TSTP Solution File: SWW470_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:32:50 EDT 2024
% Result : Theorem 2.04s 0.59s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 693
% Syntax : Number of formulae : 1871 ( 331 unt; 186 typ; 0 def)
% Number of atoms : 4735 (1254 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 5010 (1960 ~;2152 |; 284 &)
% ( 396 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 17 ( 2 avg)
% Number of types : 46 ( 45 usr)
% Number of type conns : 225 ( 111 >; 114 *; 0 +; 0 <<)
% Number of predicates : 360 ( 358 usr; 355 prp; 0-4 aty)
% Number of functors : 137 ( 137 usr; 30 con; 0-6 aty)
% Number of variables : 3493 (3313 !; 180 ?;3493 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
x_a: $tType ).
tff(type_def_6,type,
com: $tType ).
tff(type_def_7,type,
state: $tType ).
tff(type_def_8,type,
bool: $tType ).
tff(type_def_9,type,
hoare_1927711152iple_a: $tType ).
tff(type_def_10,type,
fun_a_fun_state_bool: $tType ).
tff(type_def_11,type,
fun_a_1632297036l_bool: $tType ).
tff(type_def_12,type,
fun_a_998512028e_bool: $tType ).
tff(type_def_13,type,
fun_a_2117018159e_bool: $tType ).
tff(type_def_14,type,
fun_state_bool: $tType ).
tff(type_def_15,type,
fun_st1506752259e_bool: $tType ).
tff(type_def_16,type,
fun_st2063251938l_bool: $tType ).
tff(type_def_17,type,
fun_bool_bool: $tType ).
tff(type_def_18,type,
fun_bo675861616e_bool: $tType ).
tff(type_def_19,type,
fun_bo1936561970e_bool: $tType ).
tff(type_def_20,type,
fun_bo1549164019l_bool: $tType ).
tff(type_def_21,type,
fun_Ho1877127206a_bool: $tType ).
tff(type_def_22,type,
fun_Ho843200573iple_a: $tType ).
tff(type_def_23,type,
fun_Ho957066028l_bool: $tType ).
tff(type_def_24,type,
fun_Ho440810351a_bool: $tType ).
tff(type_def_25,type,
fun_Ho333840202iple_a: $tType ).
tff(type_def_26,type,
fun_Ho525994229l_bool: $tType ).
tff(type_def_27,type,
fun_Ho1630563774a_bool: $tType ).
tff(type_def_28,type,
fun_fu2118559873l_bool: $tType ).
tff(type_def_29,type,
fun_fu1591723597e_bool: $tType ).
tff(type_def_30,type,
fun_fu2008829792e_bool: $tType ).
tff(type_def_31,type,
fun_fu222103665e_bool: $tType ).
tff(type_def_32,type,
fun_fu734682033e_bool: $tType ).
tff(type_def_33,type,
fun_fu281355805e_bool: $tType ).
tff(type_def_34,type,
fun_fu373216837e_bool: $tType ).
tff(type_def_35,type,
fun_fu1658206819l_bool: $tType ).
tff(type_def_36,type,
fun_fu402792811e_bool: $tType ).
tff(type_def_37,type,
fun_fu1219323149e_bool: $tType ).
tff(type_def_38,type,
fun_fu1047394976e_bool: $tType ).
tff(type_def_39,type,
fun_fu832487784l_bool: $tType ).
tff(type_def_40,type,
fun_fu1033095803iple_a: $tType ).
tff(type_def_41,type,
fun_fu1585556401a_bool: $tType ).
tff(type_def_42,type,
fun_fu269925879l_bool: $tType ).
tff(type_def_43,type,
fun_fu276214394a_bool: $tType ).
tff(type_def_44,type,
fun_fu1644852787l_bool: $tType ).
tff(type_def_45,type,
fun_fu1249172034a_bool: $tType ).
tff(type_def_46,type,
fun_fu1563903738a_bool: $tType ).
tff(type_def_47,type,
fun_fu893561155a_bool: $tType ).
tff(type_def_48,type,
fun_fu1192765369a_bool: $tType ).
tff(type_def_49,type,
fun_fu1905604217a_bool: $tType ).
tff(func_def_0,type,
cOMBB_160679318_state: fun_bool_bool > fun_fu373216837e_bool ).
tff(func_def_1,type,
cOMBB_213049548iple_a: fun_bool_bool > fun_fu1585556401a_bool ).
tff(func_def_2,type,
cOMBB_188601460_state: fun_bo1549164019l_bool > fun_fu1658206819l_bool ).
tff(func_def_3,type,
cOMBB_196465322iple_a: fun_bo1549164019l_bool > fun_fu269925879l_bool ).
tff(func_def_4,type,
cOMBB_1355796797bool_a: fun_fu1658206819l_bool > fun_fu2118559873l_bool ).
tff(func_def_5,type,
cOMBB_1348041619bool_a: fun_fu1219323149e_bool > fun_fu1591723597e_bool ).
tff(func_def_6,type,
cOMBB_145932198bool_a: fun_fu1047394976e_bool > fun_fu2008829792e_bool ).
tff(func_def_7,type,
cOMBB_1083611331iple_a: fun_fu832487784l_bool > fun_fu1563903738a_bool ).
tff(func_def_8,type,
cOMBC_41962815e_bool: fun_fu222103665e_bool ).
tff(func_def_9,type,
cOMBC_892787026e_bool: fun_fu734682033e_bool ).
tff(func_def_10,type,
cOMBC_2027030106e_bool: fun_fu402792811e_bool ).
tff(func_def_11,type,
cOMBC_231445413l_bool: fun_fu1219323149e_bool ).
tff(func_def_12,type,
cOMBC_671859290a_bool: fun_fu893561155a_bool ).
tff(func_def_13,type,
cOMBC_862840740l_bool: fun_fu1192765369a_bool ).
tff(func_def_14,type,
cOMBC_825881325a_bool: fun_fu1905604217a_bool ).
tff(func_def_15,type,
cOMBK_bool_state: bool > fun_state_bool ).
tff(func_def_16,type,
cOMBK_712844119iple_a: bool > fun_Ho1877127206a_bool ).
tff(func_def_17,type,
cOMBK_1458035955bool_a: fun_state_bool > fun_a_fun_state_bool ).
tff(func_def_18,type,
cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).
tff(func_def_19,type,
cOMBS_2061548107l_bool: fun_fu1249172034a_bool ).
tff(func_def_20,type,
skip: com ).
tff(func_def_21,type,
semi: ( com * com ) > com ).
tff(func_def_22,type,
finite68738179iple_a: fun_fu832487784l_bool ).
tff(func_def_23,type,
finite2098837632iple_a: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_24,type,
finite1943414032iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a ).
tff(func_def_25,type,
finite148164294iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_26,type,
finite83514413iple_a: ( fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > bool ).
tff(func_def_27,type,
finite1511031594iple_a: ( fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > bool ).
tff(func_def_28,type,
the_Ho1307659873iple_a: fun_fu1033095803iple_a ).
tff(func_def_29,type,
hoare_1617968510rivs_a: fun_Ho1877127206a_bool > fun_fu832487784l_bool ).
tff(func_def_30,type,
hoare_1652181356iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_1927711152iple_a ).
tff(func_def_31,type,
bot_bot_bool: bool ).
tff(func_def_32,type,
bot_bo1208640912a_bool: fun_Ho1877127206a_bool ).
tff(func_def_33,type,
collec829051333iple_a: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).
tff(func_def_34,type,
insert1434104874iple_a: fun_Ho1630563774a_bool ).
tff(func_def_35,type,
the_el1997360207iple_a: fun_fu1033095803iple_a ).
tff(func_def_36,type,
fFalse: bool ).
tff(func_def_37,type,
fNot: fun_bool_bool ).
tff(func_def_38,type,
fTrue: bool ).
tff(func_def_39,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_40,type,
fdisj: fun_bo1549164019l_bool ).
tff(func_def_41,type,
fequal_state: fun_st1506752259e_bool ).
tff(func_def_42,type,
fequal1440857775iple_a: fun_Ho440810351a_bool ).
tff(func_def_43,type,
fequal1285825639a_bool: fun_fu1644852787l_bool ).
tff(func_def_44,type,
fimplies: fun_bo1549164019l_bool ).
tff(func_def_45,type,
hAPP_a2036067514e_bool: ( fun_a_fun_state_bool * x_a ) > fun_state_bool ).
tff(func_def_46,type,
hAPP_a849909144l_bool: ( fun_a_1632297036l_bool * x_a ) > fun_st2063251938l_bool ).
tff(func_def_47,type,
hAPP_a723219176e_bool: ( fun_a_998512028e_bool * x_a ) > fun_bo1936561970e_bool ).
tff(func_def_48,type,
hAPP_a1200519163e_bool: ( fun_a_2117018159e_bool * x_a ) > fun_fu373216837e_bool ).
tff(func_def_49,type,
hAPP_state_bool: ( fun_state_bool * state ) > bool ).
tff(func_def_50,type,
hAPP_s1806633685e_bool: ( fun_st1506752259e_bool * state ) > fun_state_bool ).
tff(func_def_51,type,
hAPP_s58564346l_bool: ( fun_st2063251938l_bool * state ) > fun_bool_bool ).
tff(func_def_52,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(func_def_53,type,
hAPP_b540892988e_bool: ( fun_bo675861616e_bool * bool ) > fun_a_fun_state_bool ).
tff(func_def_54,type,
hAPP_b2019457360e_bool: ( fun_bo1936561970e_bool * bool ) > fun_state_bool ).
tff(func_def_55,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(func_def_56,type,
hAPP_H1448631928a_bool: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > bool ).
tff(func_def_57,type,
hAPP_H963118037iple_a: ( fun_Ho843200573iple_a * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_58,type,
hAPP_H1487873860l_bool: ( fun_Ho957066028l_bool * hoare_1927711152iple_a ) > fun_bool_bool ).
tff(func_def_59,type,
hAPP_H1027145665a_bool: ( fun_Ho440810351a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_60,type,
hAPP_H1700437986iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a ) > fun_Ho843200573iple_a ).
tff(func_def_61,type,
hAPP_H694056973l_bool: ( fun_Ho525994229l_bool * hoare_1927711152iple_a ) > fun_fu832487784l_bool ).
tff(func_def_62,type,
hAPP_H1975128022a_bool: ( fun_Ho1630563774a_bool * hoare_1927711152iple_a ) > fun_fu1585556401a_bool ).
tff(func_def_63,type,
hAPP_f1509969235l_bool: ( fun_fu2118559873l_bool * fun_a_fun_state_bool ) > fun_a_1632297036l_bool ).
tff(func_def_64,type,
hAPP_f340725611e_bool: ( fun_fu1591723597e_bool * fun_a_1632297036l_bool ) > fun_a_998512028e_bool ).
tff(func_def_65,type,
hAPP_f963367678e_bool: ( fun_fu2008829792e_bool * fun_a_1632297036l_bool ) > fun_a_2117018159e_bool ).
tff(func_def_66,type,
hAPP_f1824947087e_bool: ( fun_fu222103665e_bool * fun_a_998512028e_bool ) > fun_bo675861616e_bool ).
tff(func_def_67,type,
hAPP_f1261923407e_bool: ( fun_fu734682033e_bool * fun_a_2117018159e_bool ) > fun_fu281355805e_bool ).
tff(func_def_68,type,
hAPP_f762886889e_bool: ( fun_fu281355805e_bool * fun_state_bool ) > fun_a_fun_state_bool ).
tff(func_def_69,type,
hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).
tff(func_def_70,type,
hAPP_f1259673775l_bool: ( fun_fu1658206819l_bool * fun_state_bool ) > fun_st2063251938l_bool ).
tff(func_def_71,type,
hAPP_f817621513e_bool: ( fun_fu402792811e_bool * fun_st1506752259e_bool ) > fun_st1506752259e_bool ).
tff(func_def_72,type,
hAPP_f167292325e_bool: ( fun_fu1219323149e_bool * fun_st2063251938l_bool ) > fun_bo1936561970e_bool ).
tff(func_def_73,type,
hAPP_f644196280e_bool: ( fun_fu1047394976e_bool * fun_st2063251938l_bool ) > fun_fu373216837e_bool ).
tff(func_def_74,type,
hAPP_f1454306822l_bool: ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > bool ).
tff(func_def_75,type,
hAPP_f490779847iple_a: ( fun_fu1033095803iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_76,type,
hAPP_f16502863a_bool: ( fun_fu1585556401a_bool * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_77,type,
hAPP_f749678531l_bool: ( fun_fu269925879l_bool * fun_Ho1877127206a_bool ) > fun_Ho957066028l_bool ).
tff(func_def_78,type,
hAPP_f993216280a_bool: ( fun_fu276214394a_bool * fun_Ho1877127206a_bool ) > fun_Ho440810351a_bool ).
tff(func_def_79,type,
hAPP_f625100287l_bool: ( fun_fu1644852787l_bool * fun_Ho1877127206a_bool ) > fun_fu832487784l_bool ).
tff(func_def_80,type,
hAPP_f2112551770a_bool: ( fun_fu1249172034a_bool * fun_Ho957066028l_bool ) > fun_fu1585556401a_bool ).
tff(func_def_81,type,
hAPP_f909473944a_bool: ( fun_fu1563903738a_bool * fun_Ho440810351a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_82,type,
hAPP_f1216137953a_bool: ( fun_fu893561155a_bool * fun_Ho440810351a_bool ) > fun_Ho440810351a_bool ).
tff(func_def_83,type,
hAPP_f684479953a_bool: ( fun_fu1192765369a_bool * fun_Ho525994229l_bool ) > fun_fu1585556401a_bool ).
tff(func_def_84,type,
hAPP_f1022403729a_bool: ( fun_fu1905604217a_bool * fun_Ho1630563774a_bool ) > fun_fu276214394a_bool ).
tff(func_def_85,type,
member127332739iple_a: fun_Ho525994229l_bool ).
tff(func_def_86,type,
g: fun_Ho1877127206a_bool ).
tff(func_def_87,type,
p: fun_a_fun_state_bool ).
tff(func_def_88,type,
b: fun_state_bool ).
tff(func_def_89,type,
c: com ).
tff(func_def_90,type,
sK3: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_91,type,
sK4: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_92,type,
sK5: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_93,type,
sK6: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).
tff(func_def_94,type,
sK7: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_95,type,
sK8: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_96,type,
sK9: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).
tff(func_def_97,type,
sK10: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_98,type,
sK11: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_99,type,
sK12: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_100,type,
sK13: hoare_1927711152iple_a > fun_a_fun_state_bool ).
tff(func_def_101,type,
sK14: hoare_1927711152iple_a > com ).
tff(func_def_102,type,
sK15: hoare_1927711152iple_a > fun_a_fun_state_bool ).
tff(func_def_103,type,
sK16: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(func_def_104,type,
sK17: fun_fu832487784l_bool > fun_Ho1877127206a_bool ).
tff(func_def_105,type,
sK18: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(func_def_106,type,
sK19: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_107,type,
sK20: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(func_def_108,type,
sK21: fun_fu832487784l_bool > fun_Ho1877127206a_bool ).
tff(func_def_109,type,
sK22: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_110,type,
sK23: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_111,type,
sK24: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_112,type,
sK25: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_113,type,
sK26: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_114,type,
sK27: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_115,type,
sK28: fun_Ho333840202iple_a > hoare_1927711152iple_a ).
tff(func_def_116,type,
sK29: fun_Ho333840202iple_a > hoare_1927711152iple_a ).
tff(func_def_117,type,
sK30: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_118,type,
sK31: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_119,type,
sK32: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_120,type,
sK33: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(func_def_121,type,
sK34: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_122,type,
sK35: ( fun_Ho1877127206a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_123,type,
sK36: ( fun_Ho1877127206a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_124,type,
sK37: ( fun_a_fun_state_bool * fun_Ho1877127206a_bool * com * fun_a_fun_state_bool ) > x_a ).
tff(func_def_125,type,
sK38: ( fun_a_fun_state_bool * fun_Ho1877127206a_bool * com * fun_a_fun_state_bool ) > state ).
tff(func_def_126,type,
sK39: ( fun_a_fun_state_bool * fun_Ho1877127206a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_127,type,
sK40: ( hoare_1927711152iple_a * fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_128,type,
sK41: ( hoare_1927711152iple_a * fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_129,type,
sK42: ( hoare_1927711152iple_a * fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_130,type,
sK43: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_131,type,
sK44: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_132,type,
sK45: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_133,type,
sK46: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_134,type,
sK47: ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_135,type,
sK48: ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_136,type,
sK49: ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: fun_fu832487784l_bool > $o ).
tff(pred_def_3,type,
sP1: ( hoare_1927711152iple_a * fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > $o ).
tff(pred_def_4,type,
sP2: ( hoare_1927711152iple_a * hoare_1927711152iple_a * hoare_1927711152iple_a * hoare_1927711152iple_a ) > $o ).
tff(f7084,plain,
$false,
inference(avatar_sat_refutation,[],[f769,f774,f778,f783,f787,f791,f795,f799,f806,f810,f814,f818,f822,f830,f835,f839,f843,f847,f851,f855,f859,f863,f867,f889,f895,f901,f907,f911,f915,f919,f923,f927,f947,f951,f955,f959,f964,f969,f973,f977,f981,f985,f989,f993,f1019,f1024,f1028,f1032,f1037,f1041,f1045,f1049,f1053,f1057,f1074,f1078,f1082,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1114,f1118,f1122,f1126,f1130,f1134,f1168,f1187,f1191,f1195,f1199,f1203,f1208,f1212,f1216,f1220,f1224,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1332,f1336,f1352,f1443,f1447,f1451,f1455,f1459,f1463,f1467,f1471,f1472,f1493,f1497,f1529,f1533,f1537,f1552,f1556,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1607,f1611,f1615,f1619,f1623,f1729,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1968,f1972,f1994,f1998,f2002,f2006,f2036,f2040,f2044,f2048,f2096,f2100,f2217,f2221,f2226,f2230,f2234,f2238,f2242,f2246,f2250,f2273,f2277,f2292,f2296,f2300,f2317,f2321,f2340,f2344,f2348,f2396,f2400,f2419,f2423,f2427,f2444,f2466,f2481,f2507,f2511,f2515,f2519,f2531,f2535,f2688,f2705,f2709,f2713,f2736,f2740,f2757,f2761,f2780,f2789,f2810,f2827,f2836,f2843,f2847,f2851,f2855,f2859,f2863,f2867,f2871,f2875,f2879,f2883,f2898,f3163,f3167,f3172,f3177,f3839,f3843,f3847,f3851,f3855,f3859,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3939,f3944,f3948,f3952,f3956,f3986,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4244,f4309,f4370,f4374,f4378,f4382,f4386,f4392,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4794,f4798,f4802,f4807,f4812,f4817,f4821,f4825,f4829,f4833,f5009,f5014,f5032,f5036,f5040,f5044,f5049,f5054,f5059,f5064,f5068,f5073,f5090,f5094,f5098,f5102,f5106,f5373,f5377,f5381,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5451,f5696,f5700,f5704,f5708,f5712,f5716,f5721,f5727,f5732,f5737,f5742,f5747,f5752,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5964,f5989,f5993,f5997,f6001,f6005,f6009,f6013,f6017,f6341,f6345,f6350,f6354,f6358,f6362,f6366,f6370,f6374,f6378,f6382,f6386,f6390,f6407,f6411,f6415,f6419,f6423,f6427,f7083]) ).
tff(f7083,plain,
( spl50_15
| ~ spl50_19
| spl50_27
| ~ spl50_178
| ~ spl50_349 ),
inference(avatar_split_clause,[],[f7036,f6405,f2441,f898,f845,f827]) ).
tff(f827,plain,
( spl50_15
<=> hBOOL(bot_bot_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_15])]) ).
tff(f845,plain,
( spl50_19
<=> ! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_19])]) ).
tff(f898,plain,
( spl50_27
<=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_27])]) ).
tff(f2441,plain,
( spl50_178
<=> ( fFalse = bot_bot_bool ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_178])]) ).
tff(f6405,plain,
( spl50_349
<=> ! [X0: fun_state_bool,X3: fun_a_fun_state_bool,X2: com,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_state_bool(X0,sK36(X1,X2,X3,cOMBK_1458035955bool_a(X0))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(X0),X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_349])]) ).
tff(f7036,plain,
( hBOOL(bot_bot_bool)
| ~ spl50_19
| spl50_27
| ~ spl50_178
| ~ spl50_349 ),
inference(forward_demodulation,[],[f7035,f2443]) ).
tff(f2443,plain,
( ( fFalse = bot_bot_bool )
| ~ spl50_178 ),
inference(avatar_component_clause,[],[f2441]) ).
tff(f7035,plain,
( hBOOL(fFalse)
| ~ spl50_19
| spl50_27
| ~ spl50_349 ),
inference(forward_demodulation,[],[f7003,f846]) ).
tff(f846,plain,
( ! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 )
| ~ spl50_19 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f7003,plain,
( hBOOL(hAPP_state_bool(cOMBK_bool_state(fFalse),sK36(g,c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)))))
| spl50_27
| ~ spl50_349 ),
inference(resolution,[],[f6406,f900]) ).
tff(f900,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))
| spl50_27 ),
inference(avatar_component_clause,[],[f898]) ).
tff(f6406,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: fun_state_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_state_bool(X0,sK36(X1,X2,X3,cOMBK_1458035955bool_a(X0))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(X0),X2,X3)))) )
| ~ spl50_349 ),
inference(avatar_component_clause,[],[f6405]) ).
tff(f6427,plain,
( spl50_354
| ~ spl50_71
| ~ spl50_186 ),
inference(avatar_split_clause,[],[f2679,f2533,f1132,f6425]) ).
tff(f6425,plain,
( spl50_354
<=> ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK45(X2,X1)),sK46(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_354])]) ).
tff(f1132,plain,
( spl50_71
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_71])]) ).
tff(f2533,plain,
( spl50_186
<=> ! [X4: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X3: com,X2: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_186])]) ).
tff(f2679,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK45(X2,X1)),sK46(X2,X1))) )
| ~ spl50_71
| ~ spl50_186 ),
inference(resolution,[],[f2534,f1133]) ).
tff(f1133,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X1))))
| ~ spl50_71 ),
inference(avatar_component_clause,[],[f1132]) ).
tff(f2534,plain,
( ! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4))) )
| ~ spl50_186 ),
inference(avatar_component_clause,[],[f2533]) ).
tff(f6423,plain,
( spl50_353
| ~ spl50_71
| ~ spl50_185 ),
inference(avatar_split_clause,[],[f2673,f2529,f1132,f6421]) ).
tff(f6421,plain,
( spl50_353
<=> ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK45(X2,X1)),sK46(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_353])]) ).
tff(f2529,plain,
( spl50_185
<=> ! [X4: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X3: com,X2: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_185])]) ).
tff(f2673,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK45(X2,X1)),sK46(X2,X1))) )
| ~ spl50_71
| ~ spl50_185 ),
inference(resolution,[],[f2530,f1133]) ).
tff(f2530,plain,
( ! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4))) )
| ~ spl50_185 ),
inference(avatar_component_clause,[],[f2529]) ).
tff(f6419,plain,
( spl50_352
| ~ spl50_71
| ~ spl50_184 ),
inference(avatar_split_clause,[],[f2667,f2517,f1132,f6417]) ).
tff(f6417,plain,
( spl50_352
<=> ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK43(X1,X2)),sK44(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_352])]) ).
tff(f2517,plain,
( spl50_184
<=> ! [X4: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X3: com,X2: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_184])]) ).
tff(f2667,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK43(X1,X2)),sK44(X1,X2))) )
| ~ spl50_71
| ~ spl50_184 ),
inference(resolution,[],[f2518,f1133]) ).
tff(f2518,plain,
( ! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2))) )
| ~ spl50_184 ),
inference(avatar_component_clause,[],[f2517]) ).
tff(f6415,plain,
( spl50_351
| ~ spl50_71
| ~ spl50_183 ),
inference(avatar_split_clause,[],[f2656,f2513,f1132,f6413]) ).
tff(f6413,plain,
( spl50_351
<=> ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X1,X2)),sK44(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_351])]) ).
tff(f2513,plain,
( spl50_183
<=> ! [X4: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X3: com,X2: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_183])]) ).
tff(f2656,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X2))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X1,X2)),sK44(X1,X2))) )
| ~ spl50_71
| ~ spl50_183 ),
inference(resolution,[],[f2514,f1133]) ).
tff(f2514,plain,
( ! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2))) )
| ~ spl50_183 ),
inference(avatar_component_clause,[],[f2513]) ).
tff(f6411,plain,
( spl50_350
| ~ spl50_18
| ~ spl50_172 ),
inference(avatar_split_clause,[],[f2389,f2346,f841,f6409]) ).
tff(f6409,plain,
( spl50_350
<=> ! [X0: fun_state_bool,X3: com,X2: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_state_bool(X0,sK38(X1,X2,X3,cOMBK_1458035955bool_a(X0))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(X0),X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_350])]) ).
tff(f841,plain,
( spl50_18
<=> ! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_18])]) ).
tff(f2346,plain,
( spl50_172
<=> ! [X0: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X2: com,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_172])]) ).
tff(f2389,plain,
( ! [X2: fun_Ho1877127206a_bool,X3: com,X0: fun_state_bool,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_state_bool(X0,sK38(X1,X2,X3,cOMBK_1458035955bool_a(X0))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(X0),X3,X1)))) )
| ~ spl50_18
| ~ spl50_172 ),
inference(superposition,[],[f2347,f842]) ).
tff(f842,plain,
( ! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 )
| ~ spl50_18 ),
inference(avatar_component_clause,[],[f841]) ).
tff(f2347,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3)))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0)))) )
| ~ spl50_172 ),
inference(avatar_component_clause,[],[f2346]) ).
tff(f6407,plain,
( spl50_349
| ~ spl50_18
| ~ spl50_171 ),
inference(avatar_split_clause,[],[f2384,f2342,f841,f6405]) ).
tff(f2342,plain,
( spl50_171
<=> ! [X0: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X2: fun_a_fun_state_bool,X1: com] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_171])]) ).
tff(f2384,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: fun_state_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_state_bool(X0,sK36(X1,X2,X3,cOMBK_1458035955bool_a(X0))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(X0),X2,X3)))) )
| ~ spl50_18
| ~ spl50_171 ),
inference(superposition,[],[f2343,f842]) ).
tff(f2343,plain,
( ! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3)))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2)))) )
| ~ spl50_171 ),
inference(avatar_component_clause,[],[f2342]) ).
tff(f6390,plain,
( spl50_348
| ~ spl50_3
| ~ spl50_163 ),
inference(avatar_split_clause,[],[f2278,f2271,f776,f6388]) ).
tff(f6388,plain,
( spl50_348
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_348])]) ).
tff(f776,plain,
( spl50_3
<=> ! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_3])]) ).
tff(f2271,plain,
( spl50_163
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_163])]) ).
tff(f2278,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1)) )
| ~ spl50_3
| ~ spl50_163 ),
inference(superposition,[],[f2272,f777]) ).
tff(f777,plain,
( ! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 )
| ~ spl50_3 ),
inference(avatar_component_clause,[],[f776]) ).
tff(f2272,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1))) )
| ~ spl50_163 ),
inference(avatar_component_clause,[],[f2271]) ).
tff(f6386,plain,
( spl50_347
| ~ spl50_83
| ~ spl50_150 ),
inference(avatar_split_clause,[],[f2182,f2042,f1247,f6384]) ).
tff(f6384,plain,
( spl50_347
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( sK5(X0) = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_347])]) ).
tff(f1247,plain,
( spl50_83
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),sK6(X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_83])]) ).
tff(f2042,plain,
( spl50_150
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_150])]) ).
tff(f2182,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( sK5(X0) = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_150 ),
inference(superposition,[],[f2043,f1248]) ).
tff(f1248,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),sK6(X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83 ),
inference(avatar_component_clause,[],[f1247]) ).
tff(f2043,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)))
| ( X0 = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2)) )
| ~ spl50_150 ),
inference(avatar_component_clause,[],[f2042]) ).
tff(f6382,plain,
( spl50_346
| ~ spl50_102
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2156,f2038,f1334,f6380]) ).
tff(f6380,plain,
( spl50_346
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_346])]) ).
tff(f1334,plain,
( spl50_102
<=> ! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_102])]) ).
tff(f2038,plain,
( spl50_149
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_149])]) ).
tff(f2156,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) )
| ~ spl50_102
| ~ spl50_149 ),
inference(superposition,[],[f1335,f2039]) ).
tff(f2039,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)) )
| ~ spl50_149 ),
inference(avatar_component_clause,[],[f2038]) ).
tff(f1335,plain,
( ! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) )
| ~ spl50_102 ),
inference(avatar_component_clause,[],[f1334]) ).
tff(f6378,plain,
( spl50_345
| ~ spl50_97
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2155,f2038,f1304,f6376]) ).
tff(f6376,plain,
( spl50_345
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)),X3))
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_345])]) ).
tff(f1304,plain,
( spl50_97
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_97])]) ).
tff(f2155,plain,
( ! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)),X3))
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2),X3)) )
| ~ spl50_97
| ~ spl50_149 ),
inference(superposition,[],[f1305,f2039]) ).
tff(f1305,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) )
| ~ spl50_97 ),
inference(avatar_component_clause,[],[f1304]) ).
tff(f6374,plain,
( spl50_344
| ~ spl50_86
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2154,f2038,f1259,f6372]) ).
tff(f6372,plain,
( spl50_344
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_344])]) ).
tff(f1259,plain,
( spl50_86
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_86])]) ).
tff(f2154,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) )
| ~ spl50_86
| ~ spl50_149 ),
inference(superposition,[],[f1260,f2039]) ).
tff(f1260,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) )
| ~ spl50_86 ),
inference(avatar_component_clause,[],[f1259]) ).
tff(f6370,plain,
( spl50_343
| ~ spl50_83
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2145,f2038,f1247,f6368]) ).
