TSTP Solution File: SWW478+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW478+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:21 EDT 2023
% Result : Theorem 9.54s 3.03s
% Output : Refutation 10.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 411
% Syntax : Number of formulae : 626 ( 186 unt; 198 typ; 0 def)
% Number of atoms : 943 ( 400 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 6774 ( 162 ~; 14 |; 103 &;6097 @)
% ( 48 <=>; 350 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 269 ( 269 >; 0 *; 0 +; 0 <<)
% Number of symbols : 200 ( 198 usr; 63 con; 0-5 aty)
% Number of variables : 1586 ( 0 ^;1557 !; 29 ?;1586 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(member773094996on_val_type,type,
member773094996on_val: $i > $i > $i ).
thf(hAPP_P1886180715on_val_type,type,
hAPP_P1886180715on_val: $i > $i > $i ).
thf(hAPP_P1870962205on_val_type,type,
hAPP_P1870962205on_val: $i > $i > $i ).
thf(produc1441475159on_val_type,type,
produc1441475159on_val: $i ).
thf(hAPP_P604205461on_val_type,type,
hAPP_P604205461on_val: $i > $i > $i ).
thf(hAPP_e1659493427on_val_type,type,
hAPP_e1659493427on_val: $i > $i > $i ).
thf(produc1259058957on_val_type,type,
produc1259058957on_val: $i ).
thf(ea_type,type,
ea: $i ).
thf(hAPP_f1727192346on_val_type,type,
hAPP_f1727192346on_val: $i > $i > $i ).
thf(hAPP_f1849790461on_val_type,type,
hAPP_f1849790461on_val: $i > $i > $i ).
thf(produc899768717on_val_type,type,
produc899768717on_val: $i ).
thf(ha_type,type,
ha: $i ).
thf(fun_up1149430426on_val_type,type,
fun_up1149430426on_val: $i > $i > $i > $i ).
thf(la_type,type,
la: $i ).
thf(v_1_type,type,
v_1: $i ).
thf(some_val_type,type,
some_val: $i > $i ).
thf(v_type,type,
v: $i ).
thf(e_a_type,type,
e_a: $i ).
thf(h_a_type,type,
h_a: $i ).
thf(l_a_type,type,
l_a: $i ).
thf(red_type,type,
red: $i > $i ).
thf(p_type,type,
p: $i ).
thf(hAPP_l512744617ion_ty_type,type,
hAPP_l512744617ion_ty: $i > $i > $i ).
thf(cOMBK_1294242658t_char_type,type,
cOMBK_1294242658t_char: $i > $i ).
thf(fun_up424764369ion_ty_type,type,
fun_up424764369ion_ty: $i > $i > $i > $i ).
thf(none_ty_type,type,
none_ty: $i ).
thf(hAPP_f1175813647l_bool_type,type,
hAPP_f1175813647l_bool: $i > $i > $i ).
thf(hAPP_f850751421l_bool_type,type,
hAPP_f850751421l_bool: $i > $i > $i ).
thf(hAPP_f399538905l_bool_type,type,
hAPP_f399538905l_bool: $i > $i > $i ).
thf(cOMBB_1466889536on_val_type,type,
cOMBB_1466889536on_val: $i ).
thf(hAPP_f318082871l_bool_type,type,
hAPP_f318082871l_bool: $i > $i > $i ).
thf(hAPP_f1840640125on_val_type,type,
hAPP_f1840640125on_val: $i > $i > $i ).
thf(produc1988544340l_bool_type,type,
produc1988544340l_bool: $i ).
thf(produc1911463199l_bool_type,type,
produc1911463199l_bool: $i ).
thf(hAPP_P159683425l_bool_type,type,
hAPP_P159683425l_bool: $i > $i > $i ).
thf(hAPP_f2134824737l_bool_type,type,
hAPP_f2134824737l_bool: $i > $i > $i ).
thf(hAPP_f1308714617l_bool_type,type,
hAPP_f1308714617l_bool: $i > $i > $i ).
thf(cOMBB_338347573on_val_type,type,
cOMBB_338347573on_val: $i ).
thf(hAPP_bool_bool_type,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_e1833980889l_bool_type,type,
hAPP_e1833980889l_bool: $i > $i > $i ).
thf(hAPP_f546724245l_bool_type,type,
hAPP_f546724245l_bool: $i > $i > $i ).
thf(hAPP_f917296015l_bool_type,type,
hAPP_f917296015l_bool: $i > $i > $i ).
thf(cOMBB_740252943t_char_type,type,
cOMBB_740252943t_char: $i ).
thf(hAPP_P1708370145l_bool_type,type,
hAPP_P1708370145l_bool: $i > $i > $i ).
thf(hAPP_f926562337l_bool_type,type,
hAPP_f926562337l_bool: $i > $i > $i ).
thf(hAPP_f1560238713l_bool_type,type,
hAPP_f1560238713l_bool: $i > $i > $i ).
thf(cOMBB_672625589on_val_type,type,
cOMBB_672625589on_val: $i ).
thf(block_list_char_type,type,
block_list_char: $i > $i > $i > $i ).
thf(val_list_char_type,type,
val_list_char: $i > $i ).
thf(hAPP_f1033709212l_bool_type,type,
hAPP_f1033709212l_bool: $i > $i > $i ).
thf(hAPP_f1233687287l_bool_type,type,
hAPP_f1233687287l_bool: $i > $i > $i ).
thf(cOMBB_171276332on_val_type,type,
cOMBB_171276332on_val: $i ).
thf(hAPP_f1926378906on_val_type,type,
hAPP_f1926378906on_val: $i > $i > $i ).
thf(hAPP_f927043595l_bool_type,type,
hAPP_f927043595l_bool: $i > $i > $i ).
thf(hAPP_f1043869573l_bool_type,type,
hAPP_f1043869573l_bool: $i > $i > $i ).
thf(cOMBB_1259202826on_val_type,type,
cOMBB_1259202826on_val: $i ).
thf(hAPP_f524589473l_bool_type,type,
hAPP_f524589473l_bool: $i > $i > $i ).
thf(hAPP_f600512025on_val_type,type,
hAPP_f600512025on_val: $i > $i > $i ).
thf(some_ty_type,type,
some_ty: $i > $i ).
thf(seq_list_char_type,type,
seq_list_char: $i > $i > $i ).
thf(is_bool_type,type,
is_bool: $i > $o ).
thf(hAPP_P1116729363l_bool_type,type,
hAPP_P1116729363l_bool: $i > $i > $i ).
thf(hAPP_f1241216909l_bool_type,type,
hAPP_f1241216909l_bool: $i > $i > $i ).
thf(hAPP_f1438732387l_bool_type,type,
hAPP_f1438732387l_bool: $i > $i > $i ).
thf(cOMBB_635947099on_val_type,type,
cOMBB_635947099on_val: $i ).
thf(hAPP_f1712766199l_bool_type,type,
hAPP_f1712766199l_bool: $i > $i > $i ).
thf(hAPP_P2083594489on_val_type,type,
hAPP_P2083594489on_val: $i > $i > $i ).
thf(hAPP_f603925568l_bool_type,type,
hAPP_f603925568l_bool: $i > $i > $i ).
thf(hAPP_f181262431l_bool_type,type,
hAPP_f181262431l_bool: $i > $i > $i ).
thf(cOMBC_832625297y_bool_type,type,
cOMBC_832625297y_bool: $i ).
thf(hAPP_f1001225811y_bool_type,type,
hAPP_f1001225811y_bool: $i > $i > $i ).
thf(hAPP_f2060496320y_bool_type,type,
hAPP_f2060496320y_bool: $i > $i > $i ).
thf(produc399384568l_bool_type,type,
produc399384568l_bool: $i ).
thf(produc1815960045l_bool_type,type,
produc1815960045l_bool: $i ).
thf(hAPP_f641257349l_bool_type,type,
hAPP_f641257349l_bool: $i > $i > $i ).
thf(hAPP_f2032347769l_bool_type,type,
hAPP_f2032347769l_bool: $i > $i > $i ).
thf(cOMBB_466903633on_val_type,type,
cOMBB_466903633on_val: $i ).
thf(hAPP_f2052660463l_bool_type,type,
hAPP_f2052660463l_bool: $i > $i > $i ).
