le_Lin @ ( C @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( ( ( C @ ( A @ ( B @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(53,axiom,
arrow_1008788854le_Lin @ ( lab @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117__096Lab_A_058_ALin_096) ).
thf(395,plain,
arrow_1008788854le_Lin @ ( lab @ member641857340t_bool @ hAPP_f180608831l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(103,axiom,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_fu658952305l_bool] :
( ( D @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1418708797l_bool ) @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Pi__mem) ).
thf(624,plain,
! [A: fun_Ar2047178847t_bool,B: fun_fu103733537l_bool,C: fun_fu103733537l_bool,D: fun_fu658952305l_bool] :
( ( D @ ( C @ pi_fun953636405l_bool ) @ ( B @ member1120178292l_bool @ hAPP_f1394256759l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f1418708797l_bool ) @ ( A @ ( B @ hAPP_f1095388607l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(15,axiom,
( arrow_1880704820e_Prof
= ( arrow_1008788854le_Lin @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( top_to850136695i_bool @ pi_Arr1358199477t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Prof__def) ).
thf(277,plain,
( arrow_1880704820e_Prof
= ( arrow_1008788854le_Lin @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ ( top_to850136695i_bool @ pi_Arr1358199477t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(124,axiom,
f @ ( arrow_807483785nimity @ hAPP_f725100827l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).
thf(691,plain,
f @ ( arrow_807483785nimity @ hAPP_f725100827l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(47,axiom,
! [A: bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_350462144le_alt @ hAPP_b1848524425t_bool ) @ hAPP_P751176071t_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).
thf(369,plain,
! [A: bool,B: produc624534567le_alt] :
( ( B @ ( A @ ( cOMBK_350462144le_alt @ hAPP_b1848524425t_bool ) @ hAPP_P751176071t_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(97,axiom,
! [A: fun_fu50365883t_bool] : ( A @ ( top_to2127553399l_bool @ hAPP_f725100827l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top1I) ).
thf(607,plain,
! [A: fun_fu50365883t_bool] : ( A @ ( top_to2127553399l_bool @ hAPP_f725100827l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(7,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( fFalse @ ( if_fun95824985t_bool @ hAPP_b1702702257t_bool ) @ hAPP_f910728105t_bool ) @ hAPP_f727188501t_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp) ).
thf(254,plain,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ( B @ ( A @ ( fFalse @ ( if_fun95824985t_bool @ hAPP_b1702702257t_bool ) @ hAPP_f910728105t_bool ) @ hAPP_f727188501t_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [A: fun_bool_bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_1853791052t_bool @ hAPP_f1364914207l_bool ) @ hAPP_f626809057l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_170) ).
thf(337,plain,
! [A: fun_bool_bool,B: fun_fu50365883t_bool] :
( ( B @ ( A @ ( cOMBK_1853791052t_bool @ hAPP_f1364914207l_bool ) @ hAPP_f626809057l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(72,axiom,
! [A: arrow_501706939e_indi,B: fun_fu50365883t_bool] :
( ( arrow_1008788854le_Lin @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( arrow_1880704820e_Prof @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( A @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( C @ ( B @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
=> ( A @ ( B @ ( arrow_1322316103ctator @ hAPP_f1559864639i_bool ) @ hAPP_A1059798043i_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_dictatorI) ).
thf(469,plain,
! [A: arrow_501706939e_indi,B: fun_fu50365883t_bool] :
( ( arrow_1008788854le_Lin @ ( cOMBK_639770490t_bool @ hAPP_f459175489l_bool ) @ ( arrow_1880704820e_Prof @ pi_fun456133649t_bool ) @ ( B @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL )
=> ( ! [C: fun_Ar2047178847t_bool] :
( ( arrow_1880704820e_Prof @ ( C @ member558395596t_bool @ hAPP_f1237345129l_bool ) @ hBOOL )
=> ! [D: arrow_1621810872le_alt,E: arrow_1621810872le_alt] :
( ( D != E )
=> ( ( A @ ( C @ hAPP_A2044747691t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( C @ ( B @ hAPP_f718157575t_bool ) @ ( E @ ( D @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
=> ( A @ ( B @ ( arrow_1322316103ctator @ hAPP_f1559864639i_bool ) @ hAPP_A1059798043i_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
! [A: fun_fu383145951l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ hAPP_A1710743709l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_162) ).
thf(354,plain,
! [A: fun_fu383145951l_bool,B: arrow_501706939e_indi] :
( ( B @ ( A @ ( cOMBK_2098615510e_indi @ hAPP_f1651042461l_bool ) @ hAPP_A1710743709l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(173,axiom,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( B @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
<=> ( A @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_pred__equals__eq2) ).
thf(935,plain,
! [A: fun_Pr1639951081t_bool,B: fun_Pr1639951081t_bool] :
( ( ( B = A )
=> ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( A @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) ) )
& ( ! [C: arrow_1621810872le_alt,D: arrow_1621810872le_alt] :
( ( ( A @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( B @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL )
=> ( A @ ( D @ ( C @ produc170576535le_alt ) @ member1484933012le_alt @ hAPP_f1944886577l_bool ) @ hBOOL ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_xt1_I10_J) ).