tff(f6368,plain,
( spl50_343
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),sK6(X0))) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_343])]) ).
tff(f2145,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),sK6(X0))) )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_149 ),
inference(superposition,[],[f2039,f1248]) ).
tff(f6366,plain,
( spl50_342
| ~ spl50_96
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1951,f1757,f1300,f6364]) ).
tff(f6364,plain,
( spl50_342
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,X2)) )
| ( sK32(X1,X2,X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_342])]) ).
tff(f1300,plain,
( spl50_96
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK32(X0,X1,X2) = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_96])]) ).
tff(f1757,plain,
( spl50_141
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_141])]) ).
tff(f1951,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,X2)) )
| ( sK32(X1,X2,X0) = X0 ) )
| ~ spl50_96
| ~ spl50_141 ),
inference(resolution,[],[f1758,f1301]) ).
tff(f1301,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ( sK32(X0,X1,X2) = X2 ) )
| ~ spl50_96 ),
inference(avatar_component_clause,[],[f1300]) ).
tff(f1758,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) ) )
| ~ spl50_141 ),
inference(avatar_component_clause,[],[f1757]) ).
tff(f6362,plain,
( spl50_341
| ~ spl50_94
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1695,f1587,f1292,f6360]) ).
tff(f6360,plain,
( spl50_341
<=> ! [X0: fun_fu832487784l_bool,X3: fun_Ho957066028l_bool,X2: hoare_1927711152iple_a,X1: fun_Ho440810351a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X3),hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X3,X2),hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_341])]) ).
tff(f1292,plain,
( spl50_94
<=> ! [X2: hoare_1927711152iple_a,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] : ( hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_94])]) ).
tff(f1587,plain,
( spl50_126
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_126])]) ).
tff(f1695,plain,
( ! [X2: hoare_1927711152iple_a,X3: fun_Ho957066028l_bool,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X3),hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X3,X2),hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2))) )
| ~ spl50_94
| ~ spl50_126 ),
inference(superposition,[],[f1588,f1293]) ).
tff(f1293,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] : ( hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) )
| ~ spl50_94 ),
inference(avatar_component_clause,[],[f1292]) ).
tff(f1588,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) )
| ~ spl50_126 ),
inference(avatar_component_clause,[],[f1587]) ).
tff(f6358,plain,
( spl50_340
| ~ spl50_95
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1692,f1587,f1296,f6356]) ).
tff(f6356,plain,
( spl50_340
<=> ! [X0: fun_bool_bool,X3: fun_Ho957066028l_bool,X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X3),hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_340])]) ).
tff(f1296,plain,
( spl50_95
<=> ! [X2: hoare_1927711152iple_a,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_95])]) ).
tff(f1692,plain,
( ! [X2: hoare_1927711152iple_a,X3: fun_Ho957066028l_bool,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X3),hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2))) )
| ~ spl50_95
| ~ spl50_126 ),
inference(superposition,[],[f1588,f1297]) ).
tff(f1297,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) )
| ~ spl50_95 ),
inference(avatar_component_clause,[],[f1296]) ).
tff(f6354,plain,
( spl50_339
| ~ spl50_89
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1688,f1587,f1271,f6352]) ).
tff(f6352,plain,
( spl50_339
<=> ! [X0: fun_bo1549164019l_bool,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1)),X3),X2) = hAPP_bool_bool(hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)),hAPP_H1448631928a_bool(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_339])]) ).
tff(f1271,plain,
( spl50_89
<=> ! [X2: hoare_1927711152iple_a,X0: fun_bo1549164019l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_89])]) ).
tff(f1688,plain,
( ! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: fun_bo1549164019l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1)),X3),X2) = hAPP_bool_bool(hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)),hAPP_H1448631928a_bool(X3,X2)) )
| ~ spl50_89
| ~ spl50_126 ),
inference(superposition,[],[f1588,f1272]) ).
tff(f1272,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_bo1549164019l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)) )
| ~ spl50_89 ),
inference(avatar_component_clause,[],[f1271]) ).
tff(f6350,plain,
( spl50_338
| spl50_15
| ~ spl50_248 ),
inference(avatar_split_clause,[],[f6025,f4307,f827,f6347]) ).
tff(f6347,plain,
( spl50_338
<=> ( fTrue = hAPP_bool_bool(fNot,bot_bot_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_338])]) ).
tff(f4307,plain,
( spl50_248
<=> ! [X0: bool] :
( ( fTrue = hAPP_bool_bool(fNot,X0) )
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_248])]) ).
tff(f6025,plain,
( ( fTrue = hAPP_bool_bool(fNot,bot_bot_bool) )
| spl50_15
| ~ spl50_248 ),
inference(resolution,[],[f4308,f828]) ).
tff(f828,plain,
( ~ hBOOL(bot_bot_bool)
| spl50_15 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f4308,plain,
( ! [X0: bool] :
( hBOOL(X0)
| ( fTrue = hAPP_bool_bool(fNot,X0) ) )
| ~ spl50_248 ),
inference(avatar_component_clause,[],[f4307]) ).
tff(f6345,plain,
( spl50_337
| ~ spl50_93
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1683,f1583,f1288,f6343]) ).
tff(f6343,plain,
( spl50_337
<=> ! [X0: fun_bool_bool,X3: fun_st2063251938l_bool,X2: state,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X3),hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1)),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_state_bool(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_337])]) ).
tff(f1288,plain,
( spl50_93
<=> ! [X2: state,X0: fun_bool_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_93])]) ).
tff(f1583,plain,
( spl50_125
<=> ! [X2: state,X0: fun_st2063251938l_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_125])]) ).
tff(f1683,plain,
( ! [X2: state,X3: fun_st2063251938l_bool,X0: fun_bool_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X3),hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1)),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_state_bool(X1,X2))) )
| ~ spl50_93
| ~ spl50_125 ),
inference(superposition,[],[f1584,f1289]) ).
tff(f1289,plain,
( ! [X2: state,X0: fun_bool_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) )
| ~ spl50_93 ),
inference(avatar_component_clause,[],[f1288]) ).
tff(f1584,plain,
( ! [X2: state,X0: fun_st2063251938l_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) )
| ~ spl50_125 ),
inference(avatar_component_clause,[],[f1583]) ).
tff(f6341,plain,
( spl50_336
| ~ spl50_91
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1679,f1583,f1280,f6339]) ).
tff(f6339,plain,
( spl50_336
<=> ! [X0: fun_bo1549164019l_bool,X3: fun_state_bool,X2: state,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1)),X3),X2) = hAPP_bool_bool(hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)),hAPP_state_bool(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_336])]) ).
tff(f1280,plain,
( spl50_91
<=> ! [X2: state,X0: fun_bo1549164019l_bool,X1: fun_state_bool] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_91])]) ).
tff(f1679,plain,
( ! [X2: state,X3: fun_state_bool,X0: fun_bo1549164019l_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1)),X3),X2) = hAPP_bool_bool(hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)),hAPP_state_bool(X3,X2)) )
| ~ spl50_91
| ~ spl50_125 ),
inference(superposition,[],[f1584,f1281]) ).
tff(f1281,plain,
( ! [X2: state,X0: fun_bo1549164019l_bool,X1: fun_state_bool] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)) )
| ~ spl50_91 ),
inference(avatar_component_clause,[],[f1280]) ).
tff(f6017,plain,
( spl50_335
| ~ spl50_85
| ~ spl50_164 ),
inference(avatar_split_clause,[],[f2281,f2275,f1255,f6015]) ).
tff(f6015,plain,
( spl50_335
<=> ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK16(hoare_1617968510rivs_a(X0)))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),sK17(hoare_1617968510rivs_a(X0))))
| ~ sP0(hoare_1617968510rivs_a(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_335])]) ).
tff(f1255,plain,
( spl50_85
<=> ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK16(X0)),sK17(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_85])]) ).
tff(f2275,plain,
( spl50_164
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_164])]) ).
tff(f2281,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK16(hoare_1617968510rivs_a(X0)))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),sK17(hoare_1617968510rivs_a(X0))))
| ~ sP0(hoare_1617968510rivs_a(X0)) )
| ~ spl50_85
| ~ spl50_164 ),
inference(resolution,[],[f2276,f1256]) ).
tff(f1256,plain,
( ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK16(X0)),sK17(X0))))
| ~ sP0(X0) )
| ~ spl50_85 ),
inference(avatar_component_clause,[],[f1255]) ).
tff(f2276,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0)) )
| ~ spl50_164 ),
inference(avatar_component_clause,[],[f2275]) ).
tff(f6013,plain,
( spl50_334
| ~ spl50_3
| ~ spl50_159 ),
inference(avatar_split_clause,[],[f2261,f2236,f776,f6011]) ).
tff(f6011,plain,
( spl50_334
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_334])]) ).
tff(f2236,plain,
( spl50_159
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_159])]) ).
tff(f2261,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1) )
| ~ spl50_3
| ~ spl50_159 ),
inference(superposition,[],[f2237,f777]) ).
tff(f2237,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1)) )
| ~ spl50_159 ),
inference(avatar_component_clause,[],[f2236]) ).
tff(f6009,plain,
( spl50_333
| ~ spl50_45
| ~ spl50_151 ),
inference(avatar_split_clause,[],[f2184,f2046,f991,f6007]) ).
tff(f6007,plain,
( spl50_333
<=> ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)),sK31(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_333])]) ).
tff(f991,plain,
( spl50_45
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_45])]) ).
tff(f2046,plain,
( spl50_151
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_151])]) ).
tff(f2184,plain,
( ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)),sK31(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)) )
| ~ spl50_45
| ~ spl50_151 ),
inference(resolution,[],[f2047,f992]) ).
tff(f992,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)),X2))
| ~ spl50_45 ),
inference(avatar_component_clause,[],[f991]) ).
tff(f2047,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)) = X1 ) )
| ~ spl50_151 ),
inference(avatar_component_clause,[],[f2046]) ).
tff(f6005,plain,
( spl50_332
| ~ spl50_43
| ~ spl50_148 ),
inference(avatar_split_clause,[],[f2112,f2034,f983,f6003]) ).
tff(f6003,plain,
( spl50_332
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| hBOOL(hAPP_H1448631928a_bool(X0,sK26(X0,sK8(X0))))
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_332])]) ).
tff(f983,plain,
( spl50_43
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_43])]) ).
tff(f2034,plain,
( spl50_148
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| hBOOL(hAPP_H1448631928a_bool(X1,sK26(X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_148])]) ).
tff(f2112,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| hBOOL(hAPP_H1448631928a_bool(X0,sK26(X0,sK8(X0))))
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_43
| ~ spl50_148 ),
inference(resolution,[],[f2035,f984]) ).
tff(f984,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_43 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f2035,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| hBOOL(hAPP_H1448631928a_bool(X1,sK26(X1,X2)))
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 ) )
| ~ spl50_148 ),
inference(avatar_component_clause,[],[f2034]) ).
tff(f6001,plain,
( spl50_331
| ~ spl50_42
| ~ spl50_148 ),
inference(avatar_split_clause,[],[f2111,f2034,f979,f5999]) ).
tff(f5999,plain,
( spl50_331
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| hBOOL(hAPP_H1448631928a_bool(X0,sK26(X0,sK7(X0))))
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_331])]) ).
tff(f979,plain,
( spl50_42
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_42])]) ).
tff(f2111,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| hBOOL(hAPP_H1448631928a_bool(X0,sK26(X0,sK7(X0))))
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_42
| ~ spl50_148 ),
inference(resolution,[],[f2035,f980]) ).
tff(f980,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_42 ),
inference(avatar_component_clause,[],[f979]) ).
tff(f5997,plain,
( spl50_330
| ~ spl50_43
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2020,f2004,f983,f5995]) ).
tff(f5995,plain,
( spl50_330
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,sK8(X0)) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK8(X0)))),X0) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_330])]) ).
tff(f2004,plain,
( spl50_147
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_147])]) ).
tff(f2020,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,sK8(X0)) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK8(X0)))),X0) )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_43
| ~ spl50_147 ),
inference(resolution,[],[f2005,f984]) ).
tff(f2005,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) ) )
| ~ spl50_147 ),
inference(avatar_component_clause,[],[f2004]) ).
tff(f5993,plain,
( spl50_329
| ~ spl50_42
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2019,f2004,f979,f5991]) ).
tff(f5991,plain,
( spl50_329
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,sK7(X0)) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK7(X0)))),X0) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_329])]) ).
tff(f2019,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,sK7(X0)) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK7(X0)))),X0) )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_42
| ~ spl50_147 ),
inference(resolution,[],[f2005,f980]) ).
tff(f5989,plain,
( spl50_328
| ~ spl50_82
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1950,f1757,f1222,f5987]) ).
tff(f5987,plain,
( spl50_328
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X2))) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_328])]) ).
tff(f1222,plain,
( spl50_82
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)),X2))
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_82])]) ).
tff(f1950,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X2))) )
| ( X0 = X2 ) )
| ~ spl50_82
| ~ spl50_141 ),
inference(resolution,[],[f1758,f1223]) ).
tff(f1223,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)),X2))
| ( X1 = X2 ) )
| ~ spl50_82 ),
inference(avatar_component_clause,[],[f1222]) ).
tff(f5964,plain,
( spl50_327
| spl50_27
| ~ spl50_178
| ~ spl50_181 ),
inference(avatar_split_clause,[],[f2593,f2505,f2441,f898,f5962]) ).
tff(f5962,plain,
( spl50_327
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_327])]) ).
tff(f2505,plain,
( spl50_181
<=> ! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 )
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_181])]) ).
tff(f2593,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 )
| spl50_27
| ~ spl50_178
| ~ spl50_181 ),
inference(forward_demodulation,[],[f2570,f2443]) ).
tff(f2570,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 )
| spl50_27
| ~ spl50_181 ),
inference(resolution,[],[f2506,f900]) ).
tff(f2506,plain,
( ! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(X2)
| ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 ) )
| ~ spl50_181 ),
inference(avatar_component_clause,[],[f2505]) ).
tff(f5789,plain,
( spl50_326
| ~ spl50_67
| ~ spl50_154 ),
inference(avatar_split_clause,[],[f2251,f2215,f1116,f5787]) ).
tff(f5787,plain,
( spl50_326
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK21(X0),sK20(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_326])]) ).
tff(f1116,plain,
( spl50_67
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_67])]) ).
tff(f2215,plain,
( spl50_154
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK20(X0)),sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_154])]) ).
tff(f2251,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK21(X0),sK20(X0))) )
| ~ spl50_67
| ~ spl50_154 ),
inference(resolution,[],[f2216,f1117]) ).
tff(f1117,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
| ~ spl50_67 ),
inference(avatar_component_clause,[],[f1116]) ).
tff(f2216,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK20(X0)),sK21(X0)))
| hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) )
| ~ spl50_154 ),
inference(avatar_component_clause,[],[f2215]) ).
tff(f5785,plain,
( spl50_325
| ~ spl50_45
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2012,f2004,f991,f5783]) ).
tff(f5783,plain,
( spl50_325
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_325])]) ).
tff(f2012,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) )
| ~ spl50_45
| ~ spl50_147 ),
inference(resolution,[],[f2005,f992]) ).
tff(f5781,plain,
( spl50_324
| ~ spl50_41
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2009,f2004,f975,f5779]) ).
tff(f5779,plain,
( spl50_324
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_324])]) ).
tff(f975,plain,
( spl50_41
<=> ! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_41])]) ).
tff(f2009,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) )
| ~ spl50_41
| ~ spl50_147 ),
inference(resolution,[],[f2005,f976]) ).
tff(f976,plain,
( ! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1),X2))
| ~ spl50_41 ),
inference(avatar_component_clause,[],[f975]) ).
tff(f5777,plain,
( spl50_323
| ~ spl50_68
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1949,f1757,f1120,f5775]) ).
tff(f5775,plain,
( spl50_323
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite148164294iple_a(X1,X2,bot_bo1208640912a_bool)) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_323])]) ).
tff(f1120,plain,
( spl50_68
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ( X1 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_68])]) ).
tff(f1949,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite148164294iple_a(X1,X2,bot_bo1208640912a_bool)) )
| ( X0 = X2 ) )
| ~ spl50_68
| ~ spl50_141 ),
inference(resolution,[],[f1758,f1121]) ).
tff(f1121,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X2))
| ( X1 = X2 ) )
| ~ spl50_68 ),
inference(avatar_component_clause,[],[f1120]) ).
tff(f5773,plain,
( spl50_322
| ~ spl50_31
| ~ spl50_137 ),
inference(avatar_split_clause,[],[f1844,f1741,f917,f5771]) ).
tff(f5771,plain,
( spl50_322
<=> ! [X0: fun_fu832487784l_bool] :
( ( bot_bo1208640912a_bool = sK17(X0) )
| ( sK17(X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(sK17(X0))),sK9(sK17(X0))) )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_322])]) ).
tff(f917,plain,
( spl50_31
<=> ! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_31])]) ).
tff(f1741,plain,
( spl50_137
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(X0)),sK9(X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_137])]) ).
tff(f1844,plain,
( ! [X0: fun_fu832487784l_bool] :
( ( bot_bo1208640912a_bool = sK17(X0) )
| ( sK17(X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(sK17(X0))),sK9(sK17(X0))) )
| ~ sP0(X0) )
| ~ spl50_31
| ~ spl50_137 ),
inference(resolution,[],[f1742,f918]) ).
tff(f918,plain,
( ! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(X0)))
| ~ sP0(X0) )
| ~ spl50_31 ),
inference(avatar_component_clause,[],[f917]) ).
tff(f1742,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( bot_bo1208640912a_bool = X0 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(X0)),sK9(X0)) = X0 ) )
| ~ spl50_137 ),
inference(avatar_component_clause,[],[f1741]) ).
tff(f5769,plain,
( spl50_321
| ~ spl50_116
| ~ spl50_130 ),
inference(avatar_split_clause,[],[f1723,f1605,f1535,f5767]) ).
tff(f5767,plain,
( spl50_321
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK27(X1,X0,X2) = X0 )
| sP1(X0,X1,sK27(X1,X0,X2),X2)
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_321])]) ).
tff(f1535,plain,
( spl50_116
<=> ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),sK27(X0,X1,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_116])]) ).
tff(f1605,plain,
( spl50_130
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( sP1(X1,X0,X3,X2)
| ( X1 = X3 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_130])]) ).
tff(f1723,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK27(X1,X0,X2) = X0 )
| sP1(X0,X1,sK27(X1,X0,X2),X2)
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) )
| ~ spl50_116
| ~ spl50_130 ),
inference(resolution,[],[f1606,f1536]) ).
tff(f1536,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),sK27(X0,X1,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) )
| ~ spl50_116 ),
inference(avatar_component_clause,[],[f1535]) ).
tff(f1606,plain,
( ! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ( X1 = X3 )
| sP1(X1,X0,X3,X2) )
| ~ spl50_130 ),
inference(avatar_component_clause,[],[f1605]) ).
tff(f5765,plain,
( spl50_320
| ~ spl50_43
| ~ spl50_129 ),
inference(avatar_split_clause,[],[f1714,f1599,f983,f5763]) ).
tff(f5763,plain,
( spl50_320
<=> ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK8(finite148164294iple_a(X2,X1,X0)),X0)
| ( bot_bo1208640912a_bool = finite148164294iple_a(X2,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_320])]) ).
tff(f1599,plain,
( spl50_129
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( sP1(X1,X0,X3,X2)
| ( bot_bo1208640912a_bool = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_129])]) ).
tff(f1714,plain,
( ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK8(finite148164294iple_a(X2,X1,X0)),X0)
| ( bot_bo1208640912a_bool = finite148164294iple_a(X2,X1,X0) ) )
| ~ spl50_43
| ~ spl50_129 ),
inference(resolution,[],[f1600,f984]) ).
tff(f1600,plain,
( ! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ( bot_bo1208640912a_bool = X2 )
| sP1(X1,X0,X3,X2) )
| ~ spl50_129 ),
inference(avatar_component_clause,[],[f1599]) ).
tff(f5761,plain,
( spl50_319
| ~ spl50_42
| ~ spl50_129 ),
inference(avatar_split_clause,[],[f1713,f1599,f979,f5759]) ).
tff(f5759,plain,
( spl50_319
<=> ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK7(finite148164294iple_a(X2,X1,X0)),X0)
| ( bot_bo1208640912a_bool = finite148164294iple_a(X2,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_319])]) ).
tff(f1713,plain,
( ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK7(finite148164294iple_a(X2,X1,X0)),X0)
| ( bot_bo1208640912a_bool = finite148164294iple_a(X2,X1,X0) ) )
| ~ spl50_42
| ~ spl50_129 ),
inference(resolution,[],[f1600,f980]) ).
tff(f5757,plain,
( spl50_318
| ~ spl50_222 ),
inference(avatar_split_clause,[],[f3881,f3857,f5755]) ).
tff(f5755,plain,
( spl50_318
<=> ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK15(hoare_1652181356iple_a(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_318])]) ).
tff(f3857,plain,
( spl50_222
<=> ! [X0: hoare_1927711152iple_a,X3: fun_a_fun_state_bool,X2: com,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK15(X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_222])]) ).
tff(f3881,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK15(hoare_1652181356iple_a(X0,X1,X2)) = X2 )
| ~ spl50_222 ),
inference(equality_resolution,[],[f3858]) ).
tff(f3858,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK15(X0) = X3 ) )
| ~ spl50_222 ),
inference(avatar_component_clause,[],[f3857]) ).
tff(f5752,plain,
( spl50_317
| ~ spl50_12
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1697,f1587,f816,f5750]) ).
tff(f5750,plain,
( spl50_317
<=> ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho957066028l_bool,X1: hoare_1927711152iple_a] :
( ( fFalse = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X2),X1) )
| ( fTrue = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X1),hAPP_H1448631928a_bool(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_317])]) ).
tff(f816,plain,
( spl50_12
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_12])]) ).
tff(f1697,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho957066028l_bool,X1: hoare_1927711152iple_a] :
( ( fFalse = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X2),X1) )
| ( fTrue = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X1),hAPP_H1448631928a_bool(X2,X1)) ) )
| ~ spl50_12
| ~ spl50_126 ),
inference(superposition,[],[f1588,f817]) ).
tff(f817,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl50_12 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f5747,plain,
( spl50_316
| ~ spl50_12
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1696,f1587,f816,f5745]) ).
tff(f5745,plain,
( spl50_316
<=> ! [X2: fun_Ho957066028l_bool,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X2),X0),X1) = hAPP_bool_bool(hAPP_H1487873860l_bool(X2,X1),fFalse) )
| ( fTrue = hAPP_H1448631928a_bool(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_316])]) ).
tff(f1696,plain,
( ! [X2: fun_Ho957066028l_bool,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X2),X0),X1) = hAPP_bool_bool(hAPP_H1487873860l_bool(X2,X1),fFalse) )
| ( fTrue = hAPP_H1448631928a_bool(X0,X1) ) )
| ~ spl50_12
| ~ spl50_126 ),
inference(superposition,[],[f1588,f817]) ).
tff(f5742,plain,
( spl50_315
| ~ spl50_12
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1687,f1587,f816,f5740]) ).
tff(f5740,plain,
( spl50_315
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_315])]) ).
tff(f1687,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_126 ),
inference(superposition,[],[f1588,f817]) ).
tff(f5737,plain,
( spl50_314
| ~ spl50_12
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1686,f1583,f816,f5735]) ).
tff(f5735,plain,
( spl50_314
<=> ! [X2: fun_state_bool,X0: fun_st2063251938l_bool,X1: state] :
( ( fFalse = hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X2),X1) )
| ( fTrue = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X1),hAPP_state_bool(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_314])]) ).
tff(f1686,plain,
( ! [X2: fun_state_bool,X0: fun_st2063251938l_bool,X1: state] :
( ( fFalse = hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X2),X1) )
| ( fTrue = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X1),hAPP_state_bool(X2,X1)) ) )
| ~ spl50_12
| ~ spl50_125 ),
inference(superposition,[],[f1584,f817]) ).
tff(f5732,plain,
( spl50_313
| ~ spl50_12
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1685,f1583,f816,f5730]) ).
tff(f5730,plain,
( spl50_313
<=> ! [X2: fun_st2063251938l_bool,X0: fun_state_bool,X1: state] :
( ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X2),X0),X1) = hAPP_bool_bool(hAPP_s58564346l_bool(X2,X1),fFalse) )
| ( fTrue = hAPP_state_bool(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_313])]) ).
tff(f1685,plain,
( ! [X2: fun_st2063251938l_bool,X0: fun_state_bool,X1: state] :
( ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X2),X0),X1) = hAPP_bool_bool(hAPP_s58564346l_bool(X2,X1),fFalse) )
| ( fTrue = hAPP_state_bool(X0,X1) ) )
| ~ spl50_12
| ~ spl50_125 ),
inference(superposition,[],[f1584,f817]) ).
tff(f5727,plain,
( spl50_312
| ~ spl50_12
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1678,f1583,f816,f5725]) ).
tff(f5725,plain,
( spl50_312
<=> ! [X2: state,X0: fun_st2063251938l_bool,X1: fun_state_bool] :
( ( fFalse = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) )
| ( fTrue = hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_312])]) ).
tff(f1678,plain,
( ! [X2: state,X0: fun_st2063251938l_bool,X1: fun_state_bool] :
( ( fFalse = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) )
| ( fTrue = hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_125 ),
inference(superposition,[],[f1584,f817]) ).
tff(f5721,plain,
( spl50_311
| ~ spl50_78
| ~ spl50_296
| ~ spl50_310 ),
inference(avatar_split_clause,[],[f5717,f5714,f5383,f1205,f5719]) ).
tff(f5719,plain,
( spl50_311
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ( sK19(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_311])]) ).
tff(f1205,plain,
( spl50_78
<=> hBOOL(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_78])]) ).
tff(f5383,plain,
( spl50_296
<=> ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_296])]) ).
tff(f5714,plain,
( spl50_310
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ( sK19(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_310])]) ).
tff(f5717,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(fTrue)
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ( sK19(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) )
| ~ spl50_296
| ~ spl50_310 ),
inference(forward_demodulation,[],[f5715,f5384]) ).
tff(f5384,plain,
( ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_296 ),
inference(avatar_component_clause,[],[f5383]) ).
tff(f5715,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ( sK19(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) )
| ~ spl50_310 ),
inference(avatar_component_clause,[],[f5714]) ).
tff(f5716,plain,
( spl50_310
| ~ spl50_82
| ~ spl50_120 ),
inference(avatar_split_clause,[],[f1634,f1563,f1222,f5714]) ).
tff(f1563,plain,
( spl50_120
<=> ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),sK19(X0,X1)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_120])]) ).
tff(f1634,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ( sK19(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) )
| ~ spl50_82
| ~ spl50_120 ),
inference(resolution,[],[f1564,f1223]) ).
tff(f1564,plain,
( ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),sK19(X0,X1)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) )
| ~ spl50_120 ),
inference(avatar_component_clause,[],[f1563]) ).
tff(f5712,plain,
( spl50_309
| ~ spl50_43
| ~ spl50_111 ),
inference(avatar_split_clause,[],[f1489,f1469,f983,f5710]) ).
tff(f5710,plain,
( spl50_309
<=> ! [X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,sK8(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_309])]) ).
tff(f1469,plain,
( spl50_111
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_111])]) ).
tff(f1489,plain,
( ! [X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,sK8(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1) ) )
| ~ spl50_43
| ~ spl50_111 ),
inference(superposition,[],[f984,f1470]) ).
tff(f1470,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) )
| ~ spl50_111 ),
inference(avatar_component_clause,[],[f1469]) ).
tff(f5708,plain,
( spl50_308
| ~ spl50_221 ),
inference(avatar_split_clause,[],[f3879,f3853,f5706]) ).
tff(f5706,plain,
( spl50_308
<=> ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK14(hoare_1652181356iple_a(X0,X1,X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_308])]) ).
tff(f3853,plain,
( spl50_221
<=> ! [X0: hoare_1927711152iple_a,X3: fun_a_fun_state_bool,X2: com,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK14(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_221])]) ).
tff(f3879,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK14(hoare_1652181356iple_a(X0,X1,X2)) = X1 )
| ~ spl50_221 ),
inference(equality_resolution,[],[f3854]) ).
tff(f3854,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK14(X0) = X2 ) )
| ~ spl50_221 ),
inference(avatar_component_clause,[],[f3853]) ).
tff(f5704,plain,
( spl50_307
| ~ spl50_42
| ~ spl50_111 ),
inference(avatar_split_clause,[],[f1488,f1469,f979,f5702]) ).
tff(f5702,plain,
( spl50_307
<=> ! [X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,sK7(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_307])]) ).
tff(f1488,plain,
( ! [X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,sK7(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1) ) )
| ~ spl50_42
| ~ spl50_111 ),
inference(superposition,[],[f980,f1470]) ).
tff(f5700,plain,
( spl50_306
| ~ spl50_43
| ~ spl50_110 ),
inference(avatar_split_clause,[],[f1486,f1465,f983,f5698]) ).
tff(f5698,plain,
( spl50_306
<=> ! [X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,sK8(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_306])]) ).
tff(f1465,plain,
( spl50_110
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_110])]) ).
tff(f1486,plain,
( ! [X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,sK8(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1) ) )
| ~ spl50_43
| ~ spl50_110 ),
inference(superposition,[],[f984,f1466]) ).
tff(f1466,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) )
| ~ spl50_110 ),
inference(avatar_component_clause,[],[f1465]) ).
tff(f5696,plain,
( spl50_305
| ~ spl50_42
| ~ spl50_110 ),
inference(avatar_split_clause,[],[f1485,f1465,f979,f5694]) ).
tff(f5694,plain,
( spl50_305
<=> ! [X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,sK7(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_305])]) ).
tff(f1485,plain,
( ! [X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,sK7(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1))),X1))
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1) ) )
| ~ spl50_42
| ~ spl50_110 ),
inference(superposition,[],[f980,f1466]) ).