thf(cOMBB_1292453606on_val_type,type,
cOMBB_1292453606on_val: $i ).
thf(hAPP_P282169671l_bool_type,type,
hAPP_P282169671l_bool: $i > $i > $i ).
thf(hAPP_f602593190on_val_type,type,
hAPP_f602593190on_val: $i > $i > $i ).
thf(hAPP_l207779698on_val_type,type,
hAPP_l207779698on_val: $i > $i > $i ).
thf(cOMBK_1097134891t_char_type,type,
cOMBK_1097134891t_char: $i > $i ).
thf(member763590124on_val_type,type,
member763590124on_val: $i > $i > $i ).
thf(hAPP_f555424277l_bool_type,type,
hAPP_f555424277l_bool: $i > $i > $i ).
thf(hAPP_f1734879897l_bool_type,type,
hAPP_f1734879897l_bool: $i > $i > $i ).
thf(cOMBB_1522540928on_val_type,type,
cOMBB_1522540928on_val: $i ).
thf(hAPP_f1074020887l_bool_type,type,
hAPP_f1074020887l_bool: $i > $i > $i ).
thf(wTrt_type,type,
wTrt: $i > $i > $i > $i > $i > $i ).
thf(lAss_list_char_type,type,
lAss_list_char: $i > $i > $i ).
thf(wf_pro755087577t_char_type,type,
wf_pro755087577t_char: $i > $i > $i ).
thf(produc2128769400l_bool_type,type,
produc2128769400l_bool: $i ).
thf(produc1958875245l_bool_type,type,
produc1958875245l_bool: $i ).
thf(assigned_type,type,
assigned: $i > $i > $i ).
thf(hAPP_f550652027l_bool_type,type,
hAPP_f550652027l_bool: $i > $i > $i ).
thf(hAPP_f838396643l_bool_type,type,
hAPP_f838396643l_bool: $i > $i > $i ).
thf(cOMBC_2027949654l_bool_type,type,
cOMBC_2027949654l_bool: $i ).
thf(hAPP_f1617787571l_bool_type,type,
hAPP_f1617787571l_bool: $i > $i > $i ).
thf(hAPP_f61040418l_bool_type,type,
hAPP_f61040418l_bool: $i > $i > $i ).
thf(cOMBS_570216337l_bool_type,type,
cOMBS_570216337l_bool: $i > $i > $i ).
thf(hAPP_f1492320500l_bool_type,type,
hAPP_f1492320500l_bool: $i > $i > $i ).
thf(hAPP_f1523875321l_bool_type,type,
hAPP_f1523875321l_bool: $i > $i > $i ).
thf(hAPP_f592397849l_bool_type,type,
hAPP_f592397849l_bool: $i > $i > $i ).
thf(cOMBB_1718333400on_val_type,type,
cOMBB_1718333400on_val: $i ).
thf(hAPP_f1863694447l_bool_type,type,
hAPP_f1863694447l_bool: $i > $i > $i ).
thf(hAPP_f1145256474l_bool_type,type,
hAPP_f1145256474l_bool: $i > $i > $i ).
thf(cOMBB_383678192on_val_type,type,
cOMBB_383678192on_val: $i ).
thf(hAPP_f1301559543l_bool_type,type,
hAPP_f1301559543l_bool: $i > $i > $i ).
thf(hAPP_f1825030711l_bool_type,type,
hAPP_f1825030711l_bool: $i > $i > $i ).
thf(cOMBB_877741809on_val_type,type,
cOMBB_877741809on_val: $i ).
thf(hAPP_P1776198677on_val_type,type,
hAPP_P1776198677on_val: $i > $i > $i ).
thf(hAPP_f881985847l_bool_type,type,
hAPP_f881985847l_bool: $i > $i > $i ).
thf(cOMBB_1083177073on_val_type,type,
cOMBB_1083177073on_val: $i ).
thf(hAPP_P789556885on_val_type,type,
hAPP_P789556885on_val: $i > $i > $i ).
thf(hAPP_f1452292669l_bool_type,type,
hAPP_f1452292669l_bool: $i > $i > $i ).
thf(hAPP_f1977633121l_bool_type,type,
hAPP_f1977633121l_bool: $i > $i > $i ).
thf(cOMBB_1303934920on_val_type,type,
cOMBB_1303934920on_val: $i ).
thf(hAPP_b589554111l_bool_type,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(member840932460on_val_type,type,
member840932460on_val: $i > $i > $i ).
thf(hAPP_f857351829l_bool_type,type,
hAPP_f857351829l_bool: $i > $i > $i ).
thf(hAPP_f348318673l_bool_type,type,
hAPP_f348318673l_bool: $i > $i > $i ).
thf(cOMBB_1518282696on_val_type,type,
cOMBB_1518282696on_val: $i ).
thf(hAPP_f1213370163y_bool_type,type,
hAPP_f1213370163y_bool: $i > $i > $i ).
thf(widen_2090681816t_char_type,type,
widen_2090681816t_char: $i > $i > $i > $i ).
thf(hAPP_f653692369l_bool_type,type,
hAPP_f653692369l_bool: $i > $i > $i ).
thf(hAPP_f516738477l_bool_type,type,
hAPP_f516738477l_bool: $i > $i > $i ).
thf(cOMBB_819439237t_char_type,type,
cOMBB_819439237t_char: $i ).
thf(hAPP_e108155315on_val_type,type,
hAPP_e108155315on_val: $i > $i > $i ).
thf(e_type,type,
e: $i ).
thf(t_1_type,type,
t_1: $i ).
thf(t_type,type,
t: $i ).
thf(hAPP_f1363667773l_bool_type,type,
hAPP_f1363667773l_bool: $i > $i > $i ).
thf(hAPP_f1050935001l_bool_type,type,
hAPP_f1050935001l_bool: $i > $i > $i ).
thf(cOMBB_1153617344on_val_type,type,
cOMBB_1153617344on_val: $i ).
thf(hAPP_f1008932791l_bool_type,type,
hAPP_f1008932791l_bool: $i > $i > $i ).
thf(hAPP_f635218277l_bool_type,type,
hAPP_f635218277l_bool: $i > $i > $i ).
thf(typeSa1234865140_sconf_type,type,
typeSa1234865140_sconf: $i > $i > $i ).
thf(hAPP_f1930574389l_bool_type,type,
hAPP_f1930574389l_bool: $i > $i > $i ).
thf(redp_type,type,
redp: $i > $i > $i > $i ).
thf(hAPP_P1988153107l_bool_type,type,
hAPP_P1988153107l_bool: $i > $i > $i ).
thf(hAPP_e500528395l_bool_type,type,
hAPP_e500528395l_bool: $i > $i > $i ).
thf(hAPP_P595502227l_bool_type,type,
hAPP_P595502227l_bool: $i > $i > $i ).
thf(hAPP_f468299289l_bool_type,type,
hAPP_f468299289l_bool: $i > $i > $i ).
thf(produc2036005791l_bool_type,type,
produc2036005791l_bool: $i ).
thf(wf_J_mdecl_type,type,
wf_J_mdecl: $i ).
thf(hAPP_P1953518277l_bool_type,type,
hAPP_P1953518277l_bool: $i > $i > $i ).
thf(hAPP_P678729081l_bool_type,type,
hAPP_P678729081l_bool: $i > $i > $i ).
thf(hAPP_f1591648613l_bool_type,type,
hAPP_f1591648613l_bool: $i > $i > $i ).
thf(produc20018513l_bool_type,type,
produc20018513l_bool: $i ).
thf(fconj_type,type,
fconj: $i ).
thf(hAPP_P2024243179on_val_type,type,
hAPP_P2024243179on_val: $i > $i > $i ).
thf(hAPP_f204556415on_val_type,type,
hAPP_f204556415on_val: $i > $i > $i ).
thf(produc1148763895on_val_type,type,
produc1148763895on_val: $i ).
thf(hAPP_f2121594859l_bool_type,type,
hAPP_f2121594859l_bool: $i > $i > $i ).
thf(hAPP_f1342895119l_bool_type,type,
hAPP_f1342895119l_bool: $i > $i > $i ).