thf(775,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(130,axiom,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_fu1734842389l_bool] :
( ( D @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f626809057l_bool ) @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_PiE) ).
thf(708,plain,
! [A: fun_fu50365883t_bool,B: fun_fu1251737213l_bool,C: fun_fu1251737213l_bool,D: fun_fu1734842389l_bool] :
( ( D @ ( C @ pi_fun465500049l_bool ) @ ( B @ member326955216l_bool @ hAPP_f1827424979l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f626809057l_bool ) @ ( A @ ( B @ hAPP_f725100827l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member256508712t_bool @ hAPP_f1435434693l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_order__less__imp__not__less) ).
thf(972,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1239,plain,
$false,
inference(e,[status(thm)],[1036,628,777,1110,479,1105,1083,468,1158,1005,683,1068,308,1173,269,677,340,930,404,1001,1127,841,1046,288,320,436,257,570,785,372,587,357,1087,969,416,492,756,789,1040,646,834,348,1051,687,692,956,1072,1119,396,998,988,428,1074,1206,248,661,761,366,334,894,1091,825,952,302,297,424,275,260,1123,862,467,329,665,1079,710,974,285,522,830,1089,317,650,615,403,420,1118,1160,476,526,590,679,706,622,393,1099,701,1131,1192,984,721,605,266,360,508,311,398,888,750,618,430,279,689,375,1135,412,904,694,291,958,843,1125,572,787,498,672,1209,681,1048,377,245,599,616,1122,631,758,345,535,609,323,1162,520,251,626,769,1112,685,827,1044,299,241,658,1066,868,851,1102,663,648,1081,342,1181,490,675,426,1166,855,872,282,954,263,414,971,331,1038,1085,907,703,656,314,876,859,845,363,976,524,759,771,1108,931,539,961,963,748,351,731,1030,378,510,272,832,1077,478,1116,1133,999,967,835,422,603,735,305,326,242,294,506,767,960,532,886,1033,400,596,723,982,442,1093,395,624,277,691,369,607,254,337,469,354,935,775,708,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT171_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50 % Computer : n001.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 06:43:42 UTC 2026
% 0.23/0.51 % CPUTime :
% 0.23/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.35/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.12/1.95 % [INFO] Parsing done (577ms).
% 3.12/1.97 % [INFO] Running in sequential loop mode.
% 4.84/2.57 % [INFO] eprover registered as external prover.
% 4.84/2.59 % [INFO] Scanning for conjecture ...
% 5.70/2.86 % [INFO] Found a conjecture (or negated_conjecture) and 238 axioms. Running axiom selection ...
% 6.52/3.15 % [INFO] Axiom selection finished. Selected 238 axioms (removed 0 axioms).
% 8.07/3.59 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.42/3.63 % [INFO] Type checking passed.
% 8.42/3.65 % [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 ...
% 11.04/4.42 % [INFO] [Domain constraints] Detected constraint on bool
% 11.04/4.42 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 11.04/4.48 % [INFO] [Domain constraints] Detected constraint on bool
% 11.04/4.48 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 22.39/7.69 % External prover 'e' found a proof!
% 22.39/7.69 % [INFO] Killing All external provers ...
% 22.39/7.69 % Time passed: 6971ms (effective reasoning time: 5706ms)
% 22.39/7.69 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 22.39/7.70 % Axioms used in derivation (238): fact_115_assms_I1_J, fact_132_dictatorI, fact_113_inj__imp__inv__eq, fact_25_top1I, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_168, fact_45_top__apply, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_162, fact_65_xt1_I1_J, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_172, fact_31_UNIV__I, fact_83_less__imp__neq, fact_112_injD, fact_101_less__top, fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel, fact_127_mktop__Lin, fact_179_funcset__mem, fact_152_Pi__mem, fact_97_less__top, fact_185_funcset__mem, fact_141_PiE, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_92_UNIV__def, fact_63_ord__less__eq__trans, fact_136_PiE, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_163, fact_187_dictator__def, fact_58_order__less__trans, fact_87_not__less__iff__gr__or__eq, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__, fact_68_xt1_I9_J, fact_172_funcset__mem, fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am, fact_6__C2_C, fact_142_PiE, fact_67_ord__eq__less__trans, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel, fact_22_Pair__eq, fact_79_order__less__imp__not__less, help_fTrue_1_1_T, fact_0_assms_I3_J, fact_64_xt1_I1_J, fact_77_order__less__imp__not__eq, fact_148_PiE, fact_41_iso__tuple__UNIV__I, fact_106_inv__into__f__eq, fact_128_mkbot__Lin, fact_55_order__less__asym, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_3__096P_A_058_AProf_096, fact_161_Pi__mem, fact_75_order__less__imp__not__eq2, fact_89_order__less__irrefl, fact_43_top__apply, fact_182_funcset__mem, help_fTrue_1_1_U, fact_29_top1I, fact_40_iso__tuple__UNIV__I, fact_180_funcset__mem, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_175, fact_109_inj__on__contraD, fact_175_funcset__mem, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