tff(f5451,plain,
( spl50_304
| ~ spl50_220 ),
inference(avatar_split_clause,[],[f3877,f3849,f5449]) ).
tff(f5449,plain,
( spl50_304
<=> ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK13(hoare_1652181356iple_a(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_304])]) ).
tff(f3849,plain,
( spl50_220
<=> ! [X0: hoare_1927711152iple_a,X3: fun_a_fun_state_bool,X2: com,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK13(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_220])]) ).
tff(f3877,plain,
( ! [X2: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com] : ( sK13(hoare_1652181356iple_a(X0,X1,X2)) = X0 )
| ~ spl50_220 ),
inference(equality_resolution,[],[f3850]) ).
tff(f3850,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK13(X0) = X1 ) )
| ~ spl50_220 ),
inference(avatar_component_clause,[],[f3849]) ).
tff(f5413,plain,
( spl50_303
| ~ spl50_67
| ~ spl50_152 ),
inference(avatar_split_clause,[],[f2203,f2094,f1116,f5411]) ).
tff(f5411,plain,
( spl50_303
<=> ! [X0: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ sP1(X0,X1,X2,X3)
| ~ hBOOL(hAPP_H1448631928a_bool(sK41(X0,X1,X2,X3),sK40(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_303])]) ).
tff(f2094,plain,
( spl50_152
<=> ! [X0: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)))
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_152])]) ).
tff(f2203,plain,
( ! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ sP1(X0,X1,X2,X3)
| ~ hBOOL(hAPP_H1448631928a_bool(sK41(X0,X1,X2,X3),sK40(X0,X1,X2,X3))) )
| ~ spl50_67
| ~ spl50_152 ),
inference(resolution,[],[f2095,f1117]) ).
tff(f2095,plain,
( ! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)))
| ~ sP1(X0,X1,X2,X3) )
| ~ spl50_152 ),
inference(avatar_component_clause,[],[f2094]) ).
tff(f5409,plain,
( spl50_302
| ~ spl50_67
| ~ spl50_150 ),
inference(avatar_split_clause,[],[f2176,f2042,f1116,f5407]) ).
tff(f5407,plain,
( spl50_302
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_302])]) ).
tff(f2176,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2),X0)) )
| ~ spl50_67
| ~ spl50_150 ),
inference(resolution,[],[f2043,f1117]) ).
tff(f5405,plain,
( spl50_301
| ~ spl50_20
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2025,f2004,f849,f5403]) ).
tff(f5403,plain,
( spl50_301
<=> ! [X0: bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(X0)
| ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),cOMBK_712844119iple_a(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_301])]) ).
tff(f849,plain,
( spl50_20
<=> ! [X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_20])]) ).
tff(f2025,plain,
( ! [X0: bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(X0)
| ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),cOMBK_712844119iple_a(X0)) ) )
| ~ spl50_20
| ~ spl50_147 ),
inference(superposition,[],[f2005,f850]) ).
tff(f850,plain,
( ! [X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) = X0 )
| ~ spl50_20 ),
inference(avatar_component_clause,[],[f849]) ).
tff(f5401,plain,
( spl50_300
| ~ spl50_30
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2011,f2004,f913,f5399]) ).
tff(f5399,plain,
( spl50_300
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_300])]) ).
tff(f913,plain,
( spl50_30
<=> ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_30])]) ).
tff(f2011,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) )
| ~ spl50_30
| ~ spl50_147 ),
inference(resolution,[],[f2005,f914]) ).
tff(f914,plain,
( ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X1))
| ~ spl50_30 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f5397,plain,
( spl50_299
| ~ spl50_52
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1948,f1757,f1043,f5395]) ).
tff(f5395,plain,
( spl50_299
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_299])]) ).
tff(f1043,plain,
( spl50_52
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_52])]) ).
tff(f1948,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| ( X0 = X1 ) )
| ~ spl50_52
| ~ spl50_141 ),
inference(resolution,[],[f1758,f1044]) ).
tff(f1044,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1))
| ( X0 = X1 ) )
| ~ spl50_52 ),
inference(avatar_component_clause,[],[f1043]) ).
tff(f5393,plain,
( spl50_298
| ~ spl50_60
| ~ spl50_124 ),
inference(avatar_split_clause,[],[f1675,f1579,f1088,f5391]) ).
tff(f5391,plain,
( spl50_298
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_298])]) ).
tff(f1088,plain,
( spl50_60
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_60])]) ).
tff(f1579,plain,
( spl50_124
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_124])]) ).
tff(f1675,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) )
| ~ spl50_60
| ~ spl50_124 ),
inference(resolution,[],[f1580,f1089]) ).
tff(f1089,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)))
| ~ spl50_60 ),
inference(avatar_component_clause,[],[f1088]) ).
tff(f1580,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 ) )
| ~ spl50_124 ),
inference(avatar_component_clause,[],[f1579]) ).
tff(f5389,plain,
( spl50_297
| ~ spl50_60
| ~ spl50_123 ),
inference(avatar_split_clause,[],[f1668,f1575,f1088,f5387]) ).
tff(f5387,plain,
( spl50_297
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_297])]) ).
tff(f1575,plain,
( spl50_123
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_123])]) ).
tff(f1668,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) )
| ~ spl50_60
| ~ spl50_123 ),
inference(resolution,[],[f1576,f1089]) ).
tff(f1576,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 ) )
| ~ spl50_123 ),
inference(avatar_component_clause,[],[f1575]) ).
tff(f5385,plain,
( spl50_296
| ~ spl50_25
| ~ spl50_211 ),
inference(avatar_split_clause,[],[f2892,f2881,f887,f5383]) ).
tff(f887,plain,
( spl50_25
<=> ! [X0: bool] :
( ~ hBOOL(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_25])]) ).
tff(f2881,plain,
( spl50_211
<=> ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_211])]) ).
tff(f2892,plain,
( ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_25
| ~ spl50_211 ),
inference(resolution,[],[f2882,f888]) ).
tff(f888,plain,
( ! [X0: bool] :
( ~ hBOOL(X0)
| ( fTrue = X0 ) )
| ~ spl50_25 ),
inference(avatar_component_clause,[],[f887]) ).
tff(f2882,plain,
( ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ~ spl50_211 ),
inference(avatar_component_clause,[],[f2881]) ).
tff(f5381,plain,
( spl50_295
| ~ spl50_96
| ~ spl50_120 ),
inference(avatar_split_clause,[],[f1635,f1563,f1300,f5379]) ).
tff(f5379,plain,
( spl50_295
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( sK19(X1,X0) = sK32(X1,X0,sK19(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_295])]) ).
tff(f1635,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( sK19(X1,X0) = sK32(X1,X0,sK19(X1,X0)) ) )
| ~ spl50_96
| ~ spl50_120 ),
inference(resolution,[],[f1564,f1301]) ).
tff(f5377,plain,
( spl50_294
| ~ spl50_43
| ~ spl50_96 ),
inference(avatar_split_clause,[],[f1416,f1300,f983,f5375]) ).
tff(f5375,plain,
( spl50_294
<=> ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK8(finite2098837632iple_a(X0,X1)) = sK32(X0,X1,sK8(finite2098837632iple_a(X0,X1))) )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_294])]) ).
tff(f1416,plain,
( ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK8(finite2098837632iple_a(X0,X1)) = sK32(X0,X1,sK8(finite2098837632iple_a(X0,X1))) )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,X1) ) )
| ~ spl50_43
| ~ spl50_96 ),
inference(resolution,[],[f1301,f984]) ).
tff(f5373,plain,
( spl50_293
| ~ spl50_42
| ~ spl50_96 ),
inference(avatar_split_clause,[],[f1415,f1300,f979,f5371]) ).
tff(f5371,plain,
( spl50_293
<=> ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK7(finite2098837632iple_a(X0,X1)) = sK32(X0,X1,sK7(finite2098837632iple_a(X0,X1))) )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_293])]) ).
tff(f1415,plain,
( ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK7(finite2098837632iple_a(X0,X1)) = sK32(X0,X1,sK7(finite2098837632iple_a(X0,X1))) )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,X1) ) )
| ~ spl50_42
| ~ spl50_96 ),
inference(resolution,[],[f1301,f980]) ).
tff(f5106,plain,
( spl50_292
| ~ spl50_23
| ~ spl50_147 ),
inference(avatar_split_clause,[],[f2010,f2004,f861,f5104]) ).
tff(f5104,plain,
( spl50_292
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_292])]) ).
tff(f861,plain,
( spl50_23
<=> ! [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_23])]) ).
tff(f2010,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_23
| ~ spl50_147 ),
inference(resolution,[],[f2005,f862]) ).
tff(f862,plain,
( ! [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1))
| ~ spl50_23 ),
inference(avatar_component_clause,[],[f861]) ).
tff(f5102,plain,
( spl50_291
| ~ spl50_67
| ~ spl50_146 ),
inference(avatar_split_clause,[],[f2007,f2000,f1116,f5100]) ).
tff(f5100,plain,
( spl50_291
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(sK31(X0,X1,X2),sK30(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_291])]) ).
tff(f2000,plain,
( spl50_146
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_146])]) ).
tff(f2007,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(sK31(X0,X1,X2),sK30(X0,X1,X2))) )
| ~ spl50_67
| ~ spl50_146 ),
inference(resolution,[],[f2001,f1117]) ).
tff(f2001,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) )
| ~ spl50_146 ),
inference(avatar_component_clause,[],[f2000]) ).
tff(f5098,plain,
( spl50_290
| ~ spl50_31
| ~ spl50_143 ),
inference(avatar_split_clause,[],[f1987,f1970,f917,f5096]) ).
tff(f5096,plain,
( spl50_290
<=> ! [X0: fun_fu832487784l_bool,X1: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,sK17(X1)))
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_290])]) ).
tff(f1970,plain,
( spl50_143
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_143])]) ).
tff(f1987,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,sK17(X1)))
| ~ sP0(X1) )
| ~ spl50_31
| ~ spl50_143 ),
inference(resolution,[],[f1971,f918]) ).
tff(f1971,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,X1)) )
| ~ spl50_143 ),
inference(avatar_component_clause,[],[f1970]) ).
tff(f5094,plain,
( spl50_289
| ~ spl50_31
| ~ spl50_142 ),
inference(avatar_split_clause,[],[f1978,f1966,f917,f5092]) ).
tff(f5092,plain,
( spl50_289
<=> ! [X0: fun_fu832487784l_bool,X1: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,sK17(X1)))
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_289])]) ).
tff(f1966,plain,
( spl50_142
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_142])]) ).
tff(f1978,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,sK17(X1)))
| ~ sP0(X1) )
| ~ spl50_31
| ~ spl50_142 ),
inference(resolution,[],[f1967,f918]) ).
tff(f1967,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| hBOOL(hAPP_f1454306822l_bool(X0,X1)) )
| ~ spl50_142 ),
inference(avatar_component_clause,[],[f1966]) ).
tff(f5090,plain,
( spl50_288
| ~ spl50_83
| ~ spl50_140 ),
inference(avatar_split_clause,[],[f1945,f1753,f1247,f5088]) ).
tff(f5088,plain,
( spl50_288
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_288])]) ).
tff(f1753,plain,
( spl50_140
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_140])]) ).
tff(f1945,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_140 ),
inference(superposition,[],[f1754,f1248]) ).
tff(f1754,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) )
| ~ spl50_140 ),
inference(avatar_component_clause,[],[f1753]) ).
tff(f5073,plain,
( spl50_287
| ~ spl50_25
| ~ spl50_199 ),
inference(avatar_split_clause,[],[f5022,f2824,f887,f5070]) ).
tff(f5070,plain,
( spl50_287
<=> ( fTrue = hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_287])]) ).
tff(f2824,plain,
( spl50_199
<=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_199])]) ).
tff(f5022,plain,
( ( fTrue = hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a)) )
| ~ spl50_25
| ~ spl50_199 ),
inference(resolution,[],[f2825,f888]) ).
tff(f2825,plain,
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a)))
| ~ spl50_199 ),
inference(avatar_component_clause,[],[f2824]) ).
tff(f5068,plain,
( spl50_286
| ~ spl50_31
| ~ spl50_139 ),
inference(avatar_split_clause,[],[f1931,f1749,f917,f5066]) ).
tff(f5066,plain,
( spl50_286
<=> ! [X2: fun_Ho333840202iple_a,X0: fun_fu1033095803iple_a,X1: fun_fu832487784l_bool] :
( ( hAPP_f490779847iple_a(X0,sK17(X1)) = hAPP_f490779847iple_a(finite1943414032iple_a(X2),sK17(X1)) )
| ~ hBOOL(finite83514413iple_a(X2,X0))
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_286])]) ).
tff(f1749,plain,
( spl50_139
<=> ! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_139])]) ).
tff(f1931,plain,
( ! [X2: fun_Ho333840202iple_a,X0: fun_fu1033095803iple_a,X1: fun_fu832487784l_bool] :
( ( hAPP_f490779847iple_a(X0,sK17(X1)) = hAPP_f490779847iple_a(finite1943414032iple_a(X2),sK17(X1)) )
| ~ hBOOL(finite83514413iple_a(X2,X0))
| ~ sP0(X1) )
| ~ spl50_31
| ~ spl50_139 ),
inference(resolution,[],[f1750,f918]) ).
tff(f1750,plain,
( ! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) )
| ~ hBOOL(finite83514413iple_a(X1,X2)) )
| ~ spl50_139 ),
inference(avatar_component_clause,[],[f1749]) ).
tff(f5064,plain,
( spl50_285
| ~ spl50_83
| ~ spl50_128 ),
inference(avatar_split_clause,[],[f1709,f1595,f1247,f5062]) ).
tff(f5062,plain,
( spl50_285
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( sK5(X0) = X1 )
| hBOOL(hAPP_H1448631928a_bool(sK6(X0),X1))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_285])]) ).
tff(f1595,plain,
( spl50_128
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_128])]) ).
tff(f1709,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( sK5(X0) = X1 )
| hBOOL(hAPP_H1448631928a_bool(sK6(X0),X1))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_128 ),
inference(superposition,[],[f1596,f1248]) ).
tff(f1596,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ( X0 = X2 )
| hBOOL(hAPP_H1448631928a_bool(X1,X2)) )
| ~ spl50_128 ),
inference(avatar_component_clause,[],[f1595]) ).
tff(f5059,plain,
( spl50_284
| ~ spl50_12
| ~ spl50_111 ),
inference(avatar_split_clause,[],[f1487,f1469,f816,f5057]) ).
tff(f5057,plain,
( spl50_284
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_284])]) ).
tff(f1487,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_111 ),
inference(superposition,[],[f1470,f817]) ).
tff(f5054,plain,
( spl50_283
| ~ spl50_12
| ~ spl50_110 ),
inference(avatar_split_clause,[],[f1484,f1465,f816,f5052]) ).
tff(f5052,plain,
( spl50_283
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( ( fFalse = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_283])]) ).
tff(f1484,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] :
( ( fFalse = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_110 ),
inference(superposition,[],[f1466,f817]) ).
tff(f5049,plain,
( spl50_282
| ~ spl50_12
| ~ spl50_109 ),
inference(avatar_split_clause,[],[f1482,f1461,f816,f5047]) ).
tff(f5047,plain,
( spl50_282
<=> ! [X2: state,X0: fun_st1506752259e_bool,X1: state] :
( ( fFalse = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) )
| ( fTrue = hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_282])]) ).
tff(f1461,plain,
( spl50_109
<=> ! [X2: state,X0: fun_st1506752259e_bool,X1: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_109])]) ).
tff(f1482,plain,
( ! [X2: state,X0: fun_st1506752259e_bool,X1: state] :
( ( fFalse = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) )
| ( fTrue = hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_109 ),
inference(superposition,[],[f1462,f817]) ).
tff(f1462,plain,
( ! [X2: state,X0: fun_st1506752259e_bool,X1: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) )
| ~ spl50_109 ),
inference(avatar_component_clause,[],[f1461]) ).
tff(f5044,plain,
( spl50_281
| ~ spl50_12
| ~ spl50_108 ),
inference(avatar_split_clause,[],[f1481,f1457,f816,f5042]) ).
tff(f5042,plain,
( spl50_281
<=> ! [X2: state,X0: fun_st2063251938l_bool,X1: bool] :
( ( fFalse = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) )
| ( fTrue = hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_281])]) ).
tff(f1457,plain,
( spl50_108
<=> ! [X2: state,X0: fun_st2063251938l_bool,X1: bool] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_108])]) ).
tff(f1481,plain,
( ! [X2: state,X0: fun_st2063251938l_bool,X1: bool] :
( ( fFalse = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) )
| ( fTrue = hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_108 ),
inference(superposition,[],[f1458,f817]) ).
tff(f1458,plain,
( ! [X2: state,X0: fun_st2063251938l_bool,X1: bool] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) )
| ~ spl50_108 ),
inference(avatar_component_clause,[],[f1457]) ).
tff(f5040,plain,
( spl50_280
| ~ spl50_43
| ~ spl50_95 ),
inference(avatar_split_clause,[],[f1413,f1296,f983,f5038]) ).
tff(f5038,plain,
( spl50_280
<=> ! [X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,sK8(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_280])]) ).
tff(f1413,plain,
( ! [X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,sK8(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1) ) )
| ~ spl50_43
| ~ spl50_95 ),
inference(superposition,[],[f984,f1297]) ).
tff(f5036,plain,
( spl50_279
| ~ spl50_42
| ~ spl50_95 ),
inference(avatar_split_clause,[],[f1412,f1296,f979,f5034]) ).
tff(f5034,plain,
( spl50_279
<=> ! [X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,sK7(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_279])]) ).
tff(f1412,plain,
( ! [X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,sK7(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1) ) )
| ~ spl50_42
| ~ spl50_95 ),
inference(superposition,[],[f980,f1297]) ).
tff(f5032,plain,
( spl50_278
| ~ spl50_43
| ~ spl50_94 ),
inference(avatar_split_clause,[],[f1410,f1292,f983,f5030]) ).
tff(f5030,plain,
( spl50_278
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,sK8(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_278])]) ).
tff(f1410,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,sK8(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1) ) )
| ~ spl50_43
| ~ spl50_94 ),
inference(superposition,[],[f984,f1293]) ).
tff(f5014,plain,
( spl50_277
| ~ spl50_144
| spl50_199 ),
inference(avatar_split_clause,[],[f2831,f2824,f1992,f5011]) ).
tff(f5011,plain,
( spl50_277
<=> ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_277])]) ).
tff(f1992,plain,
( spl50_144
<=> ! [X0: bool] :
( hBOOL(X0)
| ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_144])]) ).
tff(f2831,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a))) )
| ~ spl50_144
| spl50_199 ),
inference(resolution,[],[f2826,f1993]) ).
tff(f1993,plain,
( ! [X0: bool] :
( hBOOL(X0)
| ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(X0) ) )
| ~ spl50_144 ),
inference(avatar_component_clause,[],[f1992]) ).
tff(f2826,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a)))
| spl50_199 ),
inference(avatar_component_clause,[],[f2824]) ).
tff(f5009,plain,
( spl50_276
| ~ spl50_42
| ~ spl50_94 ),
inference(avatar_split_clause,[],[f1409,f1292,f979,f5007]) ).
tff(f5007,plain,
( spl50_276
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,sK7(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_276])]) ).
tff(f1409,plain,
( ! [X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,sK7(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1)))))
| ( bot_bo1208640912a_bool = hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1) ) )
| ~ spl50_42
| ~ spl50_94 ),
inference(superposition,[],[f980,f1293]) ).
tff(f4833,plain,
( spl50_275
| ~ spl50_54
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2169,f2038,f1051,f4831]) ).
tff(f4831,plain,
( spl50_275
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_275])]) ).
tff(f1051,plain,
( spl50_54
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_54])]) ).
tff(f2169,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_54
| ~ spl50_149 ),
inference(forward_demodulation,[],[f2141,f1052]) ).
tff(f1052,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) )
| ~ spl50_54 ),
inference(avatar_component_clause,[],[f1051]) ).
tff(f2141,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_54
| ~ spl50_149 ),
inference(superposition,[],[f2039,f1052]) ).
tff(f4829,plain,
( spl50_274
| ~ spl50_20
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1956,f1757,f849,f4827]) ).
tff(f4827,plain,
( spl50_274
<=> ! [X0: bool,X1: hoare_1927711152iple_a] :
( hBOOL(X0)
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),cOMBK_712844119iple_a(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_274])]) ).
tff(f1956,plain,
( ! [X0: bool,X1: hoare_1927711152iple_a] :
( hBOOL(X0)
| ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),cOMBK_712844119iple_a(X0)) ) )
| ~ spl50_20
| ~ spl50_141 ),
inference(superposition,[],[f1758,f850]) ).
tff(f4825,plain,
( spl50_273
| ~ spl50_116
| ~ spl50_129 ),
inference(avatar_split_clause,[],[f1716,f1599,f1535,f4823]) ).
tff(f4823,plain,
( spl50_273
<=> ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK27(X2,X1,X0),X0)
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_273])]) ).
tff(f1716,plain,
( ! [X2: fun_Ho333840202iple_a,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = X0 )
| sP1(X1,X2,sK27(X2,X1,X0),X0)
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) )
| ~ spl50_116
| ~ spl50_129 ),
inference(resolution,[],[f1600,f1536]) ).
tff(f4821,plain,
( spl50_272
| ~ spl50_24
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f935,f887,f865,f4819]) ).
tff(f4819,plain,
( spl50_272
<=> ! [X0: fun_Ho1877127206a_bool] : ( fTrue = hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_272])]) ).
tff(f865,plain,
( spl50_24
<=> ! [X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_24])]) ).
tff(f935,plain,
( ! [X0: fun_Ho1877127206a_bool] : ( fTrue = hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X0) )
| ~ spl50_24
| ~ spl50_25 ),
inference(resolution,[],[f888,f866]) ).
tff(f866,plain,
( ! [X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X1),X1))
| ~ spl50_24 ),
inference(avatar_component_clause,[],[f865]) ).
tff(f4817,plain,
( spl50_271
| ~ spl50_32
| ~ spl50_127 ),
inference(avatar_split_clause,[],[f1700,f1591,f921,f4815]) ).
tff(f4815,plain,
( spl50_271
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),sK17(hoare_1617968510rivs_a(X1))))
| ~ sP0(hoare_1617968510rivs_a(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_271])]) ).
tff(f921,plain,
( spl50_32
<=> ! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,sK17(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_32])]) ).
tff(f1591,plain,
( spl50_127
<=> ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_127])]) ).
tff(f1700,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),sK17(hoare_1617968510rivs_a(X1))))
| ~ sP0(hoare_1617968510rivs_a(X1)) )
| ~ spl50_32
| ~ spl50_127 ),
inference(resolution,[],[f1592,f922]) ).
tff(f922,plain,
( ! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,sK17(X0)))
| ~ sP0(X0) )
| ~ spl50_32 ),
inference(avatar_component_clause,[],[f921]) ).
tff(f1592,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2)) )
| ~ spl50_127 ),
inference(avatar_component_clause,[],[f1591]) ).
tff(f4812,plain,
( spl50_270
| ~ spl50_12
| ~ spl50_95 ),
inference(avatar_split_clause,[],[f1411,f1296,f816,f4810]) ).
tff(f4810,plain,
( spl50_270
<=> ! [X2: hoare_1927711152iple_a,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_270])]) ).
tff(f1411,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] :
( ( fFalse = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_95 ),
inference(superposition,[],[f1297,f817]) ).
tff(f4807,plain,
( spl50_269
| ~ spl50_12
| ~ spl50_94 ),
inference(avatar_split_clause,[],[f1408,f1292,f816,f4805]) ).
tff(f4805,plain,
( spl50_269
<=> ! [X2: hoare_1927711152iple_a,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( ( fFalse = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_269])]) ).
tff(f1408,plain,
( ! [X2: hoare_1927711152iple_a,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] :
( ( fFalse = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) )
| ( fTrue = hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_94 ),
inference(superposition,[],[f1293,f817]) ).
tff(f4802,plain,
( spl50_268
| ~ spl50_12
| ~ spl50_93 ),
inference(avatar_split_clause,[],[f1407,f1288,f816,f4800]) ).
tff(f4800,plain,
( spl50_268
<=> ! [X2: state,X0: fun_bool_bool,X1: fun_state_bool] :
( ( fFalse = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) )
| ( fTrue = hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_268])]) ).
tff(f1407,plain,
( ! [X2: state,X0: fun_bool_bool,X1: fun_state_bool] :
( ( fFalse = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) )
| ( fTrue = hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) ) )
| ~ spl50_12
| ~ spl50_93 ),
inference(superposition,[],[f1289,f817]) ).
tff(f4798,plain,
( spl50_267
| ~ spl50_43
| ~ spl50_82 ),
inference(avatar_split_clause,[],[f1244,f1222,f983,f4796]) ).
tff(f4796,plain,
( spl50_267
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK8(finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) = X0 )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_267])]) ).
tff(f1244,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK8(finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) = X0 )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) )
| ~ spl50_43
| ~ spl50_82 ),
inference(resolution,[],[f1223,f984]) ).
tff(f4794,plain,
( spl50_266
| ~ spl50_42
| ~ spl50_82 ),
inference(avatar_split_clause,[],[f1243,f1222,f979,f4792]) ).
tff(f4792,plain,
( spl50_266
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK7(finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) = X0 )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_266])]) ).
tff(f1243,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK7(finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) = X0 )
| ( bot_bo1208640912a_bool = finite2098837632iple_a(X1,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) )
| ~ spl50_42
| ~ spl50_82 ),
inference(resolution,[],[f1223,f980]) ).
tff(f4539,plain,
( spl50_265
| ~ spl50_60
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2153,f2038,f1088,f4537]) ).
tff(f4537,plain,
( spl50_265
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_265])]) ).
tff(f2153,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))))
| ~ spl50_60
| ~ spl50_149 ),
inference(superposition,[],[f1089,f2039]) ).
tff(f4535,plain,
( spl50_264
| ~ spl50_66
| ~ spl50_140 ),
inference(avatar_split_clause,[],[f1940,f1753,f1112,f4533]) ).
tff(f4533,plain,
( spl50_264
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_264])]) ).
tff(f1112,plain,
( spl50_66
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_66])]) ).
tff(f1940,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1),X0)) )
| ~ spl50_66
| ~ spl50_140 ),
inference(resolution,[],[f1754,f1113]) ).
tff(f1113,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
| ~ spl50_66 ),
inference(avatar_component_clause,[],[f1112]) ).
tff(f4531,plain,
( spl50_263
| ~ spl50_20
| ~ spl50_126 ),
inference(avatar_split_clause,[],[f1689,f1587,f849,f4529]) ).
tff(f4529,plain,
( spl50_263
<=> ! [X2: fun_Ho957066028l_bool,X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X2),cOMBK_712844119iple_a(X0)),X1) = hAPP_bool_bool(hAPP_H1487873860l_bool(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_263])]) ).
tff(f1689,plain,
( ! [X2: fun_Ho957066028l_bool,X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X2),cOMBK_712844119iple_a(X0)),X1) = hAPP_bool_bool(hAPP_H1487873860l_bool(X2,X1),X0) )
| ~ spl50_20
| ~ spl50_126 ),
inference(superposition,[],[f1588,f850]) ).
tff(f4527,plain,
( spl50_262
| ~ spl50_19
| ~ spl50_125 ),
inference(avatar_split_clause,[],[f1680,f1583,f845,f4525]) ).
tff(f4525,plain,
( spl50_262
<=> ! [X2: fun_st2063251938l_bool,X0: bool,X1: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X2),cOMBK_bool_state(X0)),X1) = hAPP_bool_bool(hAPP_s58564346l_bool(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_262])]) ).
tff(f1680,plain,
( ! [X2: fun_st2063251938l_bool,X0: bool,X1: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X2),cOMBK_bool_state(X0)),X1) = hAPP_bool_bool(hAPP_s58564346l_bool(X2,X1),X0) )
| ~ spl50_19
| ~ spl50_125 ),
inference(superposition,[],[f1584,f846]) ).
tff(f4523,plain,
( spl50_261
| ~ spl50_32
| ~ spl50_253 ),
inference(avatar_split_clause,[],[f4495,f4384,f921,f4521]) ).
tff(f4521,plain,
( spl50_261
<=> ! [X0: hoare_1927711152iple_a] : ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_261])]) ).
tff(f4384,plain,
( spl50_253
<=> ! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK17(hAPP_H694056973l_bool(member127332739iple_a,X0))))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_253])]) ).
tff(f4495,plain,
( ! [X0: hoare_1927711152iple_a] : ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0))
| ~ spl50_32
| ~ spl50_253 ),
inference(duplicate_literal_removal,[],[f4485]) ).
tff(f4485,plain,
( ! [X0: hoare_1927711152iple_a] :
( ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) )
| ~ spl50_32
| ~ spl50_253 ),
inference(resolution,[],[f4385,f922]) ).
tff(f4385,plain,
( ! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK17(hAPP_H694056973l_bool(member127332739iple_a,X0))))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) )
| ~ spl50_253 ),
inference(avatar_component_clause,[],[f4384]) ).
tff(f4519,plain,
( spl50_260
| ~ spl50_58
| ~ spl50_124 ),
inference(avatar_split_clause,[],[f1673,f1579,f1080,f4517]) ).
tff(f4517,plain,
( spl50_260
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),sK25(sK12(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_260])]) ).
tff(f1080,plain,
( spl50_58
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK12(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_58])]) ).
tff(f1673,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),sK25(sK12(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_58
| ~ spl50_124 ),
inference(resolution,[],[f1580,f1081]) ).
tff(f1081,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK12(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_58 ),
inference(avatar_component_clause,[],[f1080]) ).
tff(f4515,plain,
( spl50_259
| ~ spl50_57
| ~ spl50_124 ),
inference(avatar_split_clause,[],[f1672,f1579,f1076,f4513]) ).
tff(f4513,plain,
( spl50_259
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),sK25(sK11(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_259])]) ).
tff(f1076,plain,
( spl50_57
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK11(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_57])]) ).