thf(hAPP_f639265145l_bool_type,type,
hAPP_f639265145l_bool: $i > $i > $i ).
thf(cOMBB_364363975on_val_type,type,
cOMBB_364363975on_val: $i ).
thf(hAPP_f365540729l_bool_type,type,
hAPP_f365540729l_bool: $i > $i > $i ).
thf(cOMBB_1466662571on_val_type,type,
cOMBB_1466662571on_val: $i ).
thf(hAPP_f439412817l_bool_type,type,
hAPP_f439412817l_bool: $i > $i > $i ).
thf(hAPP_f1725502637l_bool_type,type,
hAPP_f1725502637l_bool: $i > $i > $i ).
thf(cOMBB_1027621637t_char_type,type,
cOMBB_1027621637t_char: $i ).
thf(hAPP_f489055607l_bool_type,type,
hAPP_f489055607l_bool: $i > $i > $i ).
thf(hconf_97414254t_char_type,type,
hconf_97414254t_char: $i > $i ).
thf(hAPP_f2057883639l_bool_type,type,
hAPP_f2057883639l_bool: $i > $i > $i ).
thf(cOMBB_1750801836on_val_type,type,
cOMBB_1750801836on_val: $i ).
thf(hAPP_f10074679l_bool_type,type,
hAPP_f10074679l_bool: $i > $i > $i ).
thf(cOMBB_1759207793on_val_type,type,
cOMBB_1759207793on_val: $i ).
thf(unit_type,type,
unit: $i ).
thf(hAPP_P1134042693l_bool_type,type,
hAPP_P1134042693l_bool: $i > $i > $i ).
thf(hAPP_P1826803705l_bool_type,type,
hAPP_P1826803705l_bool: $i > $i > $i ).
thf(hAPP_f444383845l_bool_type,type,
hAPP_f444383845l_bool: $i > $i > $i ).
thf(produc376702929l_bool_type,type,
produc376702929l_bool: $i ).
thf(hAPP_f2011777102l_bool_type,type,
hAPP_f2011777102l_bool: $i > $i > $i ).
thf(hAPP_f2144092865l_bool_type,type,
hAPP_f2144092865l_bool: $i > $i > $i ).
thf(hAPP_P1638898323l_bool_type,type,
hAPP_P1638898323l_bool: $i > $i > $i ).
thf(hAPP_f833559503l_bool_type,type,
hAPP_f833559503l_bool: $i > $i > $i ).
thf(produc334393759l_bool_type,type,
produc334393759l_bool: $i ).
thf(v_2_type,type,
v_2: $i ).
thf(lconf_496643946t_char_type,type,
lconf_496643946t_char: $i > $i ).
thf(hAPP_f396019662l_bool_type,type,
hAPP_f396019662l_bool: $i > $i > $i ).
thf(hAPP_f2135509569l_bool_type,type,
hAPP_f2135509569l_bool: $i > $i > $i ).
thf(hAPP_f1276548047l_bool_type,type,
hAPP_f1276548047l_bool: $i > $i > $i ).
thf(produc121041439l_bool_type,type,
produc121041439l_bool: $i ).
thf(hp_type,type,
hp: $i > $i ).
thf(none_val_type,type,
none_val: $i ).
thf(hAPP_f204771371l_bool_type,type,
hAPP_f204771371l_bool: $i > $i > $i ).
thf(hAPP_f1760682521l_bool_type,type,
hAPP_f1760682521l_bool: $i > $i > $i ).
thf(produc1275132703l_bool_type,type,
produc1275132703l_bool: $i ).
thf(hAPP_e592495499l_bool_type,type,
hAPP_e592495499l_bool: $i > $i > $i ).
thf(hAPP_f1309113673on_val_type,type,
hAPP_f1309113673on_val: $i > $i > $i ).
thf(produc901351817on_val_type,type,
produc901351817on_val: $i ).
thf(hAPP_P1760219823on_val_type,type,
hAPP_P1760219823on_val: $i > $i > $i ).
thf(hAPP_f394183983on_val_type,type,
hAPP_f394183983on_val: $i > $i > $i ).
thf(produc1003071703on_val_type,type,
produc1003071703on_val: $i ).
thf(hAPP_f1520199827on_val_type,type,
hAPP_f1520199827on_val: $i > $i > $i ).
thf(produc1174947465on_val_type,type,
produc1174947465on_val: $i ).
thf(44,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f61040418l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O) ).
thf(356,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f61040418l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_prod_Osimps_I2_J) ).
thf(892,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ B ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_mem__def) ).
thf(1024,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( member840932460on_val @ A @ B ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) )
=> ( hBOOL @ ( member840932460on_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(71,axiom,
hBOOL @ ( wTrt @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( val_list_char @ v ) ) @ ea ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_InitBlockRed_I5_J) ).
thf(479,plain,
hBOOL @ ( wTrt @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( val_list_char @ v ) ) @ ea ) ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(154,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_prod_Oexhaust) ).
thf(846,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_split__conv) ).
thf(518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_mem__splitI) ).
thf(941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_splitD) ).
thf(777,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( val_list_char @ D ) ) @ ( val_list_char @ E ) ) ) @ F ) @ ( val_list_char @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_redp__redsp_ORedInitBlock) ).
thf(523,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( val_list_char @ D ) ) @ ( val_list_char @ E ) ) ) @ F ) @ ( val_list_char @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f318082871l_bool @ ( hAPP_f1233687287l_bool @ cOMBB_171276332on_val @ A ) @ B ) @ C )
= ( hAPP_P1708370145l_bool @ A @ ( hAPP_f1926378906on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).
thf(276,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f318082871l_bool @ ( hAPP_f1233687287l_bool @ cOMBB_171276332on_val @ A ) @ B ) @ C )
= ( hAPP_P1708370145l_bool @ A @ ( hAPP_f1926378906on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
=> ( ( ( hAPP_l207779698on_val @ J @ G )
= ( some_val @ B ) )
=> ( ~ ( hBOOL @ ( assigned @ G @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_redp__redsp_OBlockRedSome) ).
thf(873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
=> ( ( ( hAPP_l207779698on_val @ J @ G )
= ( some_val @ B ) )
=> ( ~ ( hBOOL @ ( assigned @ G @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_prod_Osimps_I2_J) ).
thf(1041,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splitI) ).
thf(614,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f926562337l_bool @ ( hAPP_f1560238713l_bool @ cOMBB_672625589on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f926562337l_bool @ ( hAPP_f1560238713l_bool @ cOMBB_672625589on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f653692369l_bool @ ( hAPP_f516738477l_bool @ cOMBB_819439237t_char @ A ) @ B ) @ C )
= ( hAPP_f1301559543l_bool @ A @ ( hAPP_e108155315on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008) ).
thf(472,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f653692369l_bool @ ( hAPP_f516738477l_bool @ cOMBB_819439237t_char @ A ) @ B ) @ C )
= ( hAPP_f1301559543l_bool @ A @ ( hAPP_e108155315on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(134,axiom,
! [A: $i] :
( ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f439412817l_bool @ ( hAPP_f1725502637l_bool @ cOMBB_1027621637t_char @ ( hAPP_f10074679l_bool @ cOMBB_1759207793on_val @ A ) ) @ produc1259058957on_val ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_split__eta) ).
thf(747,plain,
! [A: $i] :
( ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f439412817l_bool @ ( hAPP_f1725502637l_bool @ cOMBB_1027621637t_char @ ( hAPP_f10074679l_bool @ cOMBB_1759207793on_val @ A ) ) @ produc1259058957on_val ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( block_list_char @ A @ B @ C )
!= ( lAss_list_char @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_exp_Osimps_I143_J) ).
thf(340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( block_list_char @ A @ B @ C )
!= ( lAss_list_char @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(86,axiom,
hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms) ).
thf(538,plain,
hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_split__conv) ).
thf(841,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( seq_list_char @ A @ B )
!= ( lAss_list_char @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_exp_Osimps_I145_J) ).
thf(417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( seq_list_char @ A @ B )
!= ( lAss_list_char @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= ( fun_up1149430426on_val @ D @ B @ ( some_val @ E ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__upd__eqD1) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= ( fun_up1149430426on_val @ D @ B @ ( some_val @ E ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(207,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod_Oexhaust) ).