_170, fact_166_Pi__mem, fact_30_UNIV__I, fact_28_top1I, fact_38_iso__tuple__UNIV__I, fact_125_mem__def, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_167, fact_121_mem__def, fact_44_top__apply, fact_21_Pair__inject, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_169, fact_165_Pi__mem, fact_20_injh, fact_178_funcset__mem, fact_131_in__above, help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp, fact_107_inj__eq, fact_105_inv__into__f__f, fact_86_linorder__less__linear, fact_103_inv__f__eq, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It, fact_133_PiE, fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_168_Pi__mem, fact_160_Pi__mem, fact_177_funcset__mem, fact_183_funcset__mem, fact_153_Pi__mem, fact_23_IIA__def, fact_164_Pi__mem, fact_150_complete__Lin, fact_184_funcset__mem, fact_130_const__Lin__Prof, fact_47_not__top__less, fact_74_order__less__imp__not__eq2, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv, fact_88_linorder__neq__iff, fact_181_funcset__mem, help_fequal_1_1_fequal_000tc__Nat__Onat_T, fact_111_inj__onD, fact_140_PiE, fact_32_UNIV__I, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_, fact_70_order__less__asym_H, fact_37_iso__tuple__UNIV__I, fact_82_less__imp__neq, fact_120_mem__def, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe, fact_116__096Lba_A_058_ALin_096, fact_59_order__less__trans, fact_69_xt1_I9_J, fact_100_less__top, fact_56_xt1_I10_J, fact_138_PiE, fact_110_inj__on__iff, fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___161, fact_46_top__apply, fact_124_mem__def, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____yfv, fact_162_Pi__mem, fact_85_linorder__antisym__conv3, fact_186_funcset__mem, fact_149_PiE, fact_72_order__less__imp__triv, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000, fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am, fact_119_notin__Lin__iff, fact_91_UNIV__def, fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J, fact_52_not__top__less, fact_71_order__less__asym_H, fact_2__096c_A_126_061_Ad_096, fact_26_top1I, fact_4_in__mkbot, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_174, fact_96_pred__equals__eq2, fact_163_Pi__mem, fact_8__C4_C, fact_50_not__top__less, fact_66_ord__eq__less__trans, fact_98_less__top, fact_134_PiE, fact_171_funcset__mem, fact_57_xt1_I10_J, fact_35_UNIV__I, fact_189_Pi__UNIV, fact_99_less__top, fact_36_iso__tuple__UNIV__I, fact_49_not__top__less, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__, help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp, fact_154_Pi__mem, fact_143_PiE, fact_151_PiProf, fact_93_UNIV__def, fact_78_order__less__imp__not__less, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___171, fact_156_Pi__mem, fact_24_unanimity__def, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000, fact_90_order__less__irrefl, fact_1_u, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf, fact_9_pairwise__neutrality, fact_51_not__top__less, fact_33_UNIV__I, fact_176_funcset__mem, fact_60_xt1_I2_J, fact_14_PW, fact_27_top1I, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf, fact_188_Pi__UNIV, fact_193__096a_A_126_061_Ab_096, fact_144_PiE, fact_39_iso__tuple__UNIV__I, fact_169_Prof__def, fact_118_Lin__irrefl, fact_155_Pi__mem, fact_81_order__less__not__sym, fact_15_split__paired__All, fact_129_above__Lin, help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp, fact_126_Collect__def, fact_102_less__top, fact_76_order__less__imp__not__eq, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_166, fact_5_in__mktop, fact_7__C1_C, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_160, fact_147_PiE, fact_19_n_I1_J, fact_159_Pi__mem, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_62_ord__less__eq__trans, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_, fact_117__096Lab_A_058_ALin_096, fact_104_inv__f__f, fact_95_UNIV__def, fact_61_xt1_I2_J, fact_73_order__less__imp__triv, fact_84_linorder__neqE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_173, fact_48_not__top__less, fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai, fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_164, fact_108_inj__on__def, fact_158_Pi__mem, fact_10__C3_C, fact_139_PiE, fact_173_funcset__mem, fact_53_linorder__cases, fact_135_PiE, fact_34_UNIV__I, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe, fact_123_mem__def, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___165, fact_157_Pi__mem, fact_190_Pi__UNIV, fact_146_PiE, fact_54_order__less__asym, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_42_top__apply, fact_80_order__less__not__sym, fact_174_funcset__mem, fact_94_UNIV__def, fact_145_PiE, fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_114_injI, fact_137_PiE, fact_122_mem__def, fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0, fact_170_funcset__mem, fact_167_Pi__mem
% 22.39/7.70 % No. of inferences in proof: 480
% 22.91/7.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6971 ms resp. 5706 ms w/o parsing
% 23.99/8.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.44/8.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------