tff(f1672,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),sK25(sK11(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_57
| ~ spl50_124 ),
inference(resolution,[],[f1580,f1077]) ).
tff(f1077,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK11(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_57 ),
inference(avatar_component_clause,[],[f1076]) ).
tff(f4511,plain,
( spl50_258
| ~ spl50_56
| ~ spl50_124 ),
inference(avatar_split_clause,[],[f1671,f1579,f1072,f4509]) ).
tff(f4509,plain,
( spl50_258
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),sK25(sK3(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_258])]) ).
tff(f1072,plain,
( spl50_56
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK3(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_56])]) ).
tff(f1671,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),sK25(sK3(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_56
| ~ spl50_124 ),
inference(resolution,[],[f1580,f1073]) ).
tff(f1073,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK3(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_56 ),
inference(avatar_component_clause,[],[f1072]) ).
tff(f4507,plain,
( spl50_257
| ~ spl50_58
| ~ spl50_123 ),
inference(avatar_split_clause,[],[f1666,f1575,f1080,f4505]) ).
tff(f4505,plain,
( spl50_257
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),sK24(sK12(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_257])]) ).
tff(f1666,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),sK24(sK12(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_58
| ~ spl50_123 ),
inference(resolution,[],[f1576,f1081]) ).
tff(f4503,plain,
( spl50_256
| ~ spl50_57
| ~ spl50_123 ),
inference(avatar_split_clause,[],[f1665,f1575,f1076,f4501]) ).
tff(f4501,plain,
( spl50_256
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),sK24(sK11(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_256])]) ).
tff(f1665,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),sK24(sK11(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_57
| ~ spl50_123 ),
inference(resolution,[],[f1576,f1077]) ).
tff(f4499,plain,
( spl50_255
| ~ spl50_56
| ~ spl50_123 ),
inference(avatar_split_clause,[],[f1664,f1575,f1072,f4497]) ).
tff(f4497,plain,
( spl50_255
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),sK24(sK3(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_255])]) ).
tff(f1664,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),sK24(sK3(X0),X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_56
| ~ spl50_123 ),
inference(resolution,[],[f1576,f1073]) ).
tff(f4392,plain,
( spl50_254
| ~ spl50_23
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f932,f887,f861,f4390]) ).
tff(f4390,plain,
( spl50_254
<=> ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_254])]) ).
tff(f932,plain,
( ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X0) )
| ~ spl50_23
| ~ spl50_25 ),
inference(resolution,[],[f888,f862]) ).
tff(f4386,plain,
( spl50_253
| ~ spl50_85
| ~ spl50_140 ),
inference(avatar_split_clause,[],[f1941,f1753,f1255,f4384]) ).
tff(f1941,plain,
( ! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK17(hAPP_H694056973l_bool(member127332739iple_a,X0))))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) )
| ~ spl50_85
| ~ spl50_140 ),
inference(resolution,[],[f1754,f1256]) ).
tff(f4382,plain,
( spl50_252
| ~ spl50_67
| ~ spl50_124 ),
inference(avatar_split_clause,[],[f1674,f1579,f1116,f4380]) ).
tff(f4380,plain,
( spl50_252
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_252])]) ).
tff(f1674,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
| ~ spl50_67
| ~ spl50_124 ),
inference(resolution,[],[f1580,f1117]) ).
tff(f4378,plain,
( spl50_251
| ~ spl50_67
| ~ spl50_123 ),
inference(avatar_split_clause,[],[f1667,f1575,f1116,f4376]) ).
tff(f4376,plain,
( spl50_251
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_251])]) ).
tff(f1667,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
| ~ spl50_67
| ~ spl50_123 ),
inference(resolution,[],[f1576,f1117]) ).
tff(f4374,plain,
( spl50_250
| ~ spl50_43
| ~ spl50_68 ),
inference(avatar_split_clause,[],[f1178,f1120,f983,f4372]) ).
tff(f4372,plain,
( spl50_250
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK8(finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) = X0 )
| ( bot_bo1208640912a_bool = finite148164294iple_a(X1,X0,bot_bo1208640912a_bool) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_250])]) ).
tff(f1178,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK8(finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) = X0 )
| ( bot_bo1208640912a_bool = finite148164294iple_a(X1,X0,bot_bo1208640912a_bool) ) )
| ~ spl50_43
| ~ spl50_68 ),
inference(resolution,[],[f1121,f984]) ).
tff(f4370,plain,
( spl50_249
| ~ spl50_42
| ~ spl50_68 ),
inference(avatar_split_clause,[],[f1177,f1120,f979,f4368]) ).
tff(f4368,plain,
( spl50_249
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK7(finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) = X0 )
| ( bot_bo1208640912a_bool = finite148164294iple_a(X1,X0,bot_bo1208640912a_bool) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_249])]) ).
tff(f1177,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( sK7(finite148164294iple_a(X1,X0,bot_bo1208640912a_bool)) = X0 )
| ( bot_bo1208640912a_bool = finite148164294iple_a(X1,X0,bot_bo1208640912a_bool) ) )
| ~ spl50_42
| ~ spl50_68 ),
inference(resolution,[],[f1121,f980]) ).
tff(f4309,plain,
( spl50_248
| ~ spl50_11
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f930,f887,f812,f4307]) ).
tff(f812,plain,
( spl50_11
<=> ! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_11])]) ).
tff(f930,plain,
( ! [X0: bool] :
( ( fTrue = hAPP_bool_bool(fNot,X0) )
| hBOOL(X0) )
| ~ spl50_11
| ~ spl50_25 ),
inference(resolution,[],[f888,f813]) ).
tff(f813,plain,
( ! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) )
| ~ spl50_11 ),
inference(avatar_component_clause,[],[f812]) ).
tff(f4244,plain,
( spl50_247
| ~ spl50_41
| ~ spl50_149 ),
inference(avatar_split_clause,[],[f2152,f2038,f975,f4242]) ).
tff(f4242,plain,
( spl50_247
<=> ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_247])]) ).
tff(f2152,plain,
( ! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)),X0))
| ~ spl50_41
| ~ spl50_149 ),
inference(superposition,[],[f976,f2039]) ).
tff(f4240,plain,
( spl50_246
| ~ spl50_17
| ~ spl50_47
| ~ spl50_141 ),
inference(avatar_split_clause,[],[f1964,f1757,f1022,f837,f4238]) ).
tff(f4238,plain,
( spl50_246
<=> ! [X0: hoare_1927711152iple_a] : ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),bot_bo1208640912a_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_246])]) ).
tff(f837,plain,
( spl50_17
<=> ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,bot_bo1208640912a_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_17])]) ).
tff(f1022,plain,
( spl50_47
<=> ! [X0: fun_Ho333840202iple_a] : ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,bot_bo1208640912a_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_47])]) ).
tff(f1964,plain,
( ! [X0: hoare_1927711152iple_a] : ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),bot_bo1208640912a_bool) )
| ~ spl50_17
| ~ spl50_47
| ~ spl50_141 ),
inference(forward_demodulation,[],[f1947,f1023]) ).
tff(f1023,plain,
( ! [X0: fun_Ho333840202iple_a] : ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,bot_bo1208640912a_bool) )
| ~ spl50_47 ),
inference(avatar_component_clause,[],[f1022]) ).
tff(f1947,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),finite2098837632iple_a(X1,bot_bo1208640912a_bool)) )
| ~ spl50_17
| ~ spl50_141 ),
inference(resolution,[],[f1758,f838]) ).
tff(f838,plain,
( ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,bot_bo1208640912a_bool),X1))
| ~ spl50_17 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f4236,plain,
( spl50_245
| ~ spl50_54
| ~ spl50_115 ),
inference(avatar_split_clause,[],[f1542,f1531,f1051,f4234]) ).
tff(f4234,plain,
( spl50_245
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_245])]) ).
tff(f1531,plain,
( spl50_115
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_115])]) ).
tff(f1542,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) )
| ( X0 = X1 ) )
| ~ spl50_54
| ~ spl50_115 ),
inference(superposition,[],[f1532,f1052]) ).
tff(f1532,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) )
| ( X0 = X1 ) )
| ~ spl50_115 ),
inference(avatar_component_clause,[],[f1531]) ).
tff(f4232,plain,
( spl50_244
| ~ spl50_67
| ~ spl50_114 ),
inference(avatar_split_clause,[],[f1540,f1527,f1116,f4230]) ).
tff(f4230,plain,
( spl50_244
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK25(X0,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_244])]) ).
tff(f1527,plain,
( spl50_114
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK25(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_114])]) ).
tff(f1540,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK25(X0,X1),X0)) )
| ~ spl50_67
| ~ spl50_114 ),
inference(resolution,[],[f1528,f1117]) ).
tff(f1528,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK25(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) )
| ~ spl50_114 ),
inference(avatar_component_clause,[],[f1527]) ).
tff(f4228,plain,
( spl50_243
| ~ spl50_67
| ~ spl50_113 ),
inference(avatar_split_clause,[],[f1538,f1495,f1116,f4226]) ).
tff(f4226,plain,
( spl50_243
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK24(X0,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_243])]) ).
tff(f1495,plain,
( spl50_113
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK24(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_113])]) ).
tff(f1538,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK24(X0,X1),X0)) )
| ~ spl50_67
| ~ spl50_113 ),
inference(resolution,[],[f1496,f1117]) ).
tff(f1496,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK24(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) )
| ~ spl50_113 ),
inference(avatar_component_clause,[],[f1495]) ).
tff(f4224,plain,
( spl50_242
| ~ spl50_83
| ~ spl50_102 ),
inference(avatar_split_clause,[],[f1437,f1334,f1247,f4222]) ).
tff(f4222,plain,
( spl50_242
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_242])]) ).
tff(f1437,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_102 ),
inference(superposition,[],[f1335,f1248]) ).
tff(f4220,plain,
( spl50_241
| ~ spl50_22
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f929,f887,f857,f4218]) ).
tff(f4218,plain,
( spl50_241
<=> ! [X0: state] : ( fTrue = hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_241])]) ).
tff(f857,plain,
( spl50_22
<=> ! [X1: state] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_22])]) ).
tff(f929,plain,
( ! [X0: state] : ( fTrue = hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X0) )
| ~ spl50_22
| ~ spl50_25 ),
inference(resolution,[],[f888,f858]) ).
tff(f858,plain,
( ! [X1: state] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X1),X1))
| ~ spl50_22 ),
inference(avatar_component_clause,[],[f857]) ).
tff(f4216,plain,
( spl50_240
| ~ spl50_83
| ~ spl50_97 ),
inference(avatar_split_clause,[],[f1420,f1304,f1247,f4214]) ).
tff(f4214,plain,
( spl50_240
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK6(X0),X1))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_240])]) ).
tff(f1420,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ~ hBOOL(hAPP_H1448631928a_bool(sK6(X0),X1))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_97 ),
inference(superposition,[],[f1305,f1248]) ).
tff(f4212,plain,
( spl50_239
| ~ spl50_83
| ~ spl50_86 ),
inference(avatar_split_clause,[],[f1347,f1259,f1247,f4210]) ).
tff(f4210,plain,
( spl50_239
<=> ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_239])]) ).
tff(f1347,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_86 ),
inference(superposition,[],[f1260,f1248]) ).
tff(f3986,plain,
( spl50_238
| ~ spl50_9
| ~ spl50_12 ),
inference(avatar_split_clause,[],[f869,f816,f803,f3984]) ).
tff(f3984,plain,
( spl50_238
<=> ! [X0: bool] :
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(X0) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_238])]) ).
tff(f803,plain,
( spl50_9
<=> ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_9])]) ).
tff(f869,plain,
( ! [X0: bool] :
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(X0) )
| ( fTrue = X0 ) )
| ~ spl50_9
| ~ spl50_12 ),
inference(superposition,[],[f805,f817]) ).
tff(f805,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(fFalse) )
| ~ spl50_9 ),
inference(avatar_component_clause,[],[f803]) ).
tff(f3956,plain,
( spl50_237
| ~ spl50_2
| ~ spl50_47
| ~ spl50_59
| ~ spl50_139 ),
inference(avatar_split_clause,[],[f1935,f1749,f1084,f1022,f771,f3954]) ).
tff(f3954,plain,
( spl50_237
<=> ! [X0: fun_fu1033095803iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,bot_bo1208640912a_bool) = hAPP_f490779847iple_a(X0,bot_bo1208640912a_bool) )
| ~ hBOOL(finite83514413iple_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_237])]) ).
tff(f771,plain,
( spl50_2
<=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_2])]) ).
tff(f1084,plain,
( spl50_59
<=> ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),X1) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_59])]) ).
tff(f1935,plain,
( ! [X0: fun_fu1033095803iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,bot_bo1208640912a_bool) = hAPP_f490779847iple_a(X0,bot_bo1208640912a_bool) )
| ~ hBOOL(finite83514413iple_a(X1,X0)) )
| ~ spl50_2
| ~ spl50_47
| ~ spl50_59
| ~ spl50_139 ),
inference(forward_demodulation,[],[f1926,f1144]) ).
tff(f1144,plain,
( ! [X0: fun_Ho333840202iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),bot_bo1208640912a_bool) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,bot_bo1208640912a_bool) )
| ~ spl50_47
| ~ spl50_59 ),
inference(superposition,[],[f1085,f1023]) ).
tff(f1085,plain,
( ! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),X1) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(X0,X1)) )
| ~ spl50_59 ),
inference(avatar_component_clause,[],[f1084]) ).
tff(f1926,plain,
( ! [X0: fun_fu1033095803iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X0,bot_bo1208640912a_bool) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),bot_bo1208640912a_bool) )
| ~ hBOOL(finite83514413iple_a(X1,X0)) )
| ~ spl50_2
| ~ spl50_139 ),
inference(resolution,[],[f1750,f773]) ).
tff(f773,plain,
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool))
| ~ spl50_2 ),
inference(avatar_component_clause,[],[f771]) ).
tff(f3952,plain,
( spl50_236
| ~ spl50_83
| ~ spl50_118 ),
inference(avatar_split_clause,[],[f1626,f1554,f1247,f3950]) ).
tff(f3950,plain,
( spl50_236
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_236])]) ).
tff(f1554,plain,
( spl50_118
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_118])]) ).
tff(f1626,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_83
| ~ spl50_118 ),
inference(superposition,[],[f1555,f1248]) ).
tff(f1555,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) )
| ~ spl50_118 ),
inference(avatar_component_clause,[],[f1554]) ).
tff(f3948,plain,
( spl50_235
| ~ spl50_54
| ~ spl50_118 ),
inference(avatar_split_clause,[],[f1624,f1554,f1051,f3946]) ).
tff(f3946,plain,
( spl50_235
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_235])]) ).
tff(f1624,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) )
| ~ spl50_54
| ~ spl50_118 ),
inference(superposition,[],[f1555,f1052]) ).
tff(f3944,plain,
( spl50_234
| ~ spl50_55
| ~ spl50_110 ),
inference(avatar_split_clause,[],[f1483,f1465,f1055,f3942]) ).
tff(f3942,plain,
( spl50_234
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_234])]) ).
tff(f1055,plain,
( spl50_55
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_55])]) ).
tff(f1483,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X0) )
| ~ spl50_55
| ~ spl50_110 ),
inference(superposition,[],[f1466,f1056]) ).
tff(f1056,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0) )
| ~ spl50_55 ),
inference(avatar_component_clause,[],[f1055]) ).
tff(f3939,plain,
( spl50_233
| spl50_27
| ~ spl50_144 ),
inference(avatar_split_clause,[],[f2077,f1992,f898,f3936]) ).
tff(f3936,plain,
( spl50_233
<=> ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_233])]) ).
tff(f2077,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))) )
| spl50_27
| ~ spl50_144 ),
inference(resolution,[],[f1993,f900]) ).
tff(f3934,plain,
( spl50_232
| ~ spl50_67
| ~ spl50_104 ),
inference(avatar_split_clause,[],[f1477,f1441,f1116,f3932]) ).
tff(f3932,plain,
( spl50_232
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_232])]) ).
tff(f1441,plain,
( spl50_104
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_104])]) ).
tff(f1477,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
| ~ spl50_67
| ~ spl50_104 ),
inference(resolution,[],[f1442,f1117]) ).
tff(f1442,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 ) )
| ~ spl50_104 ),
inference(avatar_component_clause,[],[f1441]) ).
tff(f3930,plain,
( spl50_231
| ~ spl50_58
| ~ spl50_104 ),
inference(avatar_split_clause,[],[f1476,f1441,f1080,f3928]) ).
tff(f3928,plain,
( spl50_231
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_231])]) ).
tff(f1476,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK12(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_58
| ~ spl50_104 ),
inference(resolution,[],[f1442,f1081]) ).
tff(f3926,plain,
( spl50_230
| ~ spl50_57
| ~ spl50_104 ),
inference(avatar_split_clause,[],[f1475,f1441,f1076,f3924]) ).
tff(f3924,plain,
( spl50_230
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_230])]) ).
tff(f1475,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK11(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_57
| ~ spl50_104 ),
inference(resolution,[],[f1442,f1077]) ).
tff(f3922,plain,
( spl50_229
| ~ spl50_56
| ~ spl50_104 ),
inference(avatar_split_clause,[],[f1474,f1441,f1072,f3920]) ).
tff(f3920,plain,
( spl50_229
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_229])]) ).
tff(f1474,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK3(X0)),X0) = X0 )
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_56
| ~ spl50_104 ),
inference(resolution,[],[f1442,f1073]) ).
tff(f3918,plain,
( spl50_228
| ~ spl50_58
| ~ spl50_80 ),
inference(avatar_split_clause,[],[f1238,f1214,f1080,f3916]) ).
tff(f3916,plain,
( spl50_228
<=> ! [X0: hoare_1927711152iple_a] :
( ( sK12(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_228])]) ).
tff(f1214,plain,
( spl50_80
<=> ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_80])]) ).
tff(f1238,plain,
( ! [X0: hoare_1927711152iple_a] :
( ( sK12(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) )
| ~ spl50_58
| ~ spl50_80 ),
inference(resolution,[],[f1215,f1081]) ).
tff(f1215,plain,
( ! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))
| ( X0 = X1 ) )
| ~ spl50_80 ),
inference(avatar_component_clause,[],[f1214]) ).
tff(f3914,plain,
( spl50_227
| ~ spl50_57
| ~ spl50_80 ),
inference(avatar_split_clause,[],[f1237,f1214,f1076,f3912]) ).
tff(f3912,plain,
( spl50_227
<=> ! [X0: hoare_1927711152iple_a] :
( ( sK11(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_227])]) ).
tff(f1237,plain,
( ! [X0: hoare_1927711152iple_a] :
( ( sK11(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) )
| ~ spl50_57
| ~ spl50_80 ),
inference(resolution,[],[f1215,f1077]) ).
tff(f3910,plain,
( spl50_226
| ~ spl50_56
| ~ spl50_80 ),
inference(avatar_split_clause,[],[f1236,f1214,f1072,f3908]) ).
tff(f3908,plain,
( spl50_226
<=> ! [X0: hoare_1927711152iple_a] :
( ( sK3(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_226])]) ).
tff(f1236,plain,
( ! [X0: hoare_1927711152iple_a] :
( ( sK3(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) )
| ~ spl50_56
| ~ spl50_80 ),
inference(resolution,[],[f1215,f1073]) ).
tff(f3906,plain,
( spl50_225
| ~ spl50_32
| ~ spl50_66 ),
inference(avatar_split_clause,[],[f1163,f1112,f921,f3904]) ).
tff(f3904,plain,
( spl50_225
<=> ! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(sK17(hAPP_H694056973l_bool(member127332739iple_a,X0)),X0))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_225])]) ).
tff(f1163,plain,
( ! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(sK17(hAPP_H694056973l_bool(member127332739iple_a,X0)),X0))
| ~ sP0(hAPP_H694056973l_bool(member127332739iple_a,X0)) )
| ~ spl50_32
| ~ spl50_66 ),
inference(resolution,[],[f1113,f922]) ).
tff(f3902,plain,
( spl50_224
| ~ spl50_43
| ~ spl50_52 ),
inference(avatar_split_clause,[],[f1064,f1043,f983,f3900]) ).
tff(f3900,plain,
( spl50_224
<=> ! [X0: hoare_1927711152iple_a] :
( ( sK8(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_224])]) ).
tff(f1064,plain,
( ! [X0: hoare_1927711152iple_a] :
( ( sK8(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) )
| ~ spl50_43
| ~ spl50_52 ),
inference(resolution,[],[f1044,f984]) ).
tff(f3898,plain,
( spl50_223
| ~ spl50_42
| ~ spl50_52 ),
inference(avatar_split_clause,[],[f1063,f1043,f979,f3896]) ).
tff(f3896,plain,
( spl50_223
<=> ! [X0: hoare_1927711152iple_a] :
( ( sK7(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_223])]) ).
tff(f1063,plain,
( ! [X0: hoare_1927711152iple_a] :
( ( sK7(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ( bot_bo1208640912a_bool = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) )
| ~ spl50_42
| ~ spl50_52 ),
inference(resolution,[],[f1044,f980]) ).
tff(f3859,plain,
( spl50_222
| ~ spl50_50
| ~ spl50_101 ),
inference(avatar_split_clause,[],[f1431,f1330,f1035,f3857]) ).
tff(f1035,plain,
( spl50_50
<=> ! [X0: hoare_1927711152iple_a] : ( hoare_1652181356iple_a(sK13(X0),sK14(X0),sK15(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_50])]) ).
tff(f1330,plain,
( spl50_101
<=> ! [X3: fun_a_fun_state_bool,X4: com,X0: fun_a_fun_state_bool,X5: fun_a_fun_state_bool,X2: fun_a_fun_state_bool,X1: com] :
( ( X2 = X5 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_101])]) ).
tff(f1431,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK15(X0) = X3 ) )
| ~ spl50_50
| ~ spl50_101 ),
inference(superposition,[],[f1331,f1036]) ).
tff(f1036,plain,
( ! [X0: hoare_1927711152iple_a] : ( hoare_1652181356iple_a(sK13(X0),sK14(X0),sK15(X0)) = X0 )
| ~ spl50_50 ),
inference(avatar_component_clause,[],[f1035]) ).
tff(f1331,plain,
( ! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) )
| ( X2 = X5 ) )
| ~ spl50_101 ),
inference(avatar_component_clause,[],[f1330]) ).
tff(f3855,plain,
( spl50_221
| ~ spl50_50
| ~ spl50_100 ),
inference(avatar_split_clause,[],[f1427,f1316,f1035,f3853]) ).
tff(f1316,plain,
( spl50_100
<=> ! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X4: com,X0: fun_a_fun_state_bool,X5: fun_a_fun_state_bool,X1: com] :
( ( X1 = X4 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_100])]) ).
tff(f1427,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK14(X0) = X2 ) )
| ~ spl50_50
| ~ spl50_100 ),
inference(superposition,[],[f1317,f1036]) ).
tff(f1317,plain,
( ! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) )
| ( X1 = X4 ) )
| ~ spl50_100 ),
inference(avatar_component_clause,[],[f1316]) ).
tff(f3851,plain,
( spl50_220
| ~ spl50_50
| ~ spl50_99 ),
inference(avatar_split_clause,[],[f1424,f1312,f1035,f3849]) ).
tff(f1312,plain,
( spl50_99
<=> ! [X5: fun_a_fun_state_bool,X4: com,X0: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X2: fun_a_fun_state_bool,X1: com] :
( ( X0 = X3 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_99])]) ).
tff(f1424,plain,
( ! [X2: com,X3: fun_a_fun_state_bool,X0: hoare_1927711152iple_a,X1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) != X0 )
| ( sK13(X0) = X1 ) )
| ~ spl50_50
| ~ spl50_99 ),
inference(superposition,[],[f1313,f1036]) ).
tff(f1313,plain,
( ! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) )
| ( X0 = X3 ) )
| ~ spl50_99 ),
inference(avatar_component_clause,[],[f1312]) ).
tff(f3847,plain,
( spl50_219
| ~ spl50_60
| ~ spl50_83 ),
inference(avatar_split_clause,[],[f1339,f1247,f1088,f3845]) ).
tff(f3845,plain,
( spl50_219
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_219])]) ).
tff(f1339,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_60
| ~ spl50_83 ),
inference(superposition,[],[f1089,f1248]) ).
tff(f3843,plain,
( spl50_218
| ~ spl50_32
| ~ spl50_53 ),
inference(avatar_split_clause,[],[f1067,f1047,f921,f3841]) ).
tff(f3841,plain,
( spl50_218
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( sK17(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)) = X0 )
| ~ sP0(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_218])]) ).
tff(f1047,plain,
( spl50_53
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_53])]) ).
tff(f1067,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( sK17(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)) = X0 )
| ~ sP0(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)) )
| ~ spl50_32
| ~ spl50_53 ),
inference(resolution,[],[f1048,f922]) ).
tff(f1048,plain,
( ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1))
| ( X0 = X1 ) )
| ~ spl50_53 ),
inference(avatar_component_clause,[],[f1047]) ).
tff(f3839,plain,
( ~ spl50_217
| spl50_27
| ~ spl50_178 ),
inference(avatar_split_clause,[],[f2525,f2441,f898,f3836]) ).
tff(f3836,plain,
( spl50_217
<=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_217])]) ).
tff(f2525,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))
| spl50_27
| ~ spl50_178 ),
inference(superposition,[],[f900,f2443]) ).
tff(f3177,plain,
( spl50_216
| ~ spl50_67
| ~ spl50_73 ),
inference(avatar_split_clause,[],[f1225,f1185,f1116,f3175]) ).
tff(f3175,plain,
( spl50_216
<=> ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(sK6(X0),sK5(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_216])]) ).
tff(f1185,plain,
( spl50_73
<=> ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_73])]) ).
tff(f1225,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(sK6(X0),sK5(X0))) )
| ~ spl50_67
| ~ spl50_73 ),
inference(resolution,[],[f1186,f1117]) ).
tff(f1186,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_73 ),
inference(avatar_component_clause,[],[f1185]) ).
tff(f3172,plain,
( spl50_215
| ~ spl50_12
| ~ spl50_20 ),
inference(avatar_split_clause,[],[f883,f849,f816,f3170]) ).
tff(f3170,plain,
( spl50_215
<=> ! [X0: bool,X1: hoare_1927711152iple_a] :
( ( fFalse = X0 )
| ( fTrue = hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_215])]) ).
tff(f883,plain,
( ! [X0: bool,X1: hoare_1927711152iple_a] :
( ( fFalse = X0 )
| ( fTrue = hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) ) )
| ~ spl50_12
| ~ spl50_20 ),
inference(superposition,[],[f850,f817]) ).
tff(f3167,plain,
( spl50_214
| ~ spl50_12
| ~ spl50_19 ),
inference(avatar_split_clause,[],[f881,f845,f816,f3165]) ).
tff(f3165,plain,
( spl50_214
<=> ! [X0: bool,X1: state] :
( ( fFalse = X0 )
| ( fTrue = hAPP_state_bool(cOMBK_bool_state(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_214])]) ).
tff(f881,plain,
( ! [X0: bool,X1: state] :
( ( fFalse = X0 )
| ( fTrue = hAPP_state_bool(cOMBK_bool_state(X0),X1) ) )
| ~ spl50_12
| ~ spl50_19 ),
inference(superposition,[],[f846,f817]) ).
tff(f3163,plain,
( spl50_213
| ~ spl50_12 ),
inference(avatar_split_clause,[],[f868,f816,f3161]) ).
tff(f3161,plain,
( spl50_213
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_213])]) ).
tff(f868,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl50_12 ),
inference(superposition,[],[f817,f817]) ).
tff(f2898,plain,
( spl50_212
| ~ spl50_78
| ~ spl50_2
| ~ spl50_25
| ~ spl50_68
| ~ spl50_116 ),
inference(avatar_split_clause,[],[f1548,f1535,f1120,f887,f771,f1205,f2896]) ).
tff(f2896,plain,
( spl50_212
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] : ( sK27(X1,X0,bot_bo1208640912a_bool) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_212])]) ).
tff(f1548,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(fTrue)
| ( sK27(X1,X0,bot_bo1208640912a_bool) = X0 ) )
| ~ spl50_2
| ~ spl50_25
| ~ spl50_68
| ~ spl50_116 ),
inference(forward_demodulation,[],[f1545,f933]) ).
tff(f933,plain,
( ( hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool) = fTrue )
| ~ spl50_2
| ~ spl50_25 ),
inference(resolution,[],[f888,f773]) ).
tff(f1545,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool))
| ( sK27(X1,X0,bot_bo1208640912a_bool) = X0 ) )
| ~ spl50_68
| ~ spl50_116 ),
inference(resolution,[],[f1536,f1121]) ).
tff(f2883,plain,
( spl50_211
| ~ spl50_78
| ~ spl50_2
| ~ spl50_25
| ~ spl50_54
| ~ spl50_102 ),
inference(avatar_split_clause,[],[f1439,f1334,f1051,f887,f771,f1205,f2881]) ).
tff(f1439,plain,
( ! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(fTrue)
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) )
| ~ spl50_2
| ~ spl50_25
| ~ spl50_54
| ~ spl50_102 ),
inference(forward_demodulation,[],[f1436,f933]) ).
tff(f1436,plain,
( ! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)) )
| ~ spl50_54
| ~ spl50_102 ),
inference(superposition,[],[f1335,f1052]) ).
tff(f2879,plain,
( spl50_210
| ~ spl50_68
| ~ spl50_98 ),
inference(avatar_split_clause,[],[f1422,f1308,f1120,f2877]) ).
tff(f2877,plain,
( spl50_210
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ sP1(X0,X1,X2,bot_bo1208640912a_bool)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_210])]) ).
tff(f1308,plain,
( spl50_98
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ~ sP1(X1,X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_98])]) ).
tff(f1422,plain,
( ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ sP1(X0,X1,X2,bot_bo1208640912a_bool)
| ( X0 = X2 ) )
| ~ spl50_68
| ~ spl50_98 ),
inference(resolution,[],[f1309,f1121]) ).