thf(1046,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ C ) ) @ D ) ) @ ( red @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_red__reds_ORedBlock) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ C ) ) @ D ) ) @ ( red @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).
thf(619,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(39,axiom,
! [A: $i,B: $i] : ( is_bool @ ( wf_pro755087577t_char @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri) ).
thf(344,plain,
! [A: $i,B: $i] : ( is_bool @ ( wf_pro755087577t_char @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) ).
thf(421,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
= B ) )
& ( ( D != C )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
= ( hAPP_l207779698on_val @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fun__upd__def) ).
thf(606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
= B ) )
& ( ( D != C )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
= ( hAPP_l207779698on_val @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(162,axiom,
hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) @ ( red @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(881,plain,
hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) @ ( red @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P159683425l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).
thf(289,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P159683425l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1033709212l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001) ).
thf(448,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1033709212l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(32,axiom,
! [A: $i,B: $i] : ( is_bool @ ( member763590124on_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_) ).
thf(316,plain,
! [A: $i,B: $i] : ( is_bool @ ( member763590124on_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,axiom,
produc1988544340l_bool = produc1911463199l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_internal__split__def) ).
thf(261,plain,
produc1988544340l_bool = produc1911463199l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( hAPP_l512744617ion_ty @ ( cOMBK_1294242658t_char @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( hAPP_l512744617ion_ty @ ( cOMBK_1294242658t_char @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ B @ C ) @ D ) )
<=> ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) )
=> ( ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_cond__split__eta) ).
thf(492,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) )
& ( ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ B @ C ) @ D ) ) ) )
=> ( ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_WellTypeRT_OWTrt) ).
thf(321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_bool @ ( wTrt @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f489055607l_bool @ ( hAPP_f10074679l_bool @ cOMBB_1759207793on_val @ A ) @ B ) @ C )
= ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004) ).
thf(646,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f489055607l_bool @ ( hAPP_f10074679l_bool @ cOMBB_1759207793on_val @ A ) @ B ) @ C )
= ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_split__weak__cong) ).
thf(834,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l512744617ion_ty @ A @ B )
= C )
=> ( ( fun_up424764369ion_ty @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_fun__upd__idem) ).
thf(238,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l512744617ion_ty @ A @ B )
= C )
=> ( ( fun_up424764369ion_ty @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_splitE2) ).
thf(514,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_mem__splitE) ).
thf(937,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
= ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).
thf(353,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
= ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
= ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006) ).
thf(480,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
= ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( val_list_char @ A )
!= ( block_list_char @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_exp_Osimps_I82_J) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( val_list_char @ A )
!= ( block_list_char @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__induct3) ).
thf(924,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_splitE) ).
thf(1020,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(41,axiom,
! [A: $i,B: $i] : ( is_bool @ ( assigned @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_SmallStep_Oassigned) ).
thf(348,plain,
! [A: $i,B: $i] : ( is_bool @ ( assigned @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(194,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( widen_2090681816t_char @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_widen__refl) ).
thf(998,plain,
! [A: $i,B: $i] : ( hBOOL @ ( widen_2090681816t_char @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(192,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
<=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).
thf(988,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
& ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(103,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod_Oexhaust) ).
thf(602,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__caseI) ).
thf(981,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( red @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_red__reds_ORedSeq) ).
thf(512,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( red @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= ( hAPP_l207779698on_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_fun__upd__other) ).
thf(529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= ( hAPP_l207779698on_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) ) @ D )
= ( some_val @ E ) )
<=> ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l207779698on_val @ A @ D )
= ( some_val @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__upd__Some__unfold) ).
thf(793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) ) @ D )
= ( some_val @ E ) )
=> ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l207779698on_val @ A @ D )
= ( some_val @ E ) ) ) ) )
& ( ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l207779698on_val @ A @ D )
= ( some_val @ E ) ) ) )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) ) @ D )
= ( some_val @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_mem__splitI2) ).
thf(534,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mem__splitE) ).
thf(920,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= ( hAPP_l512744617ion_ty @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_fun__upd__other) ).
thf(248,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= ( hAPP_l512744617ion_ty @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P282169671l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).
thf(334,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P282169671l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( red @ I ) ) )
=> ( ( hBOOL @ ( wTrt @ I @ D @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
=> ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_red__preserves__hconf) ).
thf(598,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( red @ I ) ) )
=> ( ( hBOOL @ ( wTrt @ I @ D @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
=> ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( block_list_char @ A @ B @ C )
= ( block_list_char @ D @ E @ F ) )
<=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_exp_Osimps_I10_J) ).
thf(392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( block_list_char @ A @ B @ C )
= ( block_list_char @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( block_list_char @ A @ B @ C )
= ( block_list_char @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
produc399384568l_bool = produc1815960045l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_internal__split__def) ).
thf(297,plain,
produc399384568l_bool = produc1815960045l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f1301559543l_bool @ ( hAPP_f1825030711l_bool @ cOMBB_877741809on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_P1776198677on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003) ).
thf(424,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f1301559543l_bool @ ( hAPP_f1825030711l_bool @ cOMBB_877741809on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_P1776198677on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f555424277l_bool @ ( hAPP_f1734879897l_bool @ cOMBB_1522540928on_val @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
<=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_split__part) ).
thf(630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f555424277l_bool @ ( hAPP_f1734879897l_bool @ cOMBB_1522540928on_val @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f555424277l_bool @ ( hAPP_f1734879897l_bool @ cOMBB_1522540928on_val @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( fun_up1149430426on_val @ A @ B @ C )
= A )
<=> ( ( hAPP_l207779698on_val @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_fun__upd__idem__iff) ).
thf(815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( fun_up1149430426on_val @ A @ B @ C )
= A )
=> ( ( hAPP_l207779698on_val @ A @ B )
= C ) )
& ( ( ( hAPP_l207779698on_val @ A @ B )
= C )
=> ( ( fun_up1149430426on_val @ A @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
= ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002) ).
thf(467,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
= ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= ( fun_up424764369ion_ty @ D @ B @ ( some_ty @ E ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__upd__eqD1) ).
thf(361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= ( fun_up424764369ion_ty @ D @ B @ ( some_ty @ E ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__induct4) ).
thf(625,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_fun__upd__same) ).
thf(889,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(65,axiom,
! [A: $i,B: $i] : ( is_bool @ ( member840932460on_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J) ).
thf(461,plain,
! [A: $i,B: $i] : ( is_bool @ ( member840932460on_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitI) ).
thf(1012,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( seq_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_exp_Osimps_I197_J) ).
thf(285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( seq_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_redp__redsp_ORedSeq) ).
thf(933,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Pair__eq) ).
thf(554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l207779698on_val @ A @ B )
= ( some_val @ C ) )
=> ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_map__upd__triv) ).
thf(901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l207779698on_val @ A @ B )
= ( some_val @ C ) )
=> ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mem__splitI2) ).
thf(1016,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splitI) ).
thf(590,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(1039,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ ( red @ K ) ) )
=> ( ( ( hAPP_l207779698on_val @ J @ F )
= ( some_val @ B ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) @ ( red @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_red__reds_OInitBlockRed) ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ ( red @ K ) ) )
=> ( ( ( hAPP_l207779698on_val @ J @ F )
= ( some_val @ B ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) @ ( red @ K ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(622,plain,
! [A: $i,B: $i] :
( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(130,axiom,
( ( hAPP_l207779698on_val @ l_a @ v_1 )
= ( some_val @ v_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(738,plain,
( ( hAPP_l207779698on_val @ l_a @ v_1 )
= ( some_val @ v_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( some_val @ B ) ) ) ) ) @ ( red @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_red__reds_ORedLAss) ).
thf(654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( some_val @ B ) ) ) ) ) @ ( red @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_redp__redsp_OLAssRed) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_split__weak__cong) ).
thf(779,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_splitI2) ).
thf(503,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f546724245l_bool @ ( hAPP_f917296015l_bool @ cOMBB_740252943t_char @ A ) @ B ) @ C )
= ( hAPP_f2134824737l_bool @ A @ ( hAPP_e1833980889l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) ).
thf(266,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f546724245l_bool @ ( hAPP_f917296015l_bool @ cOMBB_740252943t_char @ A ) @ B ) @ C )
= ( hAPP_f2134824737l_bool @ A @ ( hAPP_e1833980889l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( hAPP_l207779698on_val @ ( cOMBK_1097134891t_char @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) ).
thf(311,plain,
! [A: $i,B: $i] :
( ( hAPP_l207779698on_val @ ( cOMBK_1097134891t_char @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( val_list_char @ C ) ) @ ( val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ D ) ) @ E ) ) @ ( red @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_red__reds_ORedInitBlock) ).
thf(541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( val_list_char @ C ) ) @ ( val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( val_list_char @ D ) ) @ E ) ) @ ( red @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f641257349l_bool @ ( hAPP_f2032347769l_bool @ cOMBB_466903633on_val @ ( hAPP_f1560238713l_bool @ cOMBB_672625589on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
<=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_split__part) ).
thf(953,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f641257349l_bool @ ( hAPP_f2032347769l_bool @ cOMBB_466903633on_val @ ( hAPP_f1560238713l_bool @ cOMBB_672625589on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f641257349l_bool @ ( hAPP_f2032347769l_bool @ cOMBB_466903633on_val @ ( hAPP_f1560238713l_bool @ cOMBB_672625589on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_splitE2) ).
thf(586,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ F ) ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( red @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_red__reds_OSeqRed) ).
thf(926,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ F ) ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( red @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(138,axiom,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(765,plain,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mem__splitI2) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Pair__eq) ).
thf(750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( val_list_char @ A )
= ( val_list_char @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_exp_Osimps_I3_J) ).
thf(430,plain,
! [A: $i,B: $i] :
( ( ( ( val_list_char @ A )
= ( val_list_char @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( val_list_char @ A )
= ( val_list_char @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mem__splitI) ).
thf(745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f927043595l_bool @ ( hAPP_f1043869573l_bool @ cOMBB_1259202826on_val @ A ) @ B ) @ C )
= ( hAPP_f524589473l_bool @ A @ ( hAPP_f600512025on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011) ).
thf(279,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f927043595l_bool @ ( hAPP_f1043869573l_bool @ cOMBB_1259202826on_val @ A ) @ B ) @ C )
= ( hAPP_f524589473l_bool @ A @ ( hAPP_f600512025on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( lAss_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_exp_Osimps_I142_J) ).
thf(444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( lAss_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
=> ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_cond__split__eta) ).
thf(904,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) ) ) )
=> ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P1760219823on_val @ ( hAPP_f394183983on_val @ produc1003071703on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f1241216909l_bool @ ( hAPP_f1438732387l_bool @ cOMBB_635947099on_val @ ( hAPP_f881985847l_bool @ cOMBB_1083177073on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_split__twice) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P1760219823on_val @ ( hAPP_f394183983on_val @ produc1003071703on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f1241216909l_bool @ ( hAPP_f1438732387l_bool @ cOMBB_635947099on_val @ ( hAPP_f881985847l_bool @ cOMBB_1083177073on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f1241216909l_bool @ ( hAPP_f1438732387l_bool @ cOMBB_635947099on_val @ ( hAPP_f881985847l_bool @ cOMBB_1083177073on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P1760219823on_val @ ( hAPP_f394183983on_val @ produc1003071703on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(140,axiom,
! [A: $i] :
( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_split__eta) ).
thf(772,plain,
! [A: $i] :
( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( red @ I ) ) )
=> ( ( hBOOL @ ( wTrt @ I @ D @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_red__preserves__lconf) ).
thf(743,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( red @ I ) ) )
=> ( ( hBOOL @ ( wTrt @ I @ D @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f1241216909l_bool @ ( hAPP_f1438732387l_bool @ cOMBB_635947099on_val @ A ) @ B ) @ C )
= ( hAPP_f1712766199l_bool @ A @ ( hAPP_P2083594489on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012) ).
thf(291,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f1241216909l_bool @ ( hAPP_f1438732387l_bool @ cOMBB_635947099on_val @ A ) @ B ) @ C )
= ( hAPP_f1712766199l_bool @ A @ ( hAPP_P2083594489on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) ) @ D )
= none_ty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_map__upd__nonempty) ).
thf(413,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) ) @ D )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_splitE2) ).
thf(572,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f1342895119l_bool @ ( hAPP_f639265145l_bool @ cOMBB_364363975on_val @ A ) @ B ) @ C )
= ( hAPP_f204771371l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f1342895119l_bool @ ( hAPP_f639265145l_bool @ cOMBB_364363975on_val @ A ) @ B ) @ C )
= ( hAPP_f204771371l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mem__splitI2) ).
thf(704,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_P1134042693l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1826803705l_bool @ ( hAPP_f444383845l_bool @ produc376702929l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
= ( fun_up424764369ion_ty @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_fun__upd__upd) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
= ( fun_up424764369ion_ty @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ B ) )
<=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_pred__equals__eq2) ).
thf(672,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mem__splitI) ).
thf(979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( lAss_list_char @ A @ B )
!= ( seq_list_char @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_exp_Osimps_I144_J) ).
thf(406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( lAss_list_char @ A @ B )
!= ( seq_list_char @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= B ) )
& ( ( C != D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_fun__upd__apply) ).
thf(219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= B ) )
& ( ( C != D )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
= ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
= B ) )
& ( ( D != C )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
= ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun__upd__def) ).
thf(230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
= B ) )
& ( ( D != C )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
= ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ ( cOMBK_1294242658t_char @ none_ty ) @ A @ none_ty ) @ B )
= none_ty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__upd__none) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ ( cOMBK_1294242658t_char @ none_ty ) @ A @ none_ty ) @ B )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f555424277l_bool @ ( hAPP_f1734879897l_bool @ cOMBB_1522540928on_val @ A ) @ B ) @ C )
= ( hAPP_f1074020887l_bool @ A @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) ).
thf(318,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f555424277l_bool @ ( hAPP_f1734879897l_bool @ cOMBB_1522540928on_val @ A ) @ B ) @ C )
= ( hAPP_f1074020887l_bool @ A @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(116,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
<=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_split__paired__All) ).
thf(649,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
& ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
= ( fun_up1149430426on_val @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_fun__upd__upd) ).
thf(616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
= ( fun_up1149430426on_val @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f641257349l_bool @ ( hAPP_f2032347769l_bool @ cOMBB_466903633on_val @ A ) @ B ) @ C )
= ( hAPP_f926562337l_bool @ A @ ( hAPP_P1116729363l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).
thf(303,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1116729363l_bool @ ( hAPP_f641257349l_bool @ ( hAPP_f2032347769l_bool @ cOMBB_466903633on_val @ A ) @ B ) @ C )
= ( hAPP_f926562337l_bool @ A @ ( hAPP_P1116729363l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(147,axiom,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases3) ).
thf(811,plain,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( lAss_list_char @ A @ B )
= ( lAss_list_char @ C @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exp_Osimps_I6_J) ).
thf(323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( lAss_list_char @ A @ B )
= ( lAss_list_char @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( lAss_list_char @ A @ B )
= ( lAss_list_char @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mem__splitI) ).
thf(726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Pair__eq) ).
thf(483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( fun_up424764369ion_ty @ A @ B @ C )
= A )
<=> ( ( hAPP_l512744617ion_ty @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_fun__upd__idem__iff) ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( fun_up424764369ion_ty @ A @ B @ C )
= A )
=> ( ( hAPP_l512744617ion_ty @ A @ B )
= C ) )
& ( ( ( hAPP_l512744617ion_ty @ A @ B )
= C )
=> ( ( fun_up424764369ion_ty @ A @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(203,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
<=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_split__paired__Ex) ).
thf(1029,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
& ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
=> ( ( ( hAPP_l207779698on_val @ K @ G )
= ( some_val @ B ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_redp__redsp_OInitBlockRed) ).
thf(769,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
=> ( ( ( hAPP_l207779698on_val @ K @ G )
= ( some_val @ B ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= B ) )
& ( ( C != D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= ( hAPP_l207779698on_val @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_fun__upd__apply) ).