tff(f1309,plain,
( ! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ~ sP1(X1,X0,X3,X2) )
| ~ spl50_98 ),
inference(avatar_component_clause,[],[f1308]) ).
tff(f2875,plain,
( spl50_209
| ~ spl50_12
| ~ spl50_178 ),
inference(avatar_split_clause,[],[f2520,f2441,f816,f2873]) ).
tff(f2873,plain,
( spl50_209
<=> ! [X0: bool] :
( ( bot_bot_bool = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_209])]) ).
tff(f2520,plain,
( ! [X0: bool] :
( ( bot_bot_bool = X0 )
| ( fTrue = X0 ) )
| ~ spl50_12
| ~ spl50_178 ),
inference(superposition,[],[f2443,f817]) ).
tff(f2871,plain,
( spl50_208
| ~ spl50_45
| ~ spl50_96 ),
inference(avatar_split_clause,[],[f1414,f1300,f991,f2869]) ).
tff(f2869,plain,
( spl50_208
<=> ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( sK32(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_208])]) ).
tff(f1414,plain,
( ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( sK32(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1) = X1 )
| ~ spl50_45
| ~ spl50_96 ),
inference(resolution,[],[f1301,f992]) ).
tff(f2867,plain,
( spl50_207
| ~ spl50_41
| ~ spl50_83 ),
inference(avatar_split_clause,[],[f1340,f1247,f975,f2865]) ).
tff(f2865,plain,
( spl50_207
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK5(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_207])]) ).
tff(f1340,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK5(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_41
| ~ spl50_83 ),
inference(superposition,[],[f976,f1248]) ).
tff(f2863,plain,
( spl50_206
| ~ spl50_65
| ~ spl50_67 ),
inference(avatar_split_clause,[],[f1171,f1116,f1108,f2861]) ).
tff(f2861,plain,
( spl50_206
<=> ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(sK17(X0),sK16(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_206])]) ).
tff(f1108,plain,
( spl50_65
<=> ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK16(X0)),sK17(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_65])]) ).
tff(f1171,plain,
( ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(sK17(X0),sK16(X0)))
| ~ sP0(X0) )
| ~ spl50_65
| ~ spl50_67 ),
inference(resolution,[],[f1117,f1109]) ).
tff(f1109,plain,
( ! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK16(X0)),sK17(X0)))
| ~ sP0(X0) )
| ~ spl50_65 ),
inference(avatar_component_clause,[],[f1108]) ).
tff(f2859,plain,
( spl50_205
| ~ spl50_58
| ~ spl50_66 ),
inference(avatar_split_clause,[],[f1161,f1112,f1080,f2857]) ).
tff(f2857,plain,
( spl50_205
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK12(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_205])]) ).
tff(f1161,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK12(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_58
| ~ spl50_66 ),
inference(resolution,[],[f1113,f1081]) ).
tff(f2855,plain,
( spl50_204
| ~ spl50_57
| ~ spl50_66 ),
inference(avatar_split_clause,[],[f1160,f1112,f1076,f2853]) ).
tff(f2853,plain,
( spl50_204
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK11(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_204])]) ).
tff(f1160,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK11(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_57
| ~ spl50_66 ),
inference(resolution,[],[f1113,f1077]) ).
tff(f2851,plain,
( spl50_203
| ~ spl50_56
| ~ spl50_66 ),
inference(avatar_split_clause,[],[f1159,f1112,f1072,f2849]) ).
tff(f2849,plain,
( spl50_203
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK3(X0)))
| ( bot_bo1208640912a_bool = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_203])]) ).
tff(f1159,plain,
( ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,sK3(X0)))
| ( bot_bo1208640912a_bool = X0 ) )
| ~ spl50_56
| ~ spl50_66 ),
inference(resolution,[],[f1113,f1073]) ).
tff(f2847,plain,
( spl50_202
| ~ spl50_54
| ~ spl50_60 ),
inference(avatar_split_clause,[],[f1146,f1088,f1051,f2845]) ).
tff(f2845,plain,
( spl50_202
<=> ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_202])]) ).
tff(f1146,plain,
( ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))
| ~ spl50_54
| ~ spl50_60 ),
inference(superposition,[],[f1089,f1052]) ).
tff(f2843,plain,
( spl50_201
| ~ spl50_4
| ~ spl50_12 ),
inference(avatar_split_clause,[],[f870,f816,f780,f2841]) ).
tff(f2841,plain,
( spl50_201
<=> ! [X0: bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(X0)) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_201])]) ).
tff(f780,plain,
( spl50_4
<=> ( bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_4])]) ).
tff(f870,plain,
( ! [X0: bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(X0)) )
| ( fTrue = X0 ) )
| ~ spl50_4
| ~ spl50_12 ),
inference(superposition,[],[f782,f817]) ).
tff(f782,plain,
( ( bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(fFalse)) )
| ~ spl50_4 ),
inference(avatar_component_clause,[],[f780]) ).
tff(f2836,plain,
( spl50_200
| ~ spl50_12
| spl50_27 ),
inference(avatar_split_clause,[],[f902,f898,f816,f2834]) ).
tff(f2834,plain,
( spl50_200
<=> ! [X0: bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(X0)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_200])]) ).
tff(f902,plain,
( ! [X0: bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(X0)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))
| ( fTrue = X0 ) )
| ~ spl50_12
| spl50_27 ),
inference(superposition,[],[f900,f817]) ).
tff(f2827,plain,
( ~ spl50_198
| ~ spl50_199
| ~ spl50_85
| ~ spl50_102 ),
inference(avatar_split_clause,[],[f1435,f1334,f1255,f2824,f2820]) ).
tff(f2820,plain,
( spl50_198
<=> sP0(finite68738179iple_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_198])]) ).
tff(f1435,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(finite68738179iple_a)))
| ~ sP0(finite68738179iple_a)
| ~ spl50_85
| ~ spl50_102 ),
inference(resolution,[],[f1335,f1256]) ).
tff(f2810,plain,
spl50_197,
inference(avatar_split_clause,[],[f739,f2808]) ).
tff(f2808,plain,
( spl50_197
<=> ! [X3: fun_a_fun_state_bool,X9: x_a,X7: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X6: fun_a_fun_state_bool,X2: com,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X6,X2,X7))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_197])]) ).
tff(f739,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X9: x_a,X7: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X6,X2,X7))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ),
inference(forward_demodulation,[],[f738,f688]) ).
tff(f688,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) ),
inference(forward_demodulation,[],[f455,f448]) ).
tff(f448,plain,
! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X10: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X10) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
tff(f455,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X20: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X20)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
tff(f738,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X9: x_a,X7: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f618,f688]) ).
tff(f618,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X9: x_a,X7: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f422]) ).
tff(f422,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: com,X3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool)))
| ( ! [X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7)))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39])],[f325,f421,f420]) ).
tff(f420,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: com,X3: fun_a_fun_state_bool] :
( ? [X4: x_a,X5: state] :
( ! [X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X4),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),X5)) ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5)) )
=> ( ! [X7: fun_a_fun_state_bool,X6: fun_a_fun_state_bool] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f421,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: com,X3: fun_a_fun_state_bool,X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ) )
=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7)))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),sK38(X0,X1,X2,X3))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f325,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: com,X3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool)))
| ? [X4: x_a,X5: state] :
( ! [X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X4),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),X5)) ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5)) ) ),
inference(ennf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: com,X3: fun_a_fun_state_bool] :
( ! [X4: x_a,X5: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5))
=> ? [X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ! [X8: state] :
( ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X6,X9),X5))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X7,X9),X8)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X4),X8)) )
& hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool))) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X12: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X11: com,X10: fun_a_fun_state_bool] :
( ! [X14: x_a,X15: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X10,X14),X15))
=> ? [X42: fun_a_fun_state_bool,X43: fun_a_fun_state_bool] :
( ! [X18: state] :
( ! [X19: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X42,X19),X15))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X43,X19),X18)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X12,X14),X18)) )
& hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X42,X11,X43)),bot_bo1208640912a_bool))) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_conseq) ).
tff(f2789,plain,
spl50_196,
inference(avatar_split_clause,[],[f762,f2787]) ).
tff(f2787,plain,
( spl50_196
<=> ! [X3: fun_a_fun_state_bool,X4: com,X9: x_a,X0: fun_a_fun_state_bool,X5: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_196])]) ).
tff(f762,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X9: x_a,X4: com,X5: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) ),
inference(forward_demodulation,[],[f761,f688]) ).
tff(f761,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X9: x_a,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f649,f688]) ).
tff(f649,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X9: x_a,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f441]) ).
tff(f441,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5)))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5))) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49])],[f336,f440,f439]) ).
tff(f439,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X5: fun_a_fun_state_bool] :
( ? [X6: x_a,X7: state] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X6),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),X7)) ) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,X6),X7)) )
=> ( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) ) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5))) ) ),
introduced(choice_axiom,[]) ).
tff(f440,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X5: fun_a_fun_state_bool] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) ) )
=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5)))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),sK48(X0,X1,X3,X5))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f336,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| ? [X6: x_a,X7: state] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X6),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),X7)) ) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,X6),X7)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(flattening,[],[f335]) ).
tff(f335,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| ? [X6: x_a,X7: state] :
( ? [X8: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X6),X8))
& ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),X7)) ) )
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,X6),X7)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool)))
=> ( ! [X6: x_a,X7: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,X6),X7))
=> ! [X8: state] :
( ! [X9: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X9),X7))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X5,X9),X8)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X6),X8)) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool))) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X12: fun_a_fun_state_bool,X10: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X17: fun_a_fun_state_bool,X11: com,X16: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X17,X11,X16)),bot_bo1208640912a_bool)))
=> ( ! [X14: x_a,X15: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X10,X14),X15))
=> ! [X18: state] :
( ! [X19: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X17,X19),X15))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X16,X19),X18)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X12,X14),X18)) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq12) ).
tff(f2780,plain,
spl50_195,
inference(avatar_split_clause,[],[f729,f2778]) ).
tff(f2778,plain,
( spl50_195
<=> ! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK28(X1)),sK29(X1))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK28(X1)),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK29(X1)))))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_195])]) ).
tff(f729,plain,
! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK28(X1)),sK29(X1))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK28(X1)),hAPP_H1027145665a_bool(fequal1440857775iple_a,sK29(X1)))))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(forward_demodulation,[],[f584,f688]) ).
tff(f584,plain,
! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK28(X1)),sK29(X1))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK28(X1)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK29(X1)),bot_bo1208640912a_bool))))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(cnf_transformation,[],[f405]) ).
tff(f405,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK28(X1)),sK29(X1))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK28(X1)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK29(X1)),bot_bo1208640912a_bool))))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f301,f404]) ).
tff(f404,plain,
! [X1: fun_Ho333840202iple_a] :
( ? [X3: hoare_1927711152iple_a,X4: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X3),X4)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),bot_bo1208640912a_bool))))
=> ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK28(X1)),sK29(X1))),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK28(X1)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK29(X1)),bot_bo1208640912a_bool)))) ),
introduced(choice_axiom,[]) ).
tff(f301,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ? [X3: hoare_1927711152iple_a,X4: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X3),X4)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),bot_bo1208640912a_bool))))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(flattening,[],[f300]) ).
tff(f300,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0))
| ? [X3: hoare_1927711152iple_a,X4: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X3),X4)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),bot_bo1208640912a_bool))))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X1,X2))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
=> ( ( bot_bo1208640912a_bool != X0 )
=> ( ! [X3: hoare_1927711152iple_a,X4: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X3),X4)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),bot_bo1208640912a_bool))))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X2,X0)),X0)) ) ) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X22: fun_Ho1877127206a_bool,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X44,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( ( bot_bo1208640912a_bool != X22 )
=> ( ! [X24: hoare_1927711152iple_a,X41: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X24),X41)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X41),bot_bo1208640912a_bool))))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(X45,X22)),X22)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__one_Oclosed) ).
tff(f2761,plain,
spl50_194,
inference(avatar_split_clause,[],[f737,f2759]) ).
tff(f2759,plain,
( spl50_194
<=> ! [X3: fun_a_fun_state_bool,X7: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X6: fun_a_fun_state_bool,X2: com,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X6,X2,X7))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_194])]) ).
tff(f737,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X6,X2,X7))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7))) ),
inference(forward_demodulation,[],[f736,f688]) ).
tff(f736,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f619,f688]) ).
tff(f619,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X6: fun_a_fun_state_bool,X7: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK37(X0,X1,X2,X3)),sK39(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X6,X2,X7)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f422]) ).
tff(f2757,plain,
spl50_193,
inference(avatar_split_clause,[],[f734,f2755]) ).
tff(f2755,plain,
( spl50_193
<=> ! [X0: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X2: fun_a_fun_state_bool,X1: com] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3)))))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_193])]) ).
tff(f734,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3)))))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2)))) ),
inference(forward_demodulation,[],[f733,f688]) ).
tff(f733,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3))))),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f616,f688]) ).
tff(f616,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X1,X2)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3))))),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f419]) ).
tff(f419,plain,
! [X0: fun_Ho1877127206a_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X1,X2)),bot_bo1208640912a_bool)))
| ( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3))))),bot_bo1208640912a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f324,f418]) ).
tff(f418,plain,
! [X0: fun_Ho1877127206a_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool] :
( ? [X4: x_a,X5: state] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X5)),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,X4)))),bot_bo1208640912a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5)) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK36(X0,X1,X2,X3))),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,sK35(X0,X1,X2,X3))))),bot_bo1208640912a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f324,plain,
! [X0: fun_Ho1877127206a_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X1,X2)),bot_bo1208640912a_bool)))
| ? [X4: x_a,X5: state] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X5)),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,X4)))),bot_bo1208640912a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5)) ) ),
inference(ennf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: fun_Ho1877127206a_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool] :
( ! [X4: x_a,X5: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X5)),X1,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X2,X4)))),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X1,X2)),bot_bo1208640912a_bool))) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: fun_Ho1877127206a_bool,X11: com,X12: fun_a_fun_state_bool,X10: fun_a_fun_state_bool] :
( ! [X14: x_a,X15: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X10,X14),X15))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X15)),X11,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(X12,X14)))),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
tff(f2740,plain,
spl50_192,
inference(avatar_split_clause,[],[f764,f2738]) ).
tff(f2738,plain,
( spl50_192
<=> ! [X3: fun_a_fun_state_bool,X4: com,X0: fun_a_fun_state_bool,X5: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_192])]) ).
tff(f764,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5))) ),
inference(forward_demodulation,[],[f763,f688]) ).
tff(f763,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f648,f688]) ).
tff(f648,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1,sK47(X0,X1,X3,X5)),sK48(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f441]) ).
tff(f2736,plain,
spl50_191,
inference(avatar_split_clause,[],[f760,f2734]) ).
tff(f2734,plain,
( spl50_191
<=> ! [X3: fun_a_fun_state_bool,X4: com,X0: fun_a_fun_state_bool,X5: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_191])]) ).
tff(f760,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5))) ),
inference(forward_demodulation,[],[f759,f688]) ).
tff(f759,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X4,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f650,f688]) ).
tff(f650,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X4,X0)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK47(X0,X1,X3,X5)),sK49(X0,X1,X3,X5)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f441]) ).
tff(f2713,plain,
spl50_190,
inference(avatar_split_clause,[],[f758,f2711]) ).
tff(f2711,plain,
( spl50_190
<=> ! [X3: fun_a_fun_state_bool,X4: com,X0: com,X5: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X5,X0,X1))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_190])]) ).
tff(f758,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: com,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X4,X5))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X5,X0,X1))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)))) ),
inference(forward_demodulation,[],[f757,f688]) ).
tff(f757,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: com,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X5,X0,X1))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f756,f688]) ).
tff(f756,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: com,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X5,X0,X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f647,f688]) ).
tff(f647,plain,
! [X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X0: com,X1: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X5,X0,X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: com,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X5,X0,X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(flattening,[],[f333]) ).
tff(f333,plain,
! [X0: com,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X5,X0,X1)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: com,X1: fun_a_fun_state_bool,X2: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X4,X5)),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X5,X0,X1)),bot_bo1208640912a_bool)))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,semi(X4,X0),X1)),bot_bo1208640912a_bool))) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X28: com,X29: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X10: fun_a_fun_state_bool,X11: com,X12: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X12,X28,X29)),bot_bo1208640912a_bool)))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,semi(X11,X28),X29)),bot_bo1208640912a_bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Comp) ).
tff(f2709,plain,
spl50_189,
inference(avatar_split_clause,[],[f610,f2707]) ).
tff(f2707,plain,
( spl50_189
<=> ! [X0: hoare_1927711152iple_a,X3: fun_fu1033095803iple_a,X2: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite83514413iple_a(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_189])]) ).
tff(f610,plain,
! [X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite83514413iple_a(X2,X3)) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite83514413iple_a(X2,X3)) ),
inference(flattening,[],[f318]) ).
tff(f318,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite83514413iple_a(X2,X3)) ),
inference(ennf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X2,X3))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
=> ( ( bot_bo1208640912a_bool != X1 )
=> ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) ) ) ) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X44,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
=> ( ( bot_bo1208640912a_bool != X22 )
=> ( hAPP_f490779847iple_a(X45,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X25),hAPP_f490779847iple_a(X45,X22)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_folding__one_Oinsert) ).
tff(f2705,plain,
( spl50_188
| ~ spl50_5
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f934,f887,f785,f2703]) ).
tff(f2703,plain,
( spl50_188
<=> ! [X0: fun_Ho1877127206a_bool] : ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_188])]) ).
tff(f785,plain,
( spl50_5
<=> ! [X0: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_5])]) ).
tff(f934,plain,
( ! [X0: fun_Ho1877127206a_bool] : ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool) = fTrue )
| ~ spl50_5
| ~ spl50_25 ),
inference(resolution,[],[f888,f786]) ).
tff(f786,plain,
( ! [X0: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool))
| ~ spl50_5 ),
inference(avatar_component_clause,[],[f785]) ).
tff(f2688,plain,
spl50_187,
inference(avatar_split_clause,[],[f754,f2686]) ).
tff(f2686,plain,
( spl50_187
<=> ! [X4: bool,X0: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X2: com,X1: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X2,X3))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_187])]) ).
tff(f754,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X4: bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,X2,X3))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)))) ),
inference(forward_demodulation,[],[f753,f688]) ).
tff(f753,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X4: bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3))))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X2,X3)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f646,f688]) ).
tff(f646,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X4: bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X2,X3)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool,X4: bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)),bot_bo1208640912a_bool)))
| ( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X2,X3)),bot_bo1208640912a_bool)))
& hBOOL(X4) ) ),
inference(ennf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool,X4: bool] :
( ( hBOOL(X4)
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,X2,X3)),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)),bot_bo1208640912a_bool))) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: fun_Ho1877127206a_bool,X10: fun_a_fun_state_bool,X11: com,X12: fun_a_fun_state_bool,X13: bool] :
( ( hBOOL(X13)
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X10))),X13),X11,X12)),bot_bo1208640912a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).
tff(f2535,plain,
spl50_186,
inference(avatar_split_clause,[],[f752,f2533]) ).
tff(f752,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4))) ),
inference(forward_demodulation,[],[f751,f688]) ).
tff(f751,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f643,f688]) ).
tff(f643,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f438]) ).
tff(f438,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool)))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4))) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46])],[f331,f437]) ).
tff(f437,plain,
! [X0: fun_a_fun_state_bool,X4: fun_a_fun_state_bool] :
( ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,X5),X6)) )
=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,sK45(X0,X4)),sK46(X0,X4))) ) ),
introduced(choice_axiom,[]) ).
tff(f331,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool)))
| ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,X5),X6)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(flattening,[],[f330]) ).
tff(f330,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool)))
| ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,X5),X6)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool)))
=> ( ! [X5: x_a,X6: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X4,X5),X6))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool))) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X12: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X10: fun_a_fun_state_bool,X11: com,X16: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X16)),bot_bo1208640912a_bool)))
=> ( ! [X14: x_a,X15: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X16,X14),X15))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X12,X14),X15)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conseq2) ).
tff(f2531,plain,
spl50_185,
inference(avatar_split_clause,[],[f750,f2529]) ).
tff(f750,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4))) ),
inference(forward_demodulation,[],[f749,f688]) ).
tff(f749,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X0))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f644,f688]) ).
tff(f644,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X0)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK45(X0,X4)),sK46(X0,X4)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f438]) ).
tff(f2519,plain,
spl50_184,
inference(avatar_split_clause,[],[f748,f2517]) ).
tff(f748,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2))) ),
inference(forward_demodulation,[],[f747,f688]) ).
tff(f747,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f641,f688]) ).
tff(f641,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f436]) ).
tff(f436,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool)))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2))) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f329,f435]) ).
tff(f435,plain,
! [X0: fun_a_fun_state_bool,X2: fun_a_fun_state_bool] :
( ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK43(X0,X2)),sK44(X0,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f329,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool)))
| ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(flattening,[],[f328]) ).
tff(f328,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool)))
| ? [X5: x_a,X6: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool)))
=> ( ! [X5: x_a,X6: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool))) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X10: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X17: fun_a_fun_state_bool,X11: com,X12: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X17,X11,X12)),bot_bo1208640912a_bool)))
=> ( ! [X14: x_a,X15: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X10,X14),X15))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X17,X14),X15)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,X11,X12)),bot_bo1208640912a_bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conseq1) ).
tff(f2515,plain,
spl50_183,
inference(avatar_split_clause,[],[f746,f2513]) ).
tff(f746,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2,X3,X4))))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2))) ),
inference(forward_demodulation,[],[f745,f688]) ).
tff(f745,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0,X3,X4))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(forward_demodulation,[],[f642,f688]) ).
tff(f642,plain,
! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool,X4: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0,X3,X4)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK43(X0,X2)),sK44(X0,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2,X3,X4)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f436]) ).
tff(f2511,plain,
spl50_182,
inference(avatar_split_clause,[],[f726,f2509]) ).
tff(f2509,plain,
( spl50_182
<=> ! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X0 )
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_182])]) ).
tff(f726,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X0 )
| ~ hBOOL(X2) ),
inference(forward_demodulation,[],[f725,f690]) ).
tff(f690,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0) ),
inference(forward_demodulation,[],[f689,f688]) ).
tff(f689,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0) ),
inference(forward_demodulation,[],[f456,f448]) ).
tff(f456,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)) ),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X20: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_singleton__conv) ).
tff(f725,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X0 )
| ~ hBOOL(X2) ),
inference(forward_demodulation,[],[f577,f690]) ).
tff(f577,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X0 )
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: bool] :
( ( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X1 )
| hBOOL(X2) )
& ( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X0 )
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: bool] :
( ( ~ hBOOL(X2)
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X1 ) )
& ( hBOOL(X2)
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X0 ) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X25: hoare_1927711152iple_a,X26: hoare_1927711152iple_a,X10: bool] :
( ( ~ hBOOL(X10)
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X10)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X25)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X10))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X26)))) = X26 ) )
& ( hBOOL(X10)
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X10)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X25)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X10))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X26)))) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_If__def) ).
tff(f2507,plain,
spl50_181,
inference(avatar_split_clause,[],[f724,f2505]) ).
tff(f724,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 )
| hBOOL(X2) ),
inference(forward_demodulation,[],[f723,f690]) ).
tff(f723,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))) = X1 )
| hBOOL(X2) ),
inference(forward_demodulation,[],[f578,f690]) ).
tff(f578,plain,
! [X2: bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,X2)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,X2))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X1)))) = X1 )
| hBOOL(X2) ),
inference(cnf_transformation,[],[f293]) ).
tff(f2481,plain,
spl50_180,
inference(avatar_split_clause,[],[f612,f2479]) ).
tff(f2479,plain,
( spl50_180
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_180])]) ).
tff(f612,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(cnf_transformation,[],[f417]) ).
tff(f417,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)),X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)) ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f323,f416]) ).
tff(f416,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X4,X5),X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) ) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)),X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f323,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X4,X5),X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(flattening,[],[f322]) ).
tff(f322,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X4,X5),X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(ennf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3))
=> ~ ! [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) )
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X4,X5),X3))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5)) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X44: fun_Ho333840202iple_a,X20: hoare_1927711152iple_a,X36: fun_Ho1877127206a_bool,X25: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X44,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X36)),X25))
=> ~ ! [X48: hoare_1927711152iple_a,X49: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X36) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X48),X49) )
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X48,X49),X25))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X48),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__fold1SetE) ).
tff(f2466,plain,
spl50_179,
inference(avatar_split_clause,[],[f640,f2464]) ).
tff(f2464,plain,
( spl50_179
<=> ! [X4: fun_Ho1877127206a_bool,X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X3),X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X4),X2))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_179])]) ).
tff(f640,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X3),X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X4),X2))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4)) ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X3),X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X4),X2))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4)) ),
inference(flattening,[],[f326]) ).
tff(f326,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X3),X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X4),X2))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4)) ),
inference(ennf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X4),X2))
=> hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X3),X2))) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X44: fun_Ho333840202iple_a,X46: hoare_1927711152iple_a,X26: hoare_1927711152iple_a,X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,X22),X26))
=> hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X25),X26))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_fold__graph_OinsertI) ).
tff(f2444,plain,
( spl50_178
| ~ spl50_72
| ~ spl50_167 ),
inference(avatar_split_clause,[],[f2352,f2298,f1166,f2441]) ).
tff(f1166,plain,
( spl50_72
<=> ! [X0: hoare_1927711152iple_a] : ( fFalse = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_72])]) ).
tff(f2298,plain,
( spl50_167
<=> ! [X0: hoare_1927711152iple_a] : ( bot_bot_bool = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_167])]) ).
tff(f2352,plain,
( ( fFalse = bot_bot_bool )
| ~ spl50_72
| ~ spl50_167 ),
inference(superposition,[],[f2299,f1167]) ).
tff(f1167,plain,
( ! [X0: hoare_1927711152iple_a] : ( fFalse = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) )
| ~ spl50_72 ),
inference(avatar_component_clause,[],[f1166]) ).
tff(f2299,plain,
( ! [X0: hoare_1927711152iple_a] : ( bot_bot_bool = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) )
| ~ spl50_167 ),
inference(avatar_component_clause,[],[f2298]) ).
tff(f2427,plain,
spl50_177,
inference(avatar_split_clause,[],[f677,f2425]) ).
tff(f2425,plain,
( spl50_177
<=> ! [X5: fun_Ho1877127206a_bool,X4: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X6: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( sP1(X0,X1,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_177])]) ).
tff(f677,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X6: hoare_1927711152iple_a,X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( sP1(X0,X1,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5)) ),
inference(equality_resolution,[],[f676]) ).
tff(f676,plain,
! [X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X6: hoare_1927711152iple_a,X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( sP1(X0,X1,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6),X3)
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) != X3 ) ),
inference(equality_resolution,[],[f627]) ).
tff(f627,plain,
! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X6: hoare_1927711152iple_a,X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool] :
( sP1(X0,X1,X2,X3)
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
| ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6) != X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) != X3 ) ),
inference(cnf_transformation,[],[f428]) ).
tff(f428,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ( sP1(X0,X1,X2,X3)
| ! [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
| ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6) != X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) != X3 ) ) )
& ( ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,sK41(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK40(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)) = X3 ) )
| ~ sP1(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42])],[f426,f427]) ).
tff(f427,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ? [X7: hoare_1927711152iple_a,X8: fun_Ho1877127206a_bool,X9: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X8),X9))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X7),X8))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X7),X9) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X7),X8) = X3 ) )
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,sK41(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK40(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f426,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ( sP1(X0,X1,X2,X3)
| ! [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
| ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X4),X6) != X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) != X3 ) ) )
& ( ? [X7: hoare_1927711152iple_a,X8: fun_Ho1877127206a_bool,X9: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,X8),X9))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X7),X8))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X7),X9) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X7),X8) = X3 ) )
| ~ sP1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f425]) ).
tff(f425,plain,
! [X1: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ( sP1(X1,X0,X3,X2)
| ! [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X5),X6))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
| ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X4),X6) != X3 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) != X2 ) ) )
& ( ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X5),X6))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X4),X6) = X3 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) = X2 ) )
| ~ sP1(X1,X0,X3,X2) ) ),
inference(nnf_transformation,[],[f339]) ).
tff(f339,plain,
! [X1: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( sP1(X1,X0,X3,X2)
<=> ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X5),X6))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X4),X6) = X3 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f2423,plain,
spl50_176,
inference(avatar_split_clause,[],[f608,f2421]) ).
tff(f2421,plain,
( spl50_176
<=> ! [X0: hoare_1927711152iple_a,X3: fun_fu1033095803iple_a,X2: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_176])]) ).
tff(f608,plain,
! [X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(flattening,[],[f314]) ).
tff(f314,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(ennf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X2,X3))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( ( bot_bo1208640912a_bool != X1 )
=> ( hAPP_f490779847iple_a(X3,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) ) ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X44,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( ( bot_bo1208640912a_bool != X22 )
=> ( hAPP_f490779847iple_a(X45,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X25),hAPP_f490779847iple_a(X45,X22)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_folding__one__idem_Oinsert__idem) ).
tff(f2419,plain,
spl50_175,
inference(avatar_split_clause,[],[f586,f2417]) ).
tff(f2417,plain,
( spl50_175
<=> ! [X2: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( X0 = X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_175])]) ).
tff(f586,plain,
! [X2: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( X0 = X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(cnf_transformation,[],[f406]) ).
tff(f406,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ( ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) ) ) )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(nnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(flattening,[],[f304]) ).
tff(f304,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(ennf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
=> ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X0) )
<=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X23: fun_Ho1877127206a_bool,X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X23))
=> ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X23) )
<=> ( X22 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__ident) ).
tff(f2400,plain,
spl50_174,
inference(avatar_split_clause,[],[f613,f2398]) ).
tff(f2398,plain,
( spl50_174
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)),X3))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_174])]) ).
tff(f613,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)),X3))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(cnf_transformation,[],[f417]) ).