thf(943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= B ) )
& ( ( C != D )
=> ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
= ( hAPP_l207779698on_val @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P789556885on_val @ ( hAPP_f1520199827on_val @ produc1174947465on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f653692369l_bool @ ( hAPP_f516738477l_bool @ cOMBB_819439237t_char @ ( hAPP_f1825030711l_bool @ cOMBB_877741809on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_split__twice) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P789556885on_val @ ( hAPP_f1520199827on_val @ produc1174947465on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f653692369l_bool @ ( hAPP_f516738477l_bool @ cOMBB_819439237t_char @ ( hAPP_f1825030711l_bool @ cOMBB_877741809on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f653692369l_bool @ ( hAPP_f516738477l_bool @ cOMBB_819439237t_char @ ( hAPP_f1825030711l_bool @ cOMBB_877741809on_val @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_P789556885on_val @ ( hAPP_f1520199827on_val @ produc1174947465on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
<=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_redp__red__eq) ).
thf(983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ A ) ) ) )
& ( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ A ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mem__splitE) ).
thf(959,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_prod_Osimps_I2_J) ).
thf(827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_splitI2) ).
thf(636,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f524589473l_bool @ ( hAPP_f2052660463l_bool @ cOMBB_1292453606on_val @ A ) @ B ) @ C )
= ( hAPP_P282169671l_bool @ A @ ( hAPP_f602593190on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).
thf(306,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f524589473l_bool @ ( hAPP_f2052660463l_bool @ cOMBB_1292453606on_val @ A ) @ B ) @ C )
= ( hAPP_P282169671l_bool @ A @ ( hAPP_f602593190on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P2024243179on_val @ ( hAPP_f204556415on_val @ produc1148763895on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f927043595l_bool @ ( hAPP_f1043869573l_bool @ cOMBB_1259202826on_val @ ( hAPP_f2052660463l_bool @ cOMBB_1292453606on_val @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) ) ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_split__twice) ).
thf(563,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P2024243179on_val @ ( hAPP_f204556415on_val @ produc1148763895on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f927043595l_bool @ ( hAPP_f1043869573l_bool @ cOMBB_1259202826on_val @ ( hAPP_f2052660463l_bool @ cOMBB_1292453606on_val @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f927043595l_bool @ ( hAPP_f1043869573l_bool @ cOMBB_1259202826on_val @ ( hAPP_f2052660463l_bool @ cOMBB_1292453606on_val @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P2024243179on_val @ ( hAPP_f204556415on_val @ produc1148763895on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) @ ( red @ J ) ) )
=> ( ( ( hAPP_l207779698on_val @ I @ F )
= ( some_val @ B ) )
=> ( ~ ( hBOOL @ ( assigned @ F @ C ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_red__reds_OBlockRedSome) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) @ ( red @ J ) ) )
=> ( ( ( hAPP_l207779698on_val @ I @ F )
= ( some_val @ B ) )
=> ( ~ ( hBOOL @ ( assigned @ F @ C ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( block_list_char @ A @ B @ C )
!= ( seq_list_char @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_exp_Osimps_I196_J) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( block_list_char @ A @ B @ C )
!= ( seq_list_char @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D != E )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_fun__upd__twist) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D != E )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_splitE) ).
thf(1066,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ A @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_sconf__def) ).
thf(868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(126,axiom,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases3) ).
thf(722,plain,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(204,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
<=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_split__paired__All) ).
thf(1034,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
& ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) ) @ D )
= ( some_ty @ E ) )
<=> ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l512744617ion_ty @ A @ D )
= ( some_ty @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map__upd__Some__unfold) ).
thf(374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) ) @ D )
= ( some_ty @ E ) )
=> ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l512744617ion_ty @ A @ D )
= ( some_ty @ E ) ) ) ) )
& ( ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( hAPP_l512744617ion_ty @ A @ D )
= ( some_ty @ E ) ) ) )
=> ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) ) @ D )
= ( some_ty @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(185,axiom,
! [A: $i,B: $i] : ( is_bool @ ( member773094996on_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_) ).
thf(968,plain,
! [A: $i,B: $i] : ( is_bool @ ( member773094996on_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_splitE) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
=> ~ ! [C: $i,D: $i] :
( ( B
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Pair__inject) ).
thf(855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mem__splitE) ).
thf(640,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) ) @ D )
= none_val ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_map__upd__nonempty) ).
thf(1070,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) ) @ D )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l512744617ion_ty @ A @ B )
= ( some_ty @ C ) )
=> ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_map__upd__triv) ).
thf(282,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l512744617ion_ty @ A @ B )
= ( some_ty @ C ) )
=> ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f2134824737l_bool @ ( hAPP_f1308714617l_bool @ cOMBB_338347573on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It) ).
thf(263,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P159683425l_bool @ ( hAPP_f2134824737l_bool @ ( hAPP_f1308714617l_bool @ cOMBB_338347573on_val @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(193,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
<=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_split__paired__Ex) ).
thf(993,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
=> ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
& ( ? [B: $i,C: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc2128769400l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_internal__split__conv) ).
thf(712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc2128769400l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc2128769400l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mem__splitI2) ).
thf(1003,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_e592495499l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_f1760682521l_bool @ produc1275132703l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(441,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( lAss_list_char @ A @ B )
!= ( val_list_char @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_exp_Osimps_I75_J) ).
thf(370,plain,
! [A: $i,B: $i,C: $i] :
( ( lAss_list_char @ A @ B )
!= ( val_list_char @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(717,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(75,axiom,
hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).
thf(502,plain,
hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( seq_list_char @ A @ B )
!= ( val_list_char @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_exp_Osimps_I85_J) ).
thf(463,plain,
! [A: $i,B: $i,C: $i] :
( ( seq_list_char @ A @ B )
!= ( val_list_char @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(951,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] : ( is_bool @ ( widen_2090681816t_char @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) ).
thf(470,plain,
! [A: $i,B: $i,C: $i] : ( is_bool @ ( widen_2090681816t_char @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ B @ C ) @ D ) )
<=> ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) )
=> ( ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_cond__split__eta) ).
thf(576,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ B @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) )
& ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ B @ C ) @ D ) ) ) )
=> ( ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( val_list_char @ A )
!= ( lAss_list_char @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_exp_Osimps_I74_J) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( val_list_char @ A )
!= ( lAss_list_char @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ B ) )
<=> ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_pred__equals__eq2) ).
thf(656,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ F ) ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) @ ( red @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_red__reds_OLAssRed) ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( red @ F ) ) )
=> ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) @ ( red @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_splitD) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(158,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_PairE) ).
thf(864,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1708370145l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M) ).
thf(314,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_P1708370145l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f439412817l_bool @ ( hAPP_f1725502637l_bool @ cOMBB_1027621637t_char @ A ) @ B ) @ C )
= ( hAPP_f489055607l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009) ).
thf(595,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_e1833980889l_bool @ ( hAPP_f439412817l_bool @ ( hAPP_f1725502637l_bool @ cOMBB_1027621637t_char @ A ) @ B ) @ C )
= ( hAPP_f489055607l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
thf(876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
= ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
=> ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
=> ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_WTrtSeq) ).
thf(627,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
=> ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
=> ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( seq_list_char @ A @ B )
= ( seq_list_char @ C @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_exp_Osimps_I11_J) ).
thf(450,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( seq_list_char @ A @ B )
= ( seq_list_char @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( seq_list_char @ A @ B )
= ( seq_list_char @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_mem__splitI) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l207779698on_val @ A @ B )
= C )
=> ( ( fun_up1149430426on_val @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_fun__upd__idem) ).
thf(759,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_l207779698on_val @ A @ B )
= C )
=> ( ( fun_up1149430426on_val @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(48,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1001225811y_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption) ).
thf(368,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1001225811y_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
= none_val ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_empty__upd__none) ).
thf(976,plain,
! [A: $i,B: $i] :
( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ B ) )
<=> ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pred__equals__eq2) ).
thf(688,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ A ) ) )
& ( ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_f1309113673on_val @ produc901351817on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f850751421l_bool @ ( hAPP_f399538905l_bool @ cOMBB_1466889536on_val @ ( hAPP_f1233687287l_bool @ cOMBB_171276332on_val @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) ) ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_split__twice) ).