tff(f2396,plain,
spl50_173,
inference(avatar_split_clause,[],[f609,f2394]) ).
tff(f2394,plain,
( spl50_173
<=> ! [X0: hoare_1927711152iple_a,X3: fun_fu1033095803iple_a,X2: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,X1) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_173])]) ).
tff(f609,plain,
! [X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(X3,X1) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,X1) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(flattening,[],[f316]) ).
tff(f316,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X3,X1) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(finite1511031594iple_a(X2,X3)) ),
inference(ennf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: fun_Ho333840202iple_a,X3: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X2,X3))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
=> ( hAPP_f490779847iple_a(X3,X1) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X2,X0),hAPP_f490779847iple_a(X3,X1)) ) ) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X44,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
=> ( hAPP_f490779847iple_a(X45,X22) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X25),hAPP_f490779847iple_a(X45,X22)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_folding__one__idem_Oin__idem) ).
tff(f2348,plain,
spl50_172,
inference(avatar_split_clause,[],[f740,f2346]) ).
tff(f740,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X2,X0))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) ),
inference(forward_demodulation,[],[f617,f688]) ).
tff(f617,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X2,X0)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f422]) ).
tff(f2344,plain,
spl50_171,
inference(avatar_split_clause,[],[f735,f2342]) ).
tff(f735,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X3,X1,X2))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3))) ),
inference(forward_demodulation,[],[f615,f688]) ).
tff(f615,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: com] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X3,X1,X2)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK35(X0,X1,X2,X3)),sK36(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f419]) ).
tff(f2340,plain,
spl50_170,
inference(avatar_split_clause,[],[f614,f2338]) ).
tff(f2338,plain,
( spl50_170
<=> ! [X0: fun_Ho333840202iple_a,X3: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_170])]) ).
tff(f614,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK33(X0,X1,X2,X3)),sK34(X0,X1,X2,X3)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)),X3)) ),
inference(cnf_transformation,[],[f417]) ).
tff(f2321,plain,
spl50_169,
inference(avatar_split_clause,[],[f755,f2319]) ).
tff(f2319,plain,
( spl50_169
<=> ! [X4: bool,X0: fun_Ho1877127206a_bool,X3: fun_a_fun_state_bool,X2: com,X1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3))))
| hBOOL(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_169])]) ).
tff(f755,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X4: bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3))))
| hBOOL(X4) ),
inference(forward_demodulation,[],[f645,f688]) ).
tff(f645,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool,X4: bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),X1))),X4),X2,X3)),bot_bo1208640912a_bool)))
| hBOOL(X4) ),
inference(cnf_transformation,[],[f332]) ).
tff(f2317,plain,
spl50_168,
inference(avatar_split_clause,[],[f670,f2315]) ).
tff(f2315,plain,
( spl50_168
<=> ! [X4: fun_Ho1877127206a_bool,X0: fun_Ho333840202iple_a,X5: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),X5))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_168])]) ).
tff(f670,plain,
! [X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)),X5))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5)) ),
inference(equality_resolution,[],[f669]) ).
tff(f669,plain,
! [X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X5))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) != X1 ) ),
inference(equality_resolution,[],[f599]) ).
tff(f599,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
| ( X2 != X5 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) != X1 ) ),
inference(cnf_transformation,[],[f410]) ).
tff(f410,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ! [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
| ( X2 != X5 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) != X1 ) ) )
& ( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK30(X0,X1,X2),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
& ( sK32(X0,X1,X2) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)) = X1 ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32])],[f408,f409]) ).
tff(f409,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ? [X6: hoare_1927711152iple_a,X7: fun_Ho1877127206a_bool,X8: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X6),X7))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X6,X7),X8))
& ( X2 = X8 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X6),X7) = X1 ) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK30(X0,X1,X2),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
& ( sK32(X0,X1,X2) = X2 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f408,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ! [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
| ( X2 != X5 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) != X1 ) ) )
& ( ? [X6: hoare_1927711152iple_a,X7: fun_Ho1877127206a_bool,X8: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X6),X7))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X6,X7),X8))
& ( X2 = X8 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X6),X7) = X1 ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
inference(rectify,[],[f407]) ).
tff(f407,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ! [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
| ( X2 != X5 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) != X1 ) ) )
& ( ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
& ( X2 = X5 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) = X1 ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
<=> ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool,X5: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X3,X4),X5))
& ( X2 = X5 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) = X1 ) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X44: fun_Ho333840202iple_a,X52: fun_Ho1877127206a_bool,X53: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X44,X52),X53))
<=> ? [X48: hoare_1927711152iple_a,X49: fun_Ho1877127206a_bool,X24: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X48),X49))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X48,X49),X24))
& ( X24 = X53 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X48),X49) = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_fold1Set_Osimps) ).
tff(f2300,plain,
( spl50_167
| ~ spl50_20
| ~ spl50_156 ),
inference(avatar_split_clause,[],[f2260,f2223,f849,f2298]) ).
tff(f2223,plain,
( spl50_156
<=> ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(bot_bot_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_156])]) ).
tff(f2260,plain,
( ! [X0: hoare_1927711152iple_a] : ( bot_bot_bool = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) )
| ~ spl50_20
| ~ spl50_156 ),
inference(superposition,[],[f850,f2225]) ).
tff(f2225,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(bot_bot_bool) )
| ~ spl50_156 ),
inference(avatar_component_clause,[],[f2223]) ).
tff(f2296,plain,
spl50_166,
inference(avatar_split_clause,[],[f597,f2294]) ).
tff(f2294,plain,
( spl50_166
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK30(X0,X1,X2),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_166])]) ).
tff(f597,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,sK30(X0,X1,X2),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ),
inference(cnf_transformation,[],[f410]) ).
tff(f2292,plain,
spl50_165,
inference(avatar_split_clause,[],[f534,f2290]) ).
tff(f2290,plain,
( spl50_165
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK20(X0)),sK21(X0))))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_165])]) ).
tff(f534,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK20(X0)),sK21(X0))))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f386]) ).
tff(f386,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK20(X0)),sK21(X0))))
& hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK20(X0)),sK21(X0)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0))) )
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f280,f385]) ).
tff(f385,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X3)))
& hBOOL(hAPP_f1454306822l_bool(X0,X3))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X3))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3)) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK20(X0)),sK21(X0))))
& hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK20(X0)),sK21(X0)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ? [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X3)))
& hBOOL(hAPP_f1454306822l_bool(X0,X3))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X3))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3)) )
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(flattening,[],[f279]) ).
tff(f279,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ? [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X3)))
& hBOOL(hAPP_f1454306822l_bool(X0,X3))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X3))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3)) )
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
=> ( ! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X3))
=> ( hBOOL(hAPP_f1454306822l_bool(X0,X3))
=> hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X3))) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(X0,X1)) ) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X10: fun_fu832487784l_bool,X45: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(X10,bot_bo1208640912a_bool))
=> ( ! [X24: hoare_1927711152iple_a,X51: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X51))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X51))
=> ( hBOOL(hAPP_f1454306822l_bool(X10,X51))
=> hBOOL(hAPP_f1454306822l_bool(X10,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),X51))) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(X10,X45)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__induct) ).
tff(f2277,plain,
spl50_164,
inference(avatar_split_clause,[],[f730,f2275]) ).
tff(f730,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0)) ),
inference(forward_demodulation,[],[f591,f688]) ).
tff(f591,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool))) ),
inference(flattening,[],[f309]) ).
tff(f309,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X0))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X0))) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X8: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X9: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X9),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X8))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X9),X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
tff(f2273,plain,
spl50_163,
inference(avatar_split_clause,[],[f697,f2271]) ).
tff(f697,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1))) ),
inference(forward_demodulation,[],[f500,f690]) ).
tff(f500,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1))) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X1))) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X24: hoare_1927711152iple_a,X27: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),X27) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X24))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),X27))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_insert__compr__raw) ).
tff(f2250,plain,
spl50_162,
inference(avatar_split_clause,[],[f744,f2248]) ).
tff(f2248,plain,
( spl50_162
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| sP2(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_162])]) ).
tff(f744,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| sP2(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f743,f688]) ).
tff(f743,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) )
| sP2(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f638,f688]) ).
tff(f638,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( sP2(X2,X1,X3,X0)
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) ) ),
inference(cnf_transformation,[],[f434]) ).
tff(f434,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) )
| ~ sP2(X2,X1,X3,X0) )
& ( sP2(X2,X1,X3,X0)
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) ) ) ),
inference(nnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) )
<=> sP2(X2,X1,X3,X0) ),
inference(definition_folding,[],[f260,f341]) ).
tff(f341,plain,
! [X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a] :
( sP2(X2,X1,X3,X0)
<=> ( ( ( X1 = X2 )
& ( X0 = X3 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f260,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) )
<=> ( ( ( X1 = X2 )
& ( X0 = X3 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X20: hoare_1927711152iple_a,X21: hoare_1927711152iple_a,X11: hoare_1927711152iple_a,X28: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X21),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X11),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X28),bot_bo1208640912a_bool)) )
<=> ( ( ( X11 = X21 )
& ( X20 = X28 ) )
| ( ( X21 = X28 )
& ( X11 = X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_doubleton__eq__iff) ).
tff(f2246,plain,
spl50_161,
inference(avatar_split_clause,[],[f742,f2244]) ).
tff(f2244,plain,
( spl50_161
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| ~ sP2(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_161])]) ).
tff(f742,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) )
| ~ sP2(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f741,f688]) ).
tff(f741,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_H1027145665a_bool(fequal1440857775iple_a,X3)) )
| ~ sP2(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f639,f688]) ).
tff(f639,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),bot_bo1208640912a_bool)) )
| ~ sP2(X2,X1,X3,X0) ),
inference(cnf_transformation,[],[f434]) ).
tff(f2242,plain,
spl50_160,
inference(avatar_split_clause,[],[f709,f2240]) ).
tff(f2240,plain,
( spl50_160
<=> ! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,sK18(X0))))
| hBOOL(hAPP_f1454306822l_bool(X0,X1))
| sP0(X0)
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_160])]) ).
tff(f709,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,sK18(X0))))
| hBOOL(hAPP_f1454306822l_bool(X0,X1))
| sP0(X0)
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(forward_demodulation,[],[f529,f688]) ).
tff(f529,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| sP0(X0)
| ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK18(X0)),bot_bo1208640912a_bool)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f382]) ).
tff(f382,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| sP0(X0)
| ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK18(X0)),bot_bo1208640912a_bool)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f338,f381]) ).
tff(f381,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
=> ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK18(X0)),bot_bo1208640912a_bool))) ),
introduced(choice_axiom,[]) ).
tff(f338,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| sP0(X0)
| ? [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(definition_folding,[],[f276,f337]) ).
tff(f337,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)))
& hBOOL(hAPP_f1454306822l_bool(X0,X4))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( bot_bo1208640912a_bool != X4 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X4)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f276,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)))
& hBOOL(hAPP_f1454306822l_bool(X0,X4))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( bot_bo1208640912a_bool != X4 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X4)) )
| ? [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(flattening,[],[f275]) ).
tff(f275,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)))
& hBOOL(hAPP_f1454306822l_bool(X0,X4))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( bot_bo1208640912a_bool != X4 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X4)) )
| ? [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( ( bot_bo1208640912a_bool != X1 )
=> ( ! [X2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)))
=> ( ! [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X4))
=> ( ( bot_bo1208640912a_bool != X4 )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
=> ( hBOOL(hAPP_f1454306822l_bool(X0,X4))
=> hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4))) ) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X10: fun_fu832487784l_bool,X45: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X45))
=> ( ( bot_bo1208640912a_bool != X45 )
=> ( ! [X24: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(X10,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),bot_bo1208640912a_bool)))
=> ( ! [X24: hoare_1927711152iple_a,X51: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X51))
=> ( ( bot_bo1208640912a_bool != X51 )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X51))
=> ( hBOOL(hAPP_f1454306822l_bool(X10,X51))
=> hBOOL(hAPP_f1454306822l_bool(X10,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),X51))) ) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(X10,X45)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__ne__induct) ).
tff(f2238,plain,
spl50_159,
inference(avatar_split_clause,[],[f700,f2236]) ).
tff(f700,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1)) ),
inference(forward_demodulation,[],[f699,f448]) ).
tff(f699,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),collec829051333iple_a(X1)) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)))),X1)) ),
inference(forward_demodulation,[],[f502,f690]) ).
tff(f502,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),collec829051333iple_a(X1)) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),X1)) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),collec829051333iple_a(X1)) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)))),X1)) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X20: hoare_1927711152iple_a,X10: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),collec829051333iple_a(X10)) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X20)))),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__Collect) ).
tff(f2234,plain,
spl50_158,
inference(avatar_split_clause,[],[f626,f2232]) ).
tff(f2232,plain,
( spl50_158
<=> ! [X0: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,sK41(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)))
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_158])]) ).
tff(f626,plain,
! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X1,X0,sK41(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)))
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f428]) ).
tff(f2230,plain,
spl50_157,
inference(avatar_split_clause,[],[f624,f2228]) ).
tff(f2228,plain,
( spl50_157
<=> ! [X0: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK40(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)) = X2 )
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_157])]) ).
tff(f624,plain,
! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,sK40(X0,X1,X2,X3)),sK42(X0,X1,X2,X3)) = X2 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f428]) ).
tff(f2226,plain,
( spl50_156
| spl50_15
| ~ spl50_144 ),
inference(avatar_split_clause,[],[f2052,f1992,f827,f2223]) ).
tff(f2052,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(bot_bot_bool) )
| spl50_15
| ~ spl50_144 ),
inference(resolution,[],[f1993,f828]) ).
tff(f2221,plain,
spl50_155,
inference(avatar_split_clause,[],[f623,f2219]) ).
tff(f2219,plain,
( spl50_155
<=> ! [X0: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)) = X3 )
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_155])]) ).
tff(f623,plain,
! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)) = X3 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f428]) ).
tff(f2217,plain,
spl50_154,
inference(avatar_split_clause,[],[f532,f2215]) ).
tff(f532,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK20(X0)),sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f386]) ).
tff(f2100,plain,
spl50_153,
inference(avatar_split_clause,[],[f718,f2098]) ).
tff(f2098,plain,
( spl50_153
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_153])]) ).
tff(f718,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))) ),
inference(forward_demodulation,[],[f717,f448]) ).
tff(f717,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ),
inference(forward_demodulation,[],[f716,f448]) ).
tff(f716,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ),
inference(forward_demodulation,[],[f558,f448]) ).
tff(f558,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ),
inference(cnf_transformation,[],[f401]) ).
tff(f401,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) )
& ( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ) ),
inference(flattening,[],[f400]) ).
tff(f400,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) )
& ( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1))))
<=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X10: fun_Ho1877127206a_bool,X12: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X10)),X12))))
<=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X12)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
tff(f2096,plain,
spl50_152,
inference(avatar_split_clause,[],[f625,f2094]) ).
tff(f625,plain,
! [X2: hoare_1927711152iple_a,X3: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK40(X0,X1,X2,X3)),sK41(X0,X1,X2,X3)))
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f428]) ).
tff(f2048,plain,
spl50_151,
inference(avatar_split_clause,[],[f595,f2046]) ).
tff(f595,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)) = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ),
inference(cnf_transformation,[],[f410]) ).
tff(f2044,plain,
spl50_150,
inference(avatar_split_clause,[],[f592,f2042]) ).
tff(f592,plain,
! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ),
inference(flattening,[],[f311]) ).
tff(f311,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2))) ),
inference(ennf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)))
=> ( ( X0 != X1 )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2)) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X20: hoare_1927711152iple_a,X21: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X21),X22)))
=> ( ( X20 != X21 )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_insertE) ).
tff(f2040,plain,
spl50_149,
inference(avatar_split_clause,[],[f576,f2038]) ).
tff(f576,plain,
! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X25: hoare_1927711152iple_a,X26: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X26),X22)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X26),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insert__commute) ).
tff(f2036,plain,
spl50_148,
inference(avatar_split_clause,[],[f548,f2034]) ).
tff(f548,plain,
! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| hBOOL(hAPP_H1448631928a_bool(X1,sK26(X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f396]) ).
tff(f396,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ! [X2: hoare_1927711152iple_a] :
( ( ( sK26(X1,X2) != X2 )
& hBOOL(hAPP_H1448631928a_bool(X1,sK26(X1,X2))) )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f292,f395]) ).
tff(f395,plain,
! [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ? [X3: hoare_1927711152iple_a] :
( ( X2 != X3 )
& hBOOL(hAPP_H1448631928a_bool(X1,X3)) )
=> ( ( sK26(X1,X2) != X2 )
& hBOOL(hAPP_H1448631928a_bool(X1,sK26(X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f292,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ! [X2: hoare_1927711152iple_a] :
( ? [X3: hoare_1927711152iple_a] :
( ( X2 != X3 )
& hBOOL(hAPP_H1448631928a_bool(X1,X3)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ! [X2: hoare_1927711152iple_a] :
( ? [X3: hoare_1927711152iple_a] :
( ( X2 != X3 )
& hBOOL(hAPP_H1448631928a_bool(X1,X3)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: hoare_1927711152iple_a] :
( ! [X3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X1,X3))
=> ( X2 = X3 ) )
& hBOOL(hAPP_H1448631928a_bool(X1,X2)) )
=> ( hBOOL(hAPP_H1448631928a_bool(X1,X0))
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 ) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X20: hoare_1927711152iple_a,X10: fun_Ho1877127206a_bool] :
( ? [X24: hoare_1927711152iple_a] :
( ! [X41: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X41))
=> ( X24 = X41 ) )
& hBOOL(hAPP_H1448631928a_bool(X10,X24)) )
=> ( hBOOL(hAPP_H1448631928a_bool(X10,X20))
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X10) = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_the1__equality) ).
tff(f2006,plain,
spl50_147,
inference(avatar_split_clause,[],[f703,f2004]) ).
tff(f703,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_H1027145665a_bool(fequal1440857775iple_a,X1) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(forward_demodulation,[],[f702,f688]) ).
tff(f702,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(forward_demodulation,[],[f503,f448]) ).
tff(f503,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) )
| hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
& ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> ( bot_bo1208640912a_bool = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) ) )
& ( hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X10: fun_Ho1877127206a_bool,X20: hoare_1927711152iple_a] :
( ( ~ hBOOL(hAPP_H1448631928a_bool(X10,X20))
=> ( bot_bo1208640912a_bool = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X20))),X10)) ) )
& ( hBOOL(hAPP_H1448631928a_bool(X10,X20))
=> ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X20))),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).
tff(f2002,plain,
spl50_146,
inference(avatar_split_clause,[],[f598,f2000]) ).
tff(f598,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK30(X0,X1,X2)),sK31(X0,X1,X2)))
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ),
inference(cnf_transformation,[],[f410]) ).
tff(f1998,plain,
spl50_145,
inference(avatar_split_clause,[],[f549,f1996]) ).
tff(f1996,plain,
( spl50_145
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ( sK26(X1,X2) != X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_145])]) ).
tff(f549,plain,
! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X1) = X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ( sK26(X1,X2) != X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f396]) ).
tff(f1994,plain,
( spl50_144
| ~ spl50_20
| ~ spl50_42 ),
inference(avatar_split_clause,[],[f1008,f979,f849,f1992]) ).
tff(f1008,plain,
( ! [X0: bool] :
( hBOOL(X0)
| ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(X0) ) )
| ~ spl50_20
| ~ spl50_42 ),
inference(superposition,[],[f980,f850]) ).
tff(f1972,plain,
spl50_143,
inference(avatar_split_clause,[],[f533,f1970]) ).
tff(f533,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| hBOOL(hAPP_f1454306822l_bool(X0,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f386]) ).
tff(f1968,plain,
spl50_142,
inference(avatar_split_clause,[],[f531,f1966]) ).
tff(f531,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK21(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(X0,bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f386]) ).
tff(f1759,plain,
spl50_141,
inference(avatar_split_clause,[],[f701,f1757]) ).
tff(f701,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(forward_demodulation,[],[f504,f448]) ).
tff(f504,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1))),X0)) )
| hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f1755,plain,
spl50_140,
inference(avatar_split_clause,[],[f588,f1753]) ).
tff(f588,plain,
! [X2: fun_Ho1877127206a_bool,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2)) ),
inference(ennf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2))) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X21: hoare_1927711152iple_a,X20: hoare_1927711152iple_a,X23: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),X23))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X21),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insertI2) ).
tff(f1751,plain,
spl50_139,
inference(avatar_split_clause,[],[f583,f1749]) ).
tff(f583,plain,
! [X2: fun_fu1033095803iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(flattening,[],[f298]) ).
tff(f298,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(ennf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X1,X2))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
=> ( hAPP_f490779847iple_a(X2,X0) = hAPP_f490779847iple_a(finite1943414032iple_a(X1),X0) ) ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X22: fun_Ho1877127206a_bool,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X44,X45))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( hAPP_f490779847iple_a(X45,X22) = hAPP_f490779847iple_a(finite1943414032iple_a(X44),X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_folding__one_Oeq__fold) ).
tff(f1747,plain,
spl50_138,
inference(avatar_split_clause,[],[f537,f1745]) ).
tff(f1745,plain,
( spl50_138
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| hBOOL(hAPP_H1448631928a_bool(X0,sK23(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_138])]) ).
tff(f537,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| hBOOL(hAPP_H1448631928a_bool(X0,sK23(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f390]) ).
tff(f390,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ( ( sK23(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK23(X0,X1))) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f284,f389]) ).
tff(f389,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
=> ( ( sK23(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK23(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f284,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(flattening,[],[f283]) ).
tff(f283,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> ( ! [X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X2))
=> ( X1 = X2 ) )
=> hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0))) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X10: fun_Ho1877127206a_bool,X20: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X20))
=> ( ! [X24: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X24))
=> ( X20 = X24 ) )
=> hBOOL(hAPP_H1448631928a_bool(X10,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_theI) ).
tff(f1743,plain,
spl50_137,
inference(avatar_split_clause,[],[f477,f1741]) ).
tff(f477,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(X0)),sK9(X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ),
inference(cnf_transformation,[],[f366]) ).
tff(f366,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( ! [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) != X0 ) )
& ( bot_bo1208640912a_bool != X0 ) ) )
& ( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK9(X0)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(X0)),sK9(X0)) = X0 ) )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f364,f365]) ).
tff(f365,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X3: fun_Ho1877127206a_bool,X4: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X3) = X0 ) )
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK9(X0)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK10(X0)),sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f364,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( ! [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) != X0 ) )
& ( bot_bo1208640912a_bool != X0 ) ) )
& ( ? [X3: fun_Ho1877127206a_bool,X4: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X3))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X3) = X0 ) )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
inference(rectify,[],[f363]) ).
tff(f363,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( ! [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) != X0 ) )
& ( bot_bo1208640912a_bool != X0 ) ) )
& ( ? [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) = X0 ) )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
inference(flattening,[],[f362]) ).
tff(f362,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ( ! [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) != X0 ) )
& ( bot_bo1208640912a_bool != X0 ) ) )
& ( ? [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) = X0 ) )
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
inference(nnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
<=> ( ? [X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) = X0 ) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X20: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X20))
<=> ( ? [X49: fun_Ho1877127206a_bool,X48: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X49))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X48),X49) = X20 ) )
| ( bot_bo1208640912a_bool = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).
tff(f1739,plain,
spl50_136,
inference(avatar_split_clause,[],[f462,f1737]) ).
tff(f1737,plain,
( spl50_136
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| hBOOL(hAPP_H1448631928a_bool(X0,sK4(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_136])]) ).
tff(f462,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| hBOOL(hAPP_H1448631928a_bool(X0,sK4(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f346]) ).
tff(f346,plain,
! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ! [X1: hoare_1927711152iple_a] :
( ( ( sK4(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK4(X0,X1))) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f269,f345]) ).
tff(f345,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
=> ( ( sK4(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK4(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f269,plain,
! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ! [X1: hoare_1927711152iple_a] :
( ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] :
( ! [X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X2))
=> ( X1 = X2 ) )
& hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
=> hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0))) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X10: fun_Ho1877127206a_bool] :
( ? [X24: hoare_1927711152iple_a] :
( ! [X41: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X41))
=> ( X24 = X41 ) )
& hBOOL(hAPP_H1448631928a_bool(X10,X24)) )
=> hBOOL(hAPP_H1448631928a_bool(X10,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_theI_H) ).
tff(f1735,plain,
spl50_135,
inference(avatar_split_clause,[],[f457,f1733]) ).
tff(f1733,plain,
( spl50_135
<=> ! [X0: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,X0) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f909473944a_bool(cOMBB_1083611331iple_a(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)),hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,insert1434104874iple_a),bot_bo1208640912a_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_135])]) ).
tff(f457,plain,
! [X0: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,X0) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f909473944a_bool(cOMBB_1083611331iple_a(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)),hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,insert1434104874iple_a),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,X0) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f909473944a_bool(cOMBB_1083611331iple_a(hAPP_f625100287l_bool(fequal1285825639a_bool,X0)),hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,insert1434104874iple_a),bot_bo1208640912a_bool))) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X36: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,X36) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f909473944a_bool(cOMBB_1083611331iple_a(hAPP_f625100287l_bool(fequal1285825639a_bool,X36)),hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,insert1434104874iple_a),bot_bo1208640912a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_the__elem__def) ).
tff(f1729,plain,
( spl50_78
| ~ spl50_2
| ~ spl50_119 ),
inference(avatar_split_clause,[],[f1663,f1558,f771,f1205]) ).
tff(f1558,plain,
( spl50_119
<=> ( hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_119])]) ).
tff(f1663,plain,
( hBOOL(fTrue)
| ~ spl50_2
| ~ spl50_119 ),
inference(superposition,[],[f773,f1560]) ).
tff(f1560,plain,
( ( hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool) = fTrue )
| ~ spl50_119 ),
inference(avatar_component_clause,[],[f1558]) ).
tff(f1623,plain,
spl50_134,
inference(avatar_split_clause,[],[f722,f1621]) ).
tff(f1621,plain,
( spl50_134
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_134])]) ).
tff(f722,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ),
inference(forward_demodulation,[],[f721,f448]) ).
tff(f721,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ),
inference(forward_demodulation,[],[f556,f448]) ).
tff(f556,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ),
inference(cnf_transformation,[],[f401]) ).
tff(f1619,plain,
spl50_133,
inference(avatar_split_clause,[],[f720,f1617]) ).
tff(f1617,plain,
( spl50_133
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_133])]) ).
tff(f720,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(forward_demodulation,[],[f719,f448]) ).
tff(f719,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ),
inference(forward_demodulation,[],[f557,f448]) ).
tff(f557,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),X0)),X1)))) ),
inference(cnf_transformation,[],[f401]) ).
tff(f1615,plain,
spl50_132,
inference(avatar_split_clause,[],[f714,f1613]) ).
tff(f1613,plain,
( spl50_132
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_132])]) ).
tff(f714,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))) ),
inference(forward_demodulation,[],[f713,f448]) ).
tff(f713,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1))) ),
inference(forward_demodulation,[],[f546,f448]) ).
tff(f546,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1))) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))))
| ( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0)))
& ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1))) ) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X1))) )
=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0)))) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X12: fun_Ho1877127206a_bool,X10: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X12)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X10))) )
=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X10)),X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_finite__Collect__conjI) ).
tff(f1611,plain,
spl50_131,
inference(avatar_split_clause,[],[f712,f1609]) ).
tff(f1609,plain,
( spl50_131
<=> ! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_131])]) ).
tff(f712,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))) ),
inference(forward_demodulation,[],[f711,f448]) ).
tff(f711,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ),
inference(forward_demodulation,[],[f547,f448]) ).
tff(f547,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),X1)),X0))))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(X0))) ),
inference(cnf_transformation,[],[f290]) ).
tff(f1607,plain,
spl50_130,
inference(avatar_split_clause,[],[f629,f1605]) ).
tff(f629,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( sP1(X1,X0,X3,X2)
| ( X1 = X3 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ),
inference(cnf_transformation,[],[f430]) ).
tff(f430,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ( ~ sP1(X1,X0,X3,X2)
& ( ( X1 != X3 )
| ( bot_bo1208640912a_bool != X2 ) ) ) )
& ( sP1(X1,X0,X3,X2)
| ( ( X1 = X3 )
& ( bot_bo1208640912a_bool = X2 ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ) ),
inference(flattening,[],[f429]) ).
tff(f429,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ( ~ sP1(X1,X0,X3,X2)
& ( ( X1 != X3 )
| ( bot_bo1208640912a_bool != X2 ) ) ) )
& ( sP1(X1,X0,X3,X2)
| ( ( X1 = X3 )
& ( bot_bo1208640912a_bool = X2 ) )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f340]) ).
tff(f340,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
<=> ( sP1(X1,X0,X3,X2)
| ( ( X1 = X3 )
& ( bot_bo1208640912a_bool = X2 ) ) ) ),
inference(definition_folding,[],[f259,f339]) ).
tff(f259,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
<=> ( ? [X4: hoare_1927711152iple_a,X5: fun_Ho1877127206a_bool,X6: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X5),X6))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X4),X5))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X0,X4),X6) = X3 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X4),X5) = X2 ) )
| ( ( X1 = X3 )
& ( bot_bo1208640912a_bool = X2 ) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X44: fun_Ho333840202iple_a,X46: hoare_1927711152iple_a,X52: fun_Ho1877127206a_bool,X53: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,X52),X53))
<=> ( ? [X24: hoare_1927711152iple_a,X49: fun_Ho1877127206a_bool,X41: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,X49),X41))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X49))
& ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X24),X41) = X53 )
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),X49) = X52 ) )
| ( ( X46 = X53 )
& ( bot_bo1208640912a_bool = X52 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_fold__graph_Osimps) ).
tff(f1601,plain,
spl50_129,
inference(avatar_split_clause,[],[f628,f1599]) ).
tff(f628,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( sP1(X1,X0,X3,X2)
| ( bot_bo1208640912a_bool = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ),
inference(cnf_transformation,[],[f430]) ).
tff(f1597,plain,
spl50_128,
inference(avatar_split_clause,[],[f600,f1595]) ).
tff(f600,plain,
! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2)) ),
inference(cnf_transformation,[],[f412]) ).
tff(f412,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ( ~ hBOOL(hAPP_H1448631928a_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2)) ) ),
inference(flattening,[],[f411]) ).
tff(f411,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ( ~ hBOOL(hAPP_H1448631928a_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2)) ) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
<=> ( hBOOL(hAPP_H1448631928a_bool(X1,X2))
| ( X0 = X2 ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X26: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool,X25: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X26),X22),X25))
<=> ( hBOOL(hAPP_H1448631928a_bool(X22,X25))
| ( X25 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__code) ).
tff(f1593,plain,
spl50_127,
inference(avatar_split_clause,[],[f585,f1591]) ).
tff(f585,plain,
! [X2: fun_Ho1877127206a_bool,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2)) ),
inference(flattening,[],[f302]) ).
tff(f302,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2)) ),
inference(ennf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X1),X2))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X1))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X2)) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: fun_Ho1877127206a_bool,X7: fun_Ho1877127206a_bool,X8: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X7),X8))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X7))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
tff(f1589,plain,
spl50_126,
inference(avatar_split_clause,[],[f575,f1587]) ).
tff(f575,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: fun_Ho957066028l_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_H1487873860l_bool(X0,X2),hAPP_H1448631928a_bool(X1,X2)) ),
inference(rectify,[],[f125]) ).
tff(f125,axiom,
! [X54: fun_Ho957066028l_bool,X55: fun_Ho1877127206a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,X54),X55),X58) = hAPP_bool_bool(hAPP_H1487873860l_bool(X54,X58),hAPP_H1448631928a_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00) ).
tff(f1585,plain,
spl50_125,
inference(avatar_split_clause,[],[f574,f1583]) ).
tff(f574,plain,
! [X2: state,X0: fun_st2063251938l_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: fun_st2063251938l_bool,X1: fun_state_bool,X2: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),hAPP_state_bool(X1,X2)) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X54: fun_st2063251938l_bool,X55: fun_state_bool,X58: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,X54),X55),X58) = hAPP_bool_bool(hAPP_s58564346l_bool(X54,X58),hAPP_state_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
tff(f1581,plain,
spl50_124,
inference(avatar_split_clause,[],[f542,f1579]) ).
tff(f542,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f394]) ).
tff(f394,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK25(X0,X1)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f287,f393]) ).
tff(f393,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 ) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK25(X0,X1)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK25(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f287,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
=> ? [X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X20: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),X22))
=> ? [X33: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),X33))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X33) = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert) ).
tff(f1577,plain,
spl50_123,
inference(avatar_split_clause,[],[f540,f1575]) ).
tff(f540,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f392]) ).
tff(f392,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK24(X0,X1)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f286,f391]) ).
tff(f391,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 ) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK24(X0,X1)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),sK24(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f286,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 ) )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
=> ~ ! [X2: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X2) = X1 )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X2)) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
=> ~ ! [X33: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X33) = X22 )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Set_Oset__insert) ).
tff(f1573,plain,
spl50_122,
inference(avatar_split_clause,[],[f538,f1571]) ).
tff(f1571,plain,
( spl50_122
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ( sK23(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_122])]) ).
tff(f538,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ( sK23(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f390]) ).
tff(f1569,plain,
spl50_121,
inference(avatar_split_clause,[],[f535,f1567]) ).
tff(f1567,plain,
( spl50_121
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK22(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_121])]) ).
tff(f535,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK22(X0,X1)))
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f388]) ).
tff(f388,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( ( sK22(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK22(X0,X1))) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f282,f387]) ).
tff(f387,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
=> ( ( sK22(X0,X1) != X1 )
& hBOOL(hAPP_H1448631928a_bool(X0,sK22(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(flattening,[],[f281]) ).
tff(f281,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ? [X2: hoare_1927711152iple_a] :
( ( X1 != X2 )
& hBOOL(hAPP_H1448631928a_bool(X0,X2)) )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> ( ! [X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,X2))
=> ( X1 = X2 ) )
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X10: fun_Ho1877127206a_bool,X20: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X20))
=> ( ! [X24: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X10,X24))
=> ( X20 = X24 ) )
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X10) = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_the__equality) ).
tff(f1565,plain,
spl50_120,
inference(avatar_split_clause,[],[f530,f1563]) ).
tff(f530,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),sK19(X0,X1)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(cnf_transformation,[],[f384]) ).
tff(f384,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),sK19(X0,X1)))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f278,f383]) ).
tff(f383,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
=> hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),sK19(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f278,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(flattening,[],[f277]) ).
tff(f277,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2))
| ( bot_bo1208640912a_bool = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
=> ( ( bot_bo1208640912a_bool != X1 )
=> ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X44: fun_Ho333840202iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ( ( bot_bo1208640912a_bool != X22 )
=> ? [X50: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X44,X22),X50)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__nonempty__imp__fold1Set) ).
tff(f1561,plain,
( spl50_119
| ~ spl50_2
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f933,f887,f771,f1558]) ).
tff(f1556,plain,
spl50_118,
inference(avatar_split_clause,[],[f499,f1554]) ).
tff(f499,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_insert__absorb2) ).
tff(f1552,plain,
spl50_117,
inference(avatar_split_clause,[],[f463,f1550]) ).
tff(f1550,plain,
( spl50_117
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ( sK4(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_117])]) ).
tff(f463,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(X0,hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0)))
| ( sK4(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f346]) ).
tff(f1537,plain,
spl50_116,
inference(avatar_split_clause,[],[f580,f1535]) ).
tff(f580,plain,
! [X2: fun_Ho1877127206a_bool,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),sK27(X0,X1,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) ),
inference(cnf_transformation,[],[f403]) ).
tff(f403,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),sK27(X0,X1,X2)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f295,f402]) ).
tff(f402,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ? [X3: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
=> hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),sK27(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f295,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ? [X3: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) ),
inference(ennf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2))
=> ? [X3: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3)) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X44: fun_Ho333840202iple_a,X46: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22))
=> ? [X50: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,X22),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__imp__fold__graph) ).
tff(f1533,plain,
spl50_115,
inference(avatar_split_clause,[],[f545,f1531]) ).
tff(f545,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) ) ),
inference(ennf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X20: hoare_1927711152iple_a,X21: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X21),bot_bo1208640912a_bool) )
=> ( X20 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_singleton__inject) ).
tff(f1529,plain,
spl50_114,
inference(avatar_split_clause,[],[f543,f1527]) ).
tff(f543,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK25(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f394]) ).
tff(f1497,plain,
spl50_113,
inference(avatar_split_clause,[],[f541,f1495]) ).
tff(f541,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),sK24(X0,X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f392]) ).
tff(f1493,plain,
spl50_112,
inference(avatar_split_clause,[],[f536,f1491]) ).
tff(f1491,plain,
( spl50_112
<=> ! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( sK22(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_112])]) ).
tff(f536,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,X0) = X1 )
| ( sK22(X0,X1) != X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f388]) ).
tff(f1472,plain,
( spl50_14
| ~ spl50_10
| ~ spl50_67 ),
inference(avatar_split_clause,[],[f1170,f1116,f808,f824]) ).
tff(f824,plain,
( spl50_14
<=> ! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_14])]) ).
tff(f808,plain,
( spl50_10
<=> ! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_10])]) ).
tff(f1170,plain,
( ! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| ~ spl50_10
| ~ spl50_67 ),
inference(resolution,[],[f1117,f809]) ).
tff(f809,plain,
( ! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool))
| ~ spl50_10 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f1471,plain,
spl50_111,
inference(avatar_split_clause,[],[f573,f1469]) ).
tff(f573,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: fun_Ho525994229l_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X0),X1),X2) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X0,X2),X1) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X54: fun_Ho525994229l_bool,X55: fun_Ho1877127206a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,X54),X55),X58) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_039) ).
tff(f1467,plain,
spl50_110,
inference(avatar_split_clause,[],[f572,f1465]) ).
tff(f572,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: fun_Ho440810351a_bool,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X0),X1),X2) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X0,X2),X1) ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X54: fun_Ho440810351a_bool,X55: hoare_1927711152iple_a,X58: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,X54),X55),X58) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00) ).
tff(f1463,plain,
spl50_109,
inference(avatar_split_clause,[],[f571,f1461]) ).
tff(f571,plain,
! [X2: state,X0: fun_st1506752259e_bool,X1: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: fun_st1506752259e_bool,X1: state,X2: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X0),X1),X2) = hAPP_state_bool(hAPP_s1806633685e_bool(X0,X2),X1) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X54: fun_st1506752259e_bool,X55: state,X58: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,X54),X55),X58) = hAPP_state_bool(hAPP_s1806633685e_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) ).
tff(f1459,plain,
spl50_108,
inference(avatar_split_clause,[],[f570,f1457]) ).
tff(f570,plain,
! [X2: state,X0: fun_st2063251938l_bool,X1: bool] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: fun_st2063251938l_bool,X1: bool,X2: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X0),X1),X2) = hAPP_bool_bool(hAPP_s58564346l_bool(X0,X2),X1) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X54: fun_st2063251938l_bool,X55: bool,X58: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,X54),X55),X58) = hAPP_bool_bool(hAPP_s58564346l_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
tff(f1455,plain,
spl50_107,
inference(avatar_split_clause,[],[f569,f1453]) ).
tff(f1453,plain,
( spl50_107
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho1630563774a_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1027145665a_bool(hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,X0),X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_107])]) ).
tff(f569,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1630563774a_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1027145665a_bool(hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,X0),X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: fun_Ho1630563774a_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,X0),X1),X2) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(X0,X2),X1) ),
inference(rectify,[],[f134]) ).
tff(f134,axiom,
! [X54: fun_Ho1630563774a_bool,X55: fun_Ho1877127206a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,X54),X55),X58) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_041) ).
tff(f1451,plain,
spl50_106,
inference(avatar_split_clause,[],[f568,f1449]) ).
tff(f1449,plain,
( spl50_106
<=> ! [X2: x_a,X0: fun_a_2117018159e_bool,X1: fun_state_bool] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,X0),X1),X2) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_106])]) ).
tff(f568,plain,
! [X2: x_a,X0: fun_a_2117018159e_bool,X1: fun_state_bool] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,X0),X1),X2) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: fun_a_2117018159e_bool,X1: fun_state_bool,X2: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,X0),X1),X2) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(X0,X2),X1) ),
inference(rectify,[],[f126]) ).
tff(f126,axiom,
! [X54: fun_a_2117018159e_bool,X55: fun_state_bool,X58: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,X54),X55),X58) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) ).
tff(f1447,plain,
spl50_105,
inference(avatar_split_clause,[],[f567,f1445]) ).
tff(f1445,plain,
( spl50_105
<=> ! [X2: x_a,X0: fun_a_998512028e_bool,X1: bool] : ( hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,X0),X1),X2) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_105])]) ).
tff(f567,plain,
! [X2: x_a,X0: fun_a_998512028e_bool,X1: bool] : ( hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,X0),X1),X2) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: fun_a_998512028e_bool,X1: bool,X2: x_a] : ( hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,X0),X1),X2) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(X0,X2),X1) ),
inference(rectify,[],[f119]) ).
tff(f119,axiom,
! [X54: fun_a_998512028e_bool,X55: bool,X58: x_a] : ( hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,X54),X55),X58) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(X54,X58),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) ).
tff(f1443,plain,
spl50_104,
inference(avatar_split_clause,[],[f539,f1441]) ).
tff(f539,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
=> ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) = X1 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X20: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),X22))
=> ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X22) = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
tff(f1352,plain,
( spl50_103
| ~ spl50_12
| ~ spl50_90 ),
inference(avatar_split_clause,[],[f1326,f1275,f816,f1350]) ).
tff(f1350,plain,
( spl50_103
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_103])]) ).
tff(f1275,plain,
( spl50_90
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_90])]) ).
tff(f1326,plain,
( ! [X0: bool] : ( fTrue = X0 )
| ~ spl50_12
| ~ spl50_90 ),
inference(duplicate_literal_removal,[],[f1319]) ).
tff(f1319,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fTrue = X0 ) )
| ~ spl50_12
| ~ spl50_90 ),
inference(superposition,[],[f1277,f817]) ).
tff(f1277,plain,
( ( fFalse = fTrue )
| ~ spl50_90 ),
inference(avatar_component_clause,[],[f1275]) ).
tff(f1336,plain,
spl50_102,
inference(avatar_split_clause,[],[f656,f1334]) ).
tff(f656,plain,
! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(equality_resolution,[],[f480]) ).
tff(f480,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1) != X0 ) ),
inference(cnf_transformation,[],[f366]) ).
tff(f1332,plain,
spl50_101,
inference(avatar_split_clause,[],[f653,f1330]) ).
tff(f653,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( X2 = X5 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f443]) ).
tff(f443,plain,
! [X0: fun_a_fun_state_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ( ( hoare_1652181356iple_a(X3,X4,X5) = hoare_1652181356iple_a(X0,X1,X2) )
| ( X2 != X5 )
| ( X1 != X4 )
| ( X0 != X3 ) )
& ( ( ( X2 = X5 )
& ( X1 = X4 )
& ( X0 = X3 ) )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ) ),
inference(flattening,[],[f442]) ).
tff(f442,plain,
! [X0: fun_a_fun_state_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ( ( hoare_1652181356iple_a(X3,X4,X5) = hoare_1652181356iple_a(X0,X1,X2) )
| ( X2 != X5 )
| ( X1 != X4 )
| ( X0 != X3 ) )
& ( ( ( X2 = X5 )
& ( X1 = X4 )
& ( X0 = X3 ) )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: fun_a_fun_state_bool,X1: com,X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X4: com,X5: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X3,X4,X5) = hoare_1652181356iple_a(X0,X1,X2) )
<=> ( ( X2 = X5 )
& ( X1 = X4 )
& ( X0 = X3 ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool,X4: fun_a_fun_state_bool,X5: com,X6: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(X1,X2,X3) = hoare_1652181356iple_a(X4,X5,X6) )
<=> ( ( X3 = X6 )
& ( X2 = X5 )
& ( X1 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
tff(f1318,plain,
spl50_100,
inference(avatar_split_clause,[],[f652,f1316]) ).
tff(f652,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( X1 = X4 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f443]) ).
tff(f1314,plain,
spl50_99,
inference(avatar_split_clause,[],[f651,f1312]) ).
tff(f651,plain,
! [X2: fun_a_fun_state_bool,X3: fun_a_fun_state_bool,X0: fun_a_fun_state_bool,X1: com,X4: com,X5: fun_a_fun_state_bool] :
( ( X0 = X3 )
| ( hoare_1652181356iple_a(X3,X4,X5) != hoare_1652181356iple_a(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f443]) ).
tff(f1310,plain,
spl50_98,
inference(avatar_split_clause,[],[f631,f1308]) ).
tff(f631,plain,
! [X2: fun_Ho1877127206a_bool,X3: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,X2),X3))
| ~ sP1(X1,X0,X3,X2) ),
inference(cnf_transformation,[],[f430]) ).
tff(f1306,plain,
spl50_97,
inference(avatar_split_clause,[],[f602,f1304]) ).
tff(f602,plain,
! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f412]) ).
tff(f1302,plain,
spl50_96,
inference(avatar_split_clause,[],[f596,f1300]) ).
tff(f596,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] :
( ( sK32(X0,X1,X2) = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,X1),X2)) ),
inference(cnf_transformation,[],[f410]) ).
tff(f1298,plain,
spl50_95,
inference(avatar_split_clause,[],[f566,f1296]) ).
tff(f566,plain,
! [X2: hoare_1927711152iple_a,X0: fun_bool_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: fun_bool_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ),
inference(rectify,[],[f124]) ).
tff(f124,axiom,
! [X54: fun_bool_bool,X55: fun_Ho1877127206a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(X54),X55),X58) = hAPP_bool_bool(X54,hAPP_H1448631928a_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).
tff(f1294,plain,
spl50_94,
inference(avatar_split_clause,[],[f565,f1292]) ).
tff(f565,plain,
! [X2: hoare_1927711152iple_a,X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool] : ( hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: fun_fu832487784l_bool,X1: fun_Ho440810351a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X0),X1),X2) = hAPP_f1454306822l_bool(X0,hAPP_H1027145665a_bool(X1,X2)) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X54: fun_fu832487784l_bool,X55: fun_Ho440810351a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(X54),X55),X58) = hAPP_f1454306822l_bool(X54,hAPP_H1027145665a_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).
tff(f1290,plain,
spl50_93,
inference(avatar_split_clause,[],[f564,f1288]) ).
tff(f564,plain,
! [X2: state,X0: fun_bool_bool,X1: fun_state_bool] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: fun_bool_bool,X1: fun_state_bool,X2: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X0),X1),X2) = hAPP_bool_bool(X0,hAPP_state_bool(X1,X2)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X54: fun_bool_bool,X55: fun_state_bool,X58: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(X54),X55),X58) = hAPP_bool_bool(X54,hAPP_state_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
tff(f1286,plain,
spl50_92,
inference(avatar_split_clause,[],[f563,f1284]) ).
tff(f1284,plain,
( spl50_92
<=> ! [X2: x_a,X0: fun_fu1658206819l_bool,X1: fun_a_fun_state_bool] : ( hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(X0),X1),X2) = hAPP_f1259673775l_bool(X0,hAPP_a2036067514e_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_92])]) ).
tff(f563,plain,
! [X2: x_a,X0: fun_fu1658206819l_bool,X1: fun_a_fun_state_bool] : ( hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(X0),X1),X2) = hAPP_f1259673775l_bool(X0,hAPP_a2036067514e_bool(X1,X2)) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: fun_fu1658206819l_bool,X1: fun_a_fun_state_bool,X2: x_a] : ( hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(X0),X1),X2) = hAPP_f1259673775l_bool(X0,hAPP_a2036067514e_bool(X1,X2)) ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X54: fun_fu1658206819l_bool,X55: fun_a_fun_state_bool,X58: x_a] : ( hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(X54),X55),X58) = hAPP_f1259673775l_bool(X54,hAPP_a2036067514e_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) ).
tff(f1282,plain,
spl50_91,
inference(avatar_split_clause,[],[f562,f1280]) ).
tff(f562,plain,
! [X2: state,X0: fun_bo1549164019l_bool,X1: fun_state_bool] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_state_bool,X2: state] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_state_bool(X1,X2)) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X54: fun_bo1549164019l_bool,X55: fun_state_bool,X58: state] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(X54),X55),X58) = hAPP_b589554111l_bool(X54,hAPP_state_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
tff(f1278,plain,
( spl50_90
| ~ spl50_16
| ~ spl50_25
| ~ spl50_72 ),
inference(avatar_split_clause,[],[f1169,f1166,f887,f833,f1275]) ).
tff(f833,plain,
( spl50_16
<=> ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_16])]) ).
tff(f1169,plain,
( ( fFalse = fTrue )
| ~ spl50_16
| ~ spl50_25
| ~ spl50_72 ),
inference(forward_demodulation,[],[f1167,f931]) ).
tff(f931,plain,
( ! [X0: hoare_1927711152iple_a] : ( fTrue = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) )
| ~ spl50_16
| ~ spl50_25 ),
inference(resolution,[],[f888,f834]) ).
tff(f834,plain,
( ! [X0: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| ~ spl50_16 ),
inference(avatar_component_clause,[],[f833]) ).
tff(f1273,plain,
spl50_89,
inference(avatar_split_clause,[],[f561,f1271]) ).
tff(f561,plain,
! [X2: hoare_1927711152iple_a,X0: fun_bo1549164019l_bool,X1: fun_Ho1877127206a_bool] : ( hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_Ho1877127206a_bool,X2: hoare_1927711152iple_a] : ( hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(X0),X1),X2) = hAPP_b589554111l_bool(X0,hAPP_H1448631928a_bool(X1,X2)) ),
inference(rectify,[],[f127]) ).
tff(f127,axiom,
! [X54: fun_bo1549164019l_bool,X55: fun_Ho1877127206a_bool,X58: hoare_1927711152iple_a] : ( hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(X54),X55),X58) = hAPP_b589554111l_bool(X54,hAPP_H1448631928a_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) ).
tff(f1269,plain,
spl50_88,
inference(avatar_split_clause,[],[f560,f1267]) ).
tff(f1267,plain,
( spl50_88
<=> ! [X2: x_a,X0: fun_fu1047394976e_bool,X1: fun_a_1632297036l_bool] : ( hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(X0),X1),X2) = hAPP_f644196280e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_88])]) ).
tff(f560,plain,
! [X2: x_a,X0: fun_fu1047394976e_bool,X1: fun_a_1632297036l_bool] : ( hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(X0),X1),X2) = hAPP_f644196280e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: fun_fu1047394976e_bool,X1: fun_a_1632297036l_bool,X2: x_a] : ( hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(X0),X1),X2) = hAPP_f644196280e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X54: fun_fu1047394976e_bool,X55: fun_a_1632297036l_bool,X58: x_a] : ( hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(X54),X55),X58) = hAPP_f644196280e_bool(X54,hAPP_a849909144l_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_040) ).
tff(f1265,plain,
spl50_87,
inference(avatar_split_clause,[],[f559,f1263]) ).
tff(f1263,plain,
( spl50_87
<=> ! [X2: x_a,X0: fun_fu1219323149e_bool,X1: fun_a_1632297036l_bool] : ( hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(X0),X1),X2) = hAPP_f167292325e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_87])]) ).
tff(f559,plain,
! [X2: x_a,X0: fun_fu1219323149e_bool,X1: fun_a_1632297036l_bool] : ( hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(X0),X1),X2) = hAPP_f167292325e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: fun_fu1219323149e_bool,X1: fun_a_1632297036l_bool,X2: x_a] : ( hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(X0),X1),X2) = hAPP_f167292325e_bool(X0,hAPP_a849909144l_bool(X1,X2)) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X54: fun_fu1219323149e_bool,X55: fun_a_1632297036l_bool,X58: x_a] : ( hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(X54),X55),X58) = hAPP_f167292325e_bool(X54,hAPP_a849909144l_bool(X55,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) ).
tff(f1261,plain,
spl50_86,
inference(avatar_split_clause,[],[f552,f1259]) ).
tff(f552,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ),
inference(cnf_transformation,[],[f398]) ).
tff(f398,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) )
& ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1))
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))) ) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1)))
<=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X1)) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X20: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X22)))
<=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__insert) ).
tff(f1257,plain,
spl50_85,
inference(avatar_split_clause,[],[f528,f1255]) ).
tff(f528,plain,
! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK16(X0)),sK17(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f380,plain,
! [X0: fun_fu832487784l_bool] :
( ( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK16(X0)),sK17(X0))))
& hBOOL(hAPP_f1454306822l_bool(X0,sK17(X0)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK16(X0)),sK17(X0)))
& ( bot_bo1208640912a_bool != sK17(X0) )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(X0))) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f378,f379]) ).
tff(f379,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)))
& hBOOL(hAPP_f1454306822l_bool(X0,X2))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
& ( bot_bo1208640912a_bool != X2 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK16(X0)),sK17(X0))))
& hBOOL(hAPP_f1454306822l_bool(X0,sK17(X0)))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK16(X0)),sK17(X0)))
& ( bot_bo1208640912a_bool != sK17(X0) )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f378,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2)))
& hBOOL(hAPP_f1454306822l_bool(X0,X2))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
& ( bot_bo1208640912a_bool != X2 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X2)) )
| ~ sP0(X0) ),
inference(rectify,[],[f377]) ).
tff(f377,plain,
! [X0: fun_fu832487784l_bool] :
( ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4)))
& hBOOL(hAPP_f1454306822l_bool(X0,X4))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( bot_bo1208640912a_bool != X4 )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X4)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f337]) ).
tff(f1253,plain,
spl50_84,
inference(avatar_split_clause,[],[f478,f1251]) ).
tff(f1251,plain,
( spl50_84
<=> ! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK9(X0)))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_84])]) ).
tff(f478,plain,
! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK9(X0)))
| ( bot_bo1208640912a_bool = X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,X0)) ),
inference(cnf_transformation,[],[f366]) ).
tff(f1249,plain,
spl50_83,
inference(avatar_split_clause,[],[f464,f1247]) ).
tff(f464,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),sK6(X0)) = X0 )
| ( bot_bo1208640912a_bool = X0 ) ),
inference(cnf_transformation,[],[f350]) ).
tff(f350,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != X0 ) ) )
& ( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),sK6(X0)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),sK6(X0)) = X0 ) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f348,f349]) ).
tff(f349,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) = X0 ) )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),sK6(X0)))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,sK5(X0)),sK6(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f348,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != X0 ) ) )
& ( ? [X3: hoare_1927711152iple_a,X4: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X3),X4))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X3),X4) = X0 ) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
inference(rectify,[],[f347]) ).
tff(f347,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
| ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) != X0 ) ) )
& ( ? [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = X0 ) )
| ( bot_bo1208640912a_bool = X0 ) ) ),
inference(nnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool != X0 )
<=> ? [X1: hoare_1927711152iple_a,X2: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X2))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),X2) = X0 ) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X22: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool != X22 )
<=> ? [X24: hoare_1927711152iple_a,X33: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X33))
& ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X24),X33) = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nonempty__iff) ).
tff(f1224,plain,
spl50_82,
inference(avatar_split_clause,[],[f732,f1222]) ).
tff(f732,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)),X2))
| ( X1 = X2 ) ),
inference(forward_demodulation,[],[f603,f688]) ).
tff(f603,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ( X1 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)),X2)) ),
inference(cnf_transformation,[],[f413]) ).
tff(f413,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)),X2))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)),X2)) ) ),
inference(nnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)),X2))
<=> ( X1 = X2 ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X44: fun_Ho333840202iple_a,X20: hoare_1927711152iple_a,X21: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X44,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool)),X21))
<=> ( X20 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_fold1Set__sing) ).
tff(f1220,plain,
spl50_81,
inference(avatar_split_clause,[],[f728,f1218]) ).
tff(f1218,plain,
( spl50_81
<=> ! [X2: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X2,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ~ hBOOL(finite83514413iple_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_81])]) ).
tff(f728,plain,
! [X2: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X2,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(forward_demodulation,[],[f582,f688]) ).
tff(f582,plain,
! [X2: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_f490779847iple_a(X2,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 )
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( ( hAPP_f490779847iple_a(X2,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 )
| ~ hBOOL(finite83514413iple_a(X1,X2)) ),
inference(ennf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X1,X2))
=> ( hAPP_f490779847iple_a(X2,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X25: hoare_1927711152iple_a,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(X44,X45))
=> ( hAPP_f490779847iple_a(X45,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),bot_bo1208640912a_bool)) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_folding__one_Osingleton) ).
tff(f1216,plain,
spl50_80,
inference(avatar_split_clause,[],[f710,f1214]) ).
tff(f710,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)))
| ( X0 = X1 ) ),
inference(forward_demodulation,[],[f544,f688]) ).
tff(f544,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool))) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)))
=> ( X0 = X1 ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X21: hoare_1927711152iple_a,X20: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X21),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool)))
=> ( X20 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_singletonE) ).
tff(f1212,plain,
spl50_79,
inference(avatar_split_clause,[],[f635,f1210]) ).
tff(f1210,plain,
( spl50_79
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_79])]) ).
tff(f635,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f433]) ).
tff(f433,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( ( sP2(X0,X1,X2,X3)
| ( ( ( X0 != X1 )
| ( X2 != X3 ) )
& ( ( X1 != X2 )
| ( X0 != X3 ) ) ) )
& ( ( ( X0 = X1 )
& ( X2 = X3 ) )
| ( ( X1 = X2 )
& ( X0 = X3 ) )
| ~ sP2(X0,X1,X2,X3) ) ),
inference(rectify,[],[f432]) ).
tff(f432,plain,
! [X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a] :
( ( sP2(X2,X1,X3,X0)
| ( ( ( X1 != X2 )
| ( X0 != X3 ) )
& ( ( X1 != X3 )
| ( X0 != X2 ) ) ) )
& ( ( ( X1 = X2 )
& ( X0 = X3 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) )
| ~ sP2(X2,X1,X3,X0) ) ),
inference(flattening,[],[f431]) ).
tff(f431,plain,
! [X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a] :
( ( sP2(X2,X1,X3,X0)
| ( ( ( X1 != X2 )
| ( X0 != X3 ) )
& ( ( X1 != X3 )
| ( X0 != X2 ) ) ) )
& ( ( ( X1 = X2 )
& ( X0 = X3 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) )
| ~ sP2(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f341]) ).
tff(f1208,plain,
( ~ spl50_78
| ~ spl50_10
| ~ spl50_16
| ~ spl50_25
| ~ spl50_67 ),
inference(avatar_split_clause,[],[f1175,f1116,f887,f833,f808,f1205]) ).
tff(f1175,plain,
( ~ hBOOL(fTrue)
| ~ spl50_10
| ~ spl50_16
| ~ spl50_25
| ~ spl50_67 ),
inference(forward_demodulation,[],[f1170,f931]) ).
tff(f1203,plain,
spl50_77,
inference(avatar_split_clause,[],[f634,f1201]) ).
tff(f1201,plain,
( spl50_77
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( X0 = X3 )
| ~ sP2(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_77])]) ).
tff(f634,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ( X0 = X3 )
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f433]) ).
tff(f1199,plain,
spl50_76,
inference(avatar_split_clause,[],[f633,f1197]) ).
tff(f1197,plain,
( spl50_76
<=> ! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] :
( ( X2 = X3 )
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_76])]) ).
tff(f633,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X2 = X3 )
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f433]) ).
tff(f1195,plain,
spl50_75,
inference(avatar_split_clause,[],[f632,f1193]) ).
tff(f1193,plain,
( spl50_75
<=> ! [X0: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X2: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X2 = X3 )
| ( X0 = X3 )
| ~ sP2(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_75])]) ).
tff(f632,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X2 = X3 )
| ( X0 = X3 )
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f433]) ).
tff(f1191,plain,
spl50_74,
inference(avatar_split_clause,[],[f581,f1189]) ).