thf(963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_f1309113673on_val @ produc901351817on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f850751421l_bool @ ( hAPP_f399538905l_bool @ cOMBB_1466889536on_val @ ( hAPP_f1233687287l_bool @ cOMBB_171276332on_val @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) ) ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f850751421l_bool @ ( hAPP_f399538905l_bool @ cOMBB_1466889536on_val @ ( hAPP_f1233687287l_bool @ cOMBB_171276332on_val @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) ) ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_f1309113673on_val @ produc901351817on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f850751421l_bool @ ( hAPP_f399538905l_bool @ cOMBB_1466889536on_val @ A ) @ B ) @ C )
= ( hAPP_f318082871l_bool @ A @ ( hAPP_f1840640125on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007) ).
thf(258,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( hAPP_f850751421l_bool @ ( hAPP_f399538905l_bool @ cOMBB_1466889536on_val @ A ) @ B ) @ C )
= ( hAPP_f318082871l_bool @ A @ ( hAPP_f1840640125on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(144,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_PairE) ).
thf(786,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_mem__splitI) ).
thf(568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_e500528395l_bool @ B @ C ) @ D ) ) )
=> ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P595502227l_bool @ ( hAPP_f468299289l_bool @ produc2036005791l_bool @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mem__splitI2) ).
thf(914,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( C
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1116729363l_bool @ ( hAPP_P1953518277l_bool @ B @ D ) @ E ) ) ) )
=> ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P678729081l_bool @ ( hAPP_f1591648613l_bool @ produc20018513l_bool @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__induct3) ).
thf(832,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(40,axiom,
produc2128769400l_bool = produc1958875245l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_internal__split__def) ).
thf(346,plain,
produc2128769400l_bool = produc1958875245l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ B ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_mem__def) ).
thf(549,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( member763590124on_val @ A @ B ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ B @ A ) )
=> ( hBOOL @ ( member763590124on_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( val_list_char @ D ) ) @ E ) @ ( val_list_char @ D ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_redp__redsp_ORedBlock) ).
thf(763,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( val_list_char @ D ) ) @ E ) @ ( val_list_char @ D ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( block_list_char @ A @ B @ C )
!= ( val_list_char @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_exp_Osimps_I83_J) ).
thf(272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( block_list_char @ A @ B @ C )
!= ( val_list_char @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
= ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).
thf(410,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
= ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
=> ( ( ( hAPP_l207779698on_val @ I @ F )
= none_val )
=> ( ~ ( hBOOL @ ( assigned @ F @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_redp__redsp_OBlockRedNone) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
=> ( ( ( hAPP_l207779698on_val @ I @ F )
= none_val )
=> ( ~ ( hBOOL @ ( assigned @ F @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D != E )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_fun__upd__twist) ).
thf(735,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D != E )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_fun__upd__same) ).
thf(242,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
= ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).
thf(358,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
= ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mem__splitE) ).
thf(897,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_P1988153107l_bool @ ( hAPP_f1276548047l_bool @ produc121041439l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member763590124on_val @ A @ ( hAPP_f396019662l_bool @ ( hAPP_f2135509569l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_splitD) ).
thf(532,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_redp__redsp_OSeqRed) ).
thf(720,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
= ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).
thf(294,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
= ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__caseI) ).
thf(918,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f204771371l_bool @ ( hAPP_f365540729l_bool @ cOMBB_1466662571on_val @ A ) @ B ) @ C )
= ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010) ).
thf(886,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f204771371l_bool @ ( hAPP_f365540729l_bool @ cOMBB_1466662571on_val @ A ) @ B ) @ C )
= ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( member773094996on_val @ A @ B ) )
<=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_mem__def) ).
thf(928,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( member773094996on_val @ A @ B ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) )
=> ( hBOOL @ ( member773094996on_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f1712766199l_bool @ ( hAPP_f881985847l_bool @ cOMBB_1083177073on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_P789556885on_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005) ).
thf(427,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_P1708370145l_bool @ ( hAPP_f1712766199l_bool @ ( hAPP_f881985847l_bool @ cOMBB_1083177073on_val @ A ) @ B ) @ C )
= ( hAPP_P159683425l_bool @ A @ ( hAPP_P789556885on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_splitI2) ).
thf(860,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( B
= ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( some_ty @ E ) ) @ F @ G ) )
=> ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_WTrtBlock) ).
thf(644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( some_ty @ E ) ) @ F @ G ) )
=> ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_split__conv) ).
thf(822,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(155,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
<=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_split__paired__All) ).
thf(850,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
=> ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
& ( ! [B: $i,C: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_split__weak__cong) ).
thf(728,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) )
=> ( ( hBOOL @ ( wTrt @ p @ ha @ B @ ea @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( wTrt @ p @ h_a @ B @ e_a @ C ) )
& ( hBOOL @ ( widen_2090681816t_char @ p @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_InitBlockRed_I2_J) ).
thf(740,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) )
=> ( ( hBOOL @ ( wTrt @ p @ ha @ B @ ea @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( wTrt @ p @ h_a @ B @ e_a @ C ) )
& ( hBOOL @ ( widen_2090681816t_char @ p @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( widen_2090681816t_char @ B @ C @ D ) )
=> ( ( hBOOL @ ( widen_2090681816t_char @ B @ D @ A ) )
=> ( hBOOL @ ( widen_2090681816t_char @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_widen__trans) ).
thf(935,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( widen_2090681816t_char @ B @ C @ D ) )
=> ( ( hBOOL @ ( widen_2090681816t_char @ B @ D @ A ) )
=> ( hBOOL @ ( widen_2090681816t_char @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(309,plain,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f546724245l_bool @ ( hAPP_f917296015l_bool @ cOMBB_740252943t_char @ ( hAPP_f1308714617l_bool @ cOMBB_338347573on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
<=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_split__part) ).
thf(543,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f546724245l_bool @ ( hAPP_f917296015l_bool @ cOMBB_740252943t_char @ ( hAPP_f1308714617l_bool @ cOMBB_338347573on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) )
=> ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ A )
& ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ ( hAPP_f546724245l_bool @ ( hAPP_f917296015l_bool @ cOMBB_740252943t_char @ ( hAPP_f1308714617l_bool @ cOMBB_338347573on_val @ ( hAPP_b589554111l_bool @ fconj @ A ) ) ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1,conjecture,
hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) @ ( red @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) @ ( red @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(215,plain,
~ ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) @ ( red @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( red @ G ) ) )
=> ( ( hBOOL @ ( wTrt @ G @ ( hp @ D ) @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ G @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ G @ A ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_red__preserves__sconf) ).
thf(775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( red @ G ) ) )
=> ( ( hBOOL @ ( wTrt @ G @ ( hp @ D ) @ A @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ G @ A ) @ D ) )
=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1234865140_sconf @ G @ A ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(99,axiom,
! [A: $i] :
( ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f1342895119l_bool @ ( hAPP_f639265145l_bool @ cOMBB_364363975on_val @ ( hAPP_f365540729l_bool @ cOMBB_1466662571on_val @ A ) ) @ produc1441475159on_val ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_split__eta) ).
thf(592,plain,
! [A: $i] :
( ( hAPP_f635218277l_bool @ produc1911463199l_bool @ ( hAPP_f1342895119l_bool @ ( hAPP_f639265145l_bool @ cOMBB_364363975on_val @ ( hAPP_f365540729l_bool @ cOMBB_1466662571on_val @ A ) ) @ produc1441475159on_val ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( val_list_char @ A )
!= ( seq_list_char @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_exp_Osimps_I84_J) ).
thf(364,plain,
! [A: $i,B: $i,C: $i] :
( ( val_list_char @ A )
!= ( seq_list_char @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(122,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_PairE) ).
thf(708,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mem__splitE) ).
thf(882,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_P1638898323l_bool @ ( hAPP_f833559503l_bool @ produc334393759l_bool @ B ) @ C ) ) )
=> ~ ! [D: $i,E: $i] :
( ( C
= ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
=> ~ ( hBOOL @ ( member840932460on_val @ A @ ( hAPP_f2011777102l_bool @ ( hAPP_f2144092865l_bool @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__caseI) ).
thf(1014,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1074,plain,
$false,
inference(e,[status(thm)],[356,892,1024,479,846,518,941,777,523,276,873,1041,614,269,472,747,340,538,841,417,973,1046,570,619,344,421,606,881,289,448,316,261,216,492,321,646,834,238,514,937,353,480,475,924,1020,348,998,988,507,602,981,512,529,793,534,920,248,334,598,392,297,424,630,815,467,361,625,889,461,1012,285,933,554,901,1016,590,1039,970,622,738,654,1050,779,503,266,311,541,953,586,926,765,1054,750,430,745,279,444,904,1007,772,743,291,413,572,1058,704,350,672,979,406,219,230,245,318,649,616,303,811,323,726,483,251,1029,769,943,1061,983,959,827,636,306,563,1000,299,438,1066,868,722,1034,374,968,525,855,640,1070,282,263,993,712,1003,441,370,717,502,463,951,470,576,336,656,600,1052,864,314,595,876,627,450,539,759,368,976,688,963,258,786,568,914,832,346,549,763,272,410,790,735,242,358,897,532,720,294,918,886,928,427,860,644,822,850,728,740,227,935,309,543,215,775,592,364,708,882,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWW478+1 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 22:39:50 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.62/0.67 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/0.85 % [INFO] Parsing done (176ms).
% 0.97/0.86 % [INFO] Running in sequential loop mode.
% 1.62/1.07 % [INFO] eprover registered as external prover.
% 1.62/1.07 % [INFO] cvc4 registered as external prover.
% 1.62/1.07 % [INFO] Scanning for conjecture ...
% 1.82/1.17 % [INFO] Found a conjecture and 212 axioms. Running axiom selection ...
% 2.21/1.27 % [INFO] Axiom selection finished. Selected 212 axioms (removed 0 axioms).
% 2.94/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.94/1.45 % [INFO] Type checking passed.
% 2.94/1.46 % [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 ...
% 9.54/3.02 % External prover 'e' found a proof!
% 9.54/3.02 % [INFO] Killing All external provers ...
% 9.54/3.03 % Time passed: 2637ms (effective reasoning time: 2163ms)
% 9.54/3.03 % 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)>
% 9.54/3.03 % Axioms used in derivation (212): fact_129_cond__split__eta, fact_100_splitE, fact_111_red__reds_OSeqRed, fact_4_assms, gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_69_splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_24_fun__upd__def, fact_17_Pair__inject, gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_145_exp_Osimps_I85_J, fact_63_sconf__def, fact_65_prod__caseI, fact_116_mem__splitE, fact_19_Pair__eq, fact_134_exp_Osimps_I143_J, fact_98_splitI2, help_fconj_3_1_U, fact_25_fun__upd__def, gsy_c_WellTypeRT_OWTrt, fact_5_map__upd__Some__unfold, fact_166_redp__redsp_ORedInitBlock, fact_60_PairE, fact_109_mem__splitI, fact_136_exp_Osimps_I3_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012, fact_105_mem__splitI, fact_6_map__upd__Some__unfold, fact_67_splitI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__, fact_78_internal__split__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009, fact_104_mem__splitI, fact_86_prod_Osimps_I2_J, fact_57_split__paired__Ex, fact_7_map__upd__triv, fact_11_InitBlockRed_I2_J, fact_32_fun__upd__apply, fact_139_mem__def, fact_27_fun__upd__idem, fact_54_widen__trans, fact_0_InitBlockRed_I3_J, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_23_split__paired__All, fact_2_fun__upd__triv, fact_148_exp_Osimps_I83_J, fact_91_split__conv, fact_42_red__preserves__lconf, fact_117_mem__splitE, fact_158_redp__redsp_ORedSeq, fact_33_fun__upd__apply, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006, fact_76_internal__split__def, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010, fact_114_red__reds_ORedBlock, fact_26_fun__upd__idem, fact_130_cond__split__eta, fact_140_mem__def, fact_125_mem__splitI2, fact_137_exp_Osimps_I11_J, fact_102_splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, fact_39_fun__upd__idem__iff, fact_93_split__eta, fact_66_prod__caseI, fact_46_prod__induct3, fact_28_fun__upd__other, fact_12_prod__induct4, fact_132_splitE2, fact_30_fun__upd__twist, fact_94_split__eta, fact_123_mem__splitI2, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption, gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_, fact_53_prod_Oexhaust, fact_152_exp_Osimps_I142_J, fact_151_exp_Osimps_I197_J, gsy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J, fact_126_mem__splitI2, fact_52_prod_Oexhaust, fact_71_splitD, fact_64_prod__caseI, fact_59_PairE, fact_164_redp__redsp_OBlockRedSome, fact_22_split__paired__All, fact_106_mem__splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013, fact_34_fun__upd__same, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008, fact_144_exp_Osimps_I74_J, fact_61_PairE, fact_89_split__conv, fact_142_exp_Osimps_I10_J, help_fconj_2_1_U, fact_9_map__upd__eqD1, fact_103_WTrtBlock, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007, fact_83_split__part, fact_95_red__reds_OInitBlockRed, fact_45_prod__induct3, fact_41_red__preserves__hconf, fact_38_fun__upd__idem__iff, fact_20_Pair__eq, fact_113_red__reds_ORedSeq, fact_118_mem__splitE, fact_13_prod__cases4, fact_121_mem__splitI2, fact_50_pred__equals__eq2, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004, fact_37_fun__upd__upd, fact_138_exp_Osimps_I6_J, fact_56_split__paired__Ex, fact_157_redp__redsp_OBlockRedNone, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M, fact_84_split__part, fact_131_splitE2, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis, fact_29_fun__upd__other, fact_141_mem__def, fact_10_map__upd__eqD1, fact_68_splitI, fact_101_splitE, fact_15_Pair__inject, fact_143_exp_Osimps_I84_J, fact_35_fun__upd__same, fact_55_InitBlockRed_I5_J, fact_127_red__reds_ORedLAss, fact_110_WTrtSeq, fact_36_fun__upd__upd, fact_154_red__reds_OBlockRedSome, fact_156_redp__redsp_OLAssRed, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005, fact_124_mem__splitI2, fact_107_mem__splitI, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O, fact_48_pred__equals__eq2, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, fact_161_redp__redsp_ORedBlock, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002, fact_88_prod_Osimps_I2_J, fact_155_redp__redsp_OSeqRed, fact_40_widen__refl, fact_92_split__eta, fact_162_empty__upd__none, fact_51_prod_Oexhaust, gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__, fact_82_split__twice, fact_43_prod__cases3, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_16_Pair__inject, fact_165_redp__red__eq, fact_62_internal__split__conv, help_fconj_1_1_U, fact_85_split__part, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011, fact_149_exp_Osimps_I145_J, fact_159_map__upd__nonempty, fact_122_mem__splitI2, fact_163_empty__upd__none, fact_8_map__upd__triv, fact_72_splitD, fact_74_split__weak__cong, fact_18_Pair__eq, fact_99_splitI2, fact_160_map__upd__nonempty, fact_3_fun__upd__triv, fact_1_InitBlockRed_I1_J, gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri, fact_58_split__paired__Ex, fact_147_exp_Osimps_I82_J, fact_70_splitD, fact_75_split__weak__cong, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_120_mem__splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M, fact_49_pred__equals__eq2, fact_119_mem__splitE, fact_21_split__paired__All, fact_44_prod__cases3, fact_150_exp_Osimps_I144_J, fact_81_split__twice, fact_47_red__preserves__sconf, fact_146_exp_Osimps_I75_J, fact_96_red__reds_ORedInitBlock, fact_87_prod_Osimps_I2_J, fact_128_cond__split__eta, gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_, fact_97_splitI2, fact_79_split__twice, fact_90_split__conv, gsy_c_SmallStep_Oassigned, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003, fact_133_splitE2, fact_77_internal__split__def, fact_115_mem__splitE, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_112_red__reds_OLAssRed, gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001, fact_73_split__weak__cong, fact_80_split__twice, fact_135_exp_Osimps_I196_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O, fact_153_redp__redsp_OInitBlockRed, fact_14_InitBlockRed_I4_J, fact_108_mem__splitI, fact_31_fun__upd__twist
% 9.54/3.03 % No. of inferences in proof: 428
% 9.54/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2637 ms resp. 2163 ms w/o parsing
% 10.05/3.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.05/3.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------