tff(f1189,plain,
( spl50_74
<=> ! [X2: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X0),X0) = X0 )
| ~ hBOOL(finite1511031594iple_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_74])]) ).
tff(f581,plain,
! [X2: fun_fu1033095803iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a] :
( ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X0),X0) = X0 )
| ~ hBOOL(finite1511031594iple_a(X1,X2)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X0),X0) = X0 )
| ~ hBOOL(finite1511031594iple_a(X1,X2)) ),
inference(ennf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho333840202iple_a,X2: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X1,X2))
=> ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X1,X0),X0) = X0 ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X25: hoare_1927711152iple_a,X44: fun_Ho333840202iple_a,X45: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(X44,X45))
=> ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(X44,X25),X25) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_folding__one__idem_Oidem) ).
tff(f1187,plain,
spl50_73,
inference(avatar_split_clause,[],[f465,f1185]) ).
tff(f465,plain,
! [X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK5(X0)),sK6(X0)))
| ( bot_bo1208640912a_bool = X0 ) ),
inference(cnf_transformation,[],[f350]) ).
tff(f1168,plain,
( spl50_72
| ~ spl50_9
| ~ spl50_20 ),
inference(avatar_split_clause,[],[f882,f849,f803,f1166]) ).
tff(f882,plain,
( ! [X0: hoare_1927711152iple_a] : ( fFalse = hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0) )
| ~ spl50_9
| ~ spl50_20 ),
inference(superposition,[],[f850,f805]) ).
tff(f1134,plain,
spl50_71,
inference(avatar_split_clause,[],[f696,f1132]) ).
tff(f696,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X1,skip,X1)))),
inference(forward_demodulation,[],[f498,f688]) ).
tff(f498,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,skip,X1)),bot_bo1208640912a_bool))),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X1,skip,X1)),bot_bo1208640912a_bool))),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: fun_Ho1877127206a_bool,X10: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X10,skip,X10)),bot_bo1208640912a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hoare__derivs_OSkip) ).
tff(f1130,plain,
spl50_70,
inference(avatar_split_clause,[],[f621,f1128]) ).
tff(f1128,plain,
( spl50_70
<=> ! [X2: com,X0: com,X1: com,X3: com] :
( ( X1 = X3 )
| ( semi(X0,X1) != semi(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_70])]) ).
tff(f621,plain,
! [X2: com,X3: com,X0: com,X1: com] :
( ( X1 = X3 )
| ( semi(X0,X1) != semi(X2,X3) ) ),
inference(cnf_transformation,[],[f424]) ).
tff(f424,plain,
! [X0: com,X1: com,X2: com,X3: com] :
( ( ( semi(X0,X1) = semi(X2,X3) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( semi(X0,X1) != semi(X2,X3) ) ) ),
inference(flattening,[],[f423]) ).
tff(f423,plain,
! [X0: com,X1: com,X2: com,X3: com] :
( ( ( semi(X0,X1) = semi(X2,X3) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X1 = X3 )
& ( X0 = X2 ) )
| ( semi(X0,X1) != semi(X2,X3) ) ) ),
inference(nnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: com,X1: com,X2: com,X3: com] :
( ( semi(X0,X1) = semi(X2,X3) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X37: com,X38: com,X39: com,X40: com] :
( ( semi(X37,X38) = semi(X39,X40) )
<=> ( ( X38 = X40 )
& ( X37 = X39 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Osimps_I3_J) ).
tff(f1126,plain,
spl50_69,
inference(avatar_split_clause,[],[f620,f1124]) ).
tff(f1124,plain,
( spl50_69
<=> ! [X0: com,X3: com,X2: com,X1: com] :
( ( X0 = X2 )
| ( semi(X0,X1) != semi(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_69])]) ).
tff(f620,plain,
! [X2: com,X3: com,X0: com,X1: com] :
( ( X0 = X2 )
| ( semi(X0,X1) != semi(X2,X3) ) ),
inference(cnf_transformation,[],[f424]) ).
tff(f1122,plain,
spl50_68,
inference(avatar_split_clause,[],[f590,f1120]) ).
tff(f590,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( ( X1 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X2)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a] :
( ( X1 = X2 )
| ~ hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X2)) ),
inference(ennf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a,X2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X2))
=> ( X1 = X2 ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X44: fun_Ho333840202iple_a,X46: hoare_1927711152iple_a,X25: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,bot_bo1208640912a_bool),X25))
=> ( X25 = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_empty__fold__graphE) ).
tff(f1118,plain,
spl50_67,
inference(avatar_split_clause,[],[f551,f1116]) ).
tff(f551,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) ),
inference(cnf_transformation,[],[f397]) ).
tff(f397,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
| ~ hBOOL(hAPP_H1448631928a_bool(X1,X0)) )
& ( hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ) ),
inference(nnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1))
<=> hBOOL(hAPP_H1448631928a_bool(X1,X0)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X25: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X25),X22))
<=> hBOOL(hAPP_H1448631928a_bool(X22,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
tff(f1114,plain,
spl50_66,
inference(avatar_split_clause,[],[f550,f1112]) ).
tff(f550,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(X1,X0))
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f397]) ).
tff(f1110,plain,
spl50_65,
inference(avatar_split_clause,[],[f526,f1108]) ).
tff(f526,plain,
! [X0: fun_fu832487784l_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK16(X0)),sK17(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f1106,plain,
spl50_64,
inference(avatar_split_clause,[],[f516,f1104]) ).
tff(f1104,plain,
( spl50_64
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_64])]) ).
tff(f516,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X54: bool,X55: bool] :
( hBOOL(X55)
| ~ hBOOL(X54)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X54),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
tff(f1102,plain,
spl50_63,
inference(avatar_split_clause,[],[f515,f1100]) ).
tff(f1100,plain,
( spl50_63
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_63])]) ).
tff(f515,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X54: bool,X55: bool] :
( hBOOL(X55)
| hBOOL(X54)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X54),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
tff(f1098,plain,
spl50_62,
inference(avatar_split_clause,[],[f507,f1096]) ).
tff(f1096,plain,
( spl50_62
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_62])]) ).
tff(f507,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X55: bool,X54: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X54),X55))
| ~ hBOOL(X55)
| ~ hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f1094,plain,
( spl50_61
| ~ spl50_29
| ~ spl50_54 ),
inference(avatar_split_clause,[],[f1070,f1051,f909,f1092]) ).
tff(f1092,plain,
( spl50_61
<=> ! [X0: hoare_1927711152iple_a] : ( bot_bo1208640912a_bool != hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_61])]) ).
tff(f909,plain,
( spl50_29
<=> ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_29])]) ).
tff(f1070,plain,
( ! [X0: hoare_1927711152iple_a] : ( bot_bo1208640912a_bool != hAPP_H1027145665a_bool(fequal1440857775iple_a,X0) )
| ~ spl50_29
| ~ spl50_54 ),
inference(superposition,[],[f910,f1052]) ).
tff(f910,plain,
( ! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) )
| ~ spl50_29 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f1090,plain,
spl50_60,
inference(avatar_split_clause,[],[f497,f1088]) ).
tff(f497,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1))),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X20: hoare_1927711152iple_a,X23: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X20),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertI1) ).
tff(f1086,plain,
spl50_59,
inference(avatar_split_clause,[],[f495,f1084]) ).
tff(f495,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),X1) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(X0,X1)) ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: fun_Ho333840202iple_a,X1: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),X1) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(X0,X1)) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X44: fun_Ho333840202iple_a,X22: fun_Ho1877127206a_bool] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X44),X22) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(X44,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1__def) ).
tff(f1082,plain,
spl50_58,
inference(avatar_split_clause,[],[f484,f1080]) ).
tff(f484,plain,
! [X0: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK12(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) ),
inference(cnf_transformation,[],[f374]) ).
tff(f374,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK12(X0)),X0))
| ( bot_bo1208640912a_bool = X0 ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f372,f373]) ).
tff(f373,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK12(X0)),X0)) ),
introduced(choice_axiom,[]) ).
tff(f372,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( bot_bo1208640912a_bool = X0 ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X0)) ) ),
inference(rectify,[],[f371]) ).
tff(f371,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( bot_bo1208640912a_bool = X0 ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ) ),
inference(nnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
<=> ( bot_bo1208640912a_bool != X0 ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X22: fun_Ho1877127206a_bool] :
( ? [X24: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X22))
<=> ( bot_bo1208640912a_bool != X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ex__in__conv) ).
tff(f1078,plain,
spl50_57,
inference(avatar_split_clause,[],[f481,f1076]) ).
tff(f481,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK11(X0)),X0)) ),
inference(cnf_transformation,[],[f370]) ).
tff(f370,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( bot_bo1208640912a_bool != X0 ) )
& ( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK11(X0)),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f368,f369]) ).
tff(f369,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X0))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK11(X0)),X0)) ),
introduced(choice_axiom,[]) ).
tff(f368,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( bot_bo1208640912a_bool != X0 ) )
& ( ( bot_bo1208640912a_bool = X0 )
| ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X0)) ) ),
inference(rectify,[],[f367]) ).
tff(f367,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( bot_bo1208640912a_bool != X0 ) )
& ( ( bot_bo1208640912a_bool = X0 )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ) ),
inference(nnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: fun_Ho1877127206a_bool] :
( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
<=> ( bot_bo1208640912a_bool = X0 ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X22: fun_Ho1877127206a_bool] :
( ! [X24: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X24),X22))
<=> ( bot_bo1208640912a_bool = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).
tff(f1074,plain,
spl50_56,
inference(avatar_split_clause,[],[f461,f1072]) ).
tff(f461,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK3(X0)),X0)) ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK3(X0)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f268,f343]) ).
tff(f343,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK3(X0)),X0)) ),
introduced(choice_axiom,[]) ).
tff(f268,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: fun_Ho1877127206a_bool] :
( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
=> ( bot_bo1208640912a_bool = X0 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X22: fun_Ho1877127206a_bool] :
( ! [X41: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X41),X22))
=> ( bot_bo1208640912a_bool = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_equals0I) ).
tff(f1057,plain,
spl50_55,
inference(avatar_split_clause,[],[f690,f1055]) ).
tff(f1053,plain,
spl50_54,
inference(avatar_split_clause,[],[f688,f1051]) ).
tff(f1049,plain,
spl50_53,
inference(avatar_split_clause,[],[f521,f1047]) ).
tff(f521,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1)) ),
inference(rectify,[],[f122]) ).
tff(f122,axiom,
! [X56: fun_Ho1877127206a_bool,X57: fun_Ho1877127206a_bool] :
( ( X56 = X57 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X56),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).
tff(f1045,plain,
spl50_52,
inference(avatar_split_clause,[],[f520,f1043]) ).
tff(f520,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1)) ),
inference(rectify,[],[f117]) ).
tff(f117,axiom,
! [X56: hoare_1927711152iple_a,X57: hoare_1927711152iple_a] :
( ( X56 = X57 )
| ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X56),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_) ).
tff(f1041,plain,
spl50_51,
inference(avatar_split_clause,[],[f519,f1039]) ).
tff(f1039,plain,
( spl50_51
<=> ! [X0: state,X1: state] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_51])]) ).
tff(f519,plain,
! [X0: state,X1: state] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X1)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: state,X1: state] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X1)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X56: state,X57: state] :
( ( X56 = X57 )
| ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X56),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).
tff(f1037,plain,
spl50_50,
inference(avatar_split_clause,[],[f485,f1035]) ).
tff(f485,plain,
! [X0: hoare_1927711152iple_a] : ( hoare_1652181356iple_a(sK13(X0),sK14(X0),sK15(X0)) = X0 ),
inference(cnf_transformation,[],[f376]) ).
tff(f376,plain,
! [X0: hoare_1927711152iple_a] : ( hoare_1652181356iple_a(sK13(X0),sK14(X0),sK15(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f270,f375]) ).
tff(f375,plain,
! [X0: hoare_1927711152iple_a] :
( ? [X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool] : ( hoare_1652181356iple_a(X1,X2,X3) = X0 )
=> ( hoare_1652181356iple_a(sK13(X0),sK14(X0),sK15(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f270,plain,
! [X0: hoare_1927711152iple_a] :
? [X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool] : ( hoare_1652181356iple_a(X1,X2,X3) = X0 ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: hoare_1927711152iple_a] :
~ ! [X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool] : ( hoare_1652181356iple_a(X1,X2,X3) != X0 ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X26: hoare_1927711152iple_a] :
~ ! [X30: fun_a_fun_state_bool,X31: com,X32: fun_a_fun_state_bool] : ( hoare_1652181356iple_a(X30,X31,X32) != X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_triple_Oexhaust) ).
tff(f1032,plain,
spl50_49,
inference(avatar_split_clause,[],[f454,f1030]) ).
tff(f1030,plain,
( spl50_49
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_49])]) ).
tff(f454,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)) = X0 ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X0)) = X0 ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X20: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_the__eq__trivial) ).
tff(f1028,plain,
( spl50_48
| ~ spl50_46 ),
inference(avatar_split_clause,[],[f1020,f1017,f1026]) ).
tff(f1026,plain,
( spl50_48
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_48])]) ).
tff(f1017,plain,
( spl50_46
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_46])]) ).
tff(f1020,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 )
| ~ spl50_46 ),
inference(forward_demodulation,[],[f1018,f688]) ).
tff(f1018,plain,
( ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 )
| ~ spl50_46 ),
inference(avatar_component_clause,[],[f1017]) ).
tff(f1024,plain,
( spl50_47
| ~ spl50_17
| ~ spl50_42 ),
inference(avatar_split_clause,[],[f1006,f979,f837,f1022]) ).
tff(f1006,plain,
( ! [X0: fun_Ho333840202iple_a] : ( bot_bo1208640912a_bool = finite2098837632iple_a(X0,bot_bo1208640912a_bool) )
| ~ spl50_17
| ~ spl50_42 ),
inference(resolution,[],[f980,f838]) ).
tff(f1019,plain,
spl50_46,
inference(avatar_split_clause,[],[f453,f1017]) ).
tff(f453,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool)) = X0 ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X25: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X25),bot_bo1208640912a_bool)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_the__elem__eq) ).
tff(f993,plain,
spl50_45,
inference(avatar_split_clause,[],[f731,f991]) ).
tff(f731,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_H1027145665a_bool(fequal1440857775iple_a,X2)),X2)),
inference(forward_demodulation,[],[f672,f688]) ).
tff(f672,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),bot_bo1208640912a_bool)),X2)),
inference(equality_resolution,[],[f604]) ).
tff(f604,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)),X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f413]) ).
tff(f989,plain,
spl50_44,
inference(avatar_split_clause,[],[f695,f987]) ).
tff(f987,plain,
( spl50_44
<=> ! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_44])]) ).
tff(f695,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),hAPP_H1027145665a_bool(fequal1440857775iple_a,X1)) = X1 ),
inference(forward_demodulation,[],[f496,f688]) ).
tff(f496,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = X1 ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X0),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X1),bot_bo1208640912a_bool)) = X1 ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X44: fun_Ho333840202iple_a,X20: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(finite1943414032iple_a(X44),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),bot_bo1208640912a_bool)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_fold1__singleton) ).
tff(f985,plain,
spl50_43,
inference(avatar_split_clause,[],[f693,f983]) ).
tff(f693,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0))) ),
inference(forward_demodulation,[],[f470,f448]) ).
tff(f470,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0))) ),
inference(cnf_transformation,[],[f358]) ).
tff(f358,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0))) )
& ( ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X2))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f356,f357]) ).
tff(f357,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> hBOOL(hAPP_H1448631928a_bool(X0,sK8(X0))) ),
introduced(choice_axiom,[]) ).
tff(f356,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
& ( ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X2))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(rectify,[],[f355]) ).
tff(f355,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
& ( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(nnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
<=> ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X10: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X10) )
<=> ! [X24: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X10,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).
tff(f981,plain,
spl50_42,
inference(avatar_split_clause,[],[f691,f979]) ).
tff(f691,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = X0 )
| hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0))) ),
inference(forward_demodulation,[],[f468,f448]) ).
tff(f468,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0))) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0))) )
& ( ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X2))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f352,f353]) ).
tff(f353,plain,
! [X0: fun_Ho1877127206a_bool] :
( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1))
=> hBOOL(hAPP_H1448631928a_bool(X0,sK7(X0))) ),
introduced(choice_axiom,[]) ).
tff(f352,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
& ( ! [X2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X2))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(rectify,[],[f351]) ).
tff(f351,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
| ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(X0,X1)) )
& ( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X1))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ) ),
inference(nnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X0) )
<=> ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X0,X1)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X10: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(X10) )
<=> ! [X24: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(X10,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
tff(f977,plain,
spl50_41,
inference(avatar_split_clause,[],[f671,f975]) ).
tff(f671,plain,
! [X2: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X2),X1),X2)),
inference(equality_resolution,[],[f601]) ).
tff(f601,plain,
! [X2: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1),X2))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f412]) ).
tff(f973,plain,
spl50_40,
inference(avatar_split_clause,[],[f518,f971]) ).
tff(f971,plain,
( spl50_40
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_40])]) ).
tff(f518,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X54: bool,X55: bool] :
( hBOOL(X55)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X54),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f969,plain,
spl50_39,
inference(avatar_split_clause,[],[f517,f967]) ).
tff(f967,plain,
( spl50_39
<=> ! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_39])]) ).
tff(f517,plain,
! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X54: bool,X55: bool] :
( hBOOL(X54)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X54),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f964,plain,
( spl50_38
| ~ spl50_15
| ~ spl50_25 ),
inference(avatar_split_clause,[],[f928,f887,f827,f961]) ).
tff(f961,plain,
( spl50_38
<=> ( bot_bot_bool = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_38])]) ).
tff(f928,plain,
( ( bot_bot_bool = fTrue )
| ~ spl50_15
| ~ spl50_25 ),
inference(resolution,[],[f888,f829]) ).
tff(f829,plain,
( hBOOL(bot_bot_bool)
| ~ spl50_15 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f959,plain,
spl50_37,
inference(avatar_split_clause,[],[f511,f957]) ).
tff(f957,plain,
( spl50_37
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_37])]) ).
tff(f511,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X55: bool,X54: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X54),X55))
| hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
tff(f955,plain,
spl50_36,
inference(avatar_split_clause,[],[f510,f953]) ).
tff(f953,plain,
( spl50_36
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_36])]) ).
tff(f510,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X54: bool,X55: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X54),X55))
| ~ hBOOL(X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
tff(f951,plain,
spl50_35,
inference(avatar_split_clause,[],[f509,f949]) ).
tff(f949,plain,
( spl50_35
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_35])]) ).
tff(f509,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X55: bool,X54: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X54),X55))
| ~ hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
tff(f947,plain,
spl50_34,
inference(avatar_split_clause,[],[f508,f945]) ).
tff(f945,plain,
( spl50_34
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_34])]) ).
tff(f508,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X54: bool,X55: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X54),X55))
| ~ hBOOL(X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
tff(f927,plain,
spl50_33,
inference(avatar_split_clause,[],[f692,f925]) ).
tff(f925,plain,
( spl50_33
<=> ! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool != X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_33])]) ).
tff(f692,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool != X0 )
| ~ hBOOL(hAPP_H1448631928a_bool(X0,X2)) ),
inference(forward_demodulation,[],[f467,f448]) ).
tff(f467,plain,
! [X2: hoare_1927711152iple_a,X0: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_H1448631928a_bool(X0,X2))
| ( bot_bo1208640912a_bool != collec829051333iple_a(X0) ) ),
inference(cnf_transformation,[],[f354]) ).
tff(f923,plain,
spl50_32,
inference(avatar_split_clause,[],[f527,f921]) ).
tff(f527,plain,
! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(X0,sK17(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f919,plain,
spl50_31,
inference(avatar_split_clause,[],[f524,f917]) ).
tff(f524,plain,
! [X0: fun_fu832487784l_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,sK17(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f915,plain,
spl50_30,
inference(avatar_split_clause,[],[f494,f913]) ).
tff(f494,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X1)),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X0,X1,bot_bo1208640912a_bool),X1)),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X44: fun_Ho333840202iple_a,X46: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(X44,X46,bot_bo1208640912a_bool),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fold__graph_OemptyI) ).
tff(f911,plain,
spl50_29,
inference(avatar_split_clause,[],[f492,f909]) ).
tff(f492,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: hoare_1927711152iple_a,X1: fun_Ho1877127206a_bool] : ( bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),X1) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X20: hoare_1927711152iple_a,X22: fun_Ho1877127206a_bool] : ( bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).
tff(f907,plain,
spl50_28,
inference(avatar_split_clause,[],[f452,f905]) ).
tff(f905,plain,
( spl50_28
<=> ! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_28])]) ).
tff(f452,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = X0 ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X25: hoare_1927711152iple_a] : ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__sym__eq__trivial) ).
tff(f901,plain,
( ~ spl50_27
| spl50_26 ),
inference(avatar_split_clause,[],[f896,f892,f898]) ).
tff(f892,plain,
( spl50_26
<=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_26])]) ).
tff(f896,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))))
| spl50_26 ),
inference(forward_demodulation,[],[f894,f688]) ).
tff(f894,plain,
( ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool)))
| spl50_26 ),
inference(avatar_component_clause,[],[f892]) ).
tff(f895,plain,
~ spl50_26,
inference(avatar_split_clause,[],[f444,f892]) ).
tff(f444,plain,
~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))),
inference(flattening,[],[f136]) ).
tff(f136,negated_conjecture,
~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))),
inference(negated_conjecture,[],[f135]) ).
tff(f135,conjecture,
hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f889,plain,
( spl50_25
| spl50_1
| ~ spl50_12 ),
inference(avatar_split_clause,[],[f871,f816,f766,f887]) ).
tff(f766,plain,
( spl50_1
<=> hBOOL(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_1])]) ).
tff(f871,plain,
( ! [X0: bool] :
( ~ hBOOL(X0)
| ( fTrue = X0 ) )
| spl50_1
| ~ spl50_12 ),
inference(superposition,[],[f768,f817]) ).
tff(f768,plain,
( ~ hBOOL(fFalse)
| spl50_1 ),
inference(avatar_component_clause,[],[f766]) ).
tff(f867,plain,
spl50_24,
inference(avatar_split_clause,[],[f662,f865]) ).
tff(f662,plain,
! [X1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X1),X1)),
inference(equality_resolution,[],[f514]) ).
tff(f514,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: fun_Ho1877127206a_bool,X1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X56: fun_Ho1877127206a_bool,X57: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X56),X57))
| ( X56 != X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).
tff(f863,plain,
spl50_23,
inference(avatar_split_clause,[],[f661,f861]) ).
tff(f661,plain,
! [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X1),X1)),
inference(equality_resolution,[],[f513]) ).
tff(f513,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f118]) ).
tff(f118,axiom,
! [X56: hoare_1927711152iple_a,X57: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X56),X57))
| ( X56 != X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_) ).
tff(f859,plain,
spl50_22,
inference(avatar_split_clause,[],[f660,f857]) ).
tff(f660,plain,
! [X1: state] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X1),X1)),
inference(equality_resolution,[],[f512]) ).
tff(f512,plain,
! [X0: state,X1: state] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: state,X1: state] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X56: state,X57: state] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X56),X57))
| ( X56 != X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).
tff(f855,plain,
spl50_21,
inference(avatar_split_clause,[],[f525,f853]) ).
tff(f853,plain,
( spl50_21
<=> ! [X0: fun_fu832487784l_bool] :
( ( bot_bo1208640912a_bool != sK17(X0) )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_21])]) ).
tff(f525,plain,
! [X0: fun_fu832487784l_bool] :
( ( bot_bo1208640912a_bool != sK17(X0) )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f851,plain,
spl50_20,
inference(avatar_split_clause,[],[f491,f849]) ).
tff(f491,plain,
! [X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) = X0 ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: bool,X1: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X0),X1) = X0 ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X54: bool,X55: hoare_1927711152iple_a] : ( hAPP_H1448631928a_bool(cOMBK_712844119iple_a(X54),X55) = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__) ).
tff(f847,plain,
spl50_19,
inference(avatar_split_clause,[],[f490,f845]) ).
tff(f490,plain,
! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 ),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X54: bool,X55: state] : ( hAPP_state_bool(cOMBK_bool_state(X54),X55) = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
tff(f843,plain,
spl50_18,
inference(avatar_split_clause,[],[f489,f841]) ).
tff(f489,plain,
! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X54: fun_state_bool,X55: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X54),X55) = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
tff(f839,plain,
spl50_17,
inference(avatar_split_clause,[],[f488,f837]) ).
tff(f488,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,bot_bo1208640912a_bool),X1)),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: fun_Ho333840202iple_a,X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X0,bot_bo1208640912a_bool),X1)),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X44: fun_Ho333840202iple_a,X25: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(X44,bot_bo1208640912a_bool),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__fold1SetE) ).
tff(f835,plain,
( ~ spl50_15
| spl50_16 ),
inference(avatar_split_clause,[],[f472,f833,f827]) ).
tff(f472,plain,
! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f359]) ).
tff(f359,plain,
! [X0: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ) ),
inference(nnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X25: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X25))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).
tff(f830,plain,
( spl50_14
| spl50_15 ),
inference(avatar_split_clause,[],[f471,f827,f824]) ).
tff(f471,plain,
! [X0: hoare_1927711152iple_a] :
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ),
inference(cnf_transformation,[],[f359]) ).
tff(f822,plain,
spl50_13,
inference(avatar_split_clause,[],[f460,f820]) ).
tff(f820,plain,
( spl50_13
<=> ! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_13])]) ).
tff(f460,plain,
! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X54: bool] :
( ~ hBOOL(X54)
| ~ hBOOL(hAPP_bool_bool(fNot,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
tff(f818,plain,
spl50_12,
inference(avatar_split_clause,[],[f459,f816]) ).
tff(f459,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X54: bool] :
( ( fFalse = X54 )
| ( fTrue = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f814,plain,
spl50_11,
inference(avatar_split_clause,[],[f458,f812]) ).
tff(f458,plain,
! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X54: bool] :
( hBOOL(hAPP_bool_bool(fNot,X54))
| hBOOL(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
tff(f810,plain,
spl50_10,
inference(avatar_split_clause,[],[f450,f808]) ).
tff(f450,plain,
! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X11: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X11),bot_bo1208640912a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__iff) ).
tff(f806,plain,
( spl50_9
| ~ spl50_3
| ~ spl50_4 ),
inference(avatar_split_clause,[],[f800,f780,f776,f803]) ).
tff(f800,plain,
( ( bot_bo1208640912a_bool = cOMBK_712844119iple_a(fFalse) )
| ~ spl50_3
| ~ spl50_4 ),
inference(superposition,[],[f782,f777]) ).
tff(f799,plain,
spl50_8,
inference(avatar_split_clause,[],[f683,f797]) ).
tff(f797,plain,
( spl50_8
<=> ! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] : sP2(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_8])]) ).
tff(f683,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] : sP2(X3,X2,X2,X3),
inference(equality_resolution,[],[f682]) ).
tff(f682,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a] :
( sP2(X0,X2,X2,X3)
| ( X0 != X3 ) ),
inference(equality_resolution,[],[f636]) ).
tff(f636,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( sP2(X0,X1,X2,X3)
| ( X1 != X2 )
| ( X0 != X3 ) ),
inference(cnf_transformation,[],[f433]) ).
tff(f795,plain,
spl50_7,
inference(avatar_split_clause,[],[f681,f793]) ).
tff(f793,plain,
( spl50_7
<=> ! [X1: hoare_1927711152iple_a,X3: hoare_1927711152iple_a] : sP2(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_7])]) ).
tff(f681,plain,
! [X3: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] : sP2(X1,X1,X3,X3),
inference(equality_resolution,[],[f680]) ).
tff(f680,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( sP2(X1,X1,X2,X3)
| ( X2 != X3 ) ),
inference(equality_resolution,[],[f637]) ).
tff(f637,plain,
! [X2: hoare_1927711152iple_a,X3: hoare_1927711152iple_a,X0: hoare_1927711152iple_a,X1: hoare_1927711152iple_a] :
( sP2(X0,X1,X2,X3)
| ( X0 != X1 )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f433]) ).
tff(f791,plain,
spl50_6,
inference(avatar_split_clause,[],[f486,f789]) ).
tff(f789,plain,
( spl50_6
<=> ! [X0: com,X1: com] : ( skip != semi(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_6])]) ).
tff(f486,plain,
! [X0: com,X1: com] : ( skip != semi(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: com,X1: com] : ( skip != semi(X0,X1) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X34: com,X35: com] : ( skip != semi(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_com_Osimps_I13_J) ).
tff(f787,plain,
spl50_5,
inference(avatar_split_clause,[],[f449,f785]) ).
tff(f449,plain,
! [X0: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0),bot_bo1208640912a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
tff(f783,plain,
spl50_4,
inference(avatar_split_clause,[],[f447,f780]) ).
tff(f447,plain,
bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(fFalse)),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__def) ).
tff(f778,plain,
spl50_3,
inference(avatar_split_clause,[],[f448,f776]) ).
tff(f774,plain,
spl50_2,
inference(avatar_split_clause,[],[f446,f771]) ).
tff(f446,plain,
hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)),
inference(cnf_transformation,[],[f72]) ).
tff(f72,axiom,
hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).
tff(f769,plain,
~ spl50_1,
inference(avatar_split_clause,[],[f445,f766]) ).
tff(f445,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% 0.04/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.28 % Computer : n020.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Tue Apr 30 03:14:17 EDT 2024
% 0.07/0.28 % CPUTime :
% 0.07/0.28 % (25329)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.30 % (25332)WARNING: value z3 for option sas not known
% 0.07/0.30 % (25330)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.30 % (25331)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.30 % (25334)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.30 % (25333)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.30 % (25332)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.30 % (25335)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.30 % (25336)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.40 TRYING [1]
% 0.12/0.42 TRYING [2]
% 0.12/0.47 Detected minimum model sizes of [1,1,1,1,1,1,1,1]
% 0.12/0.47 Detected maximum model sizes of [max,max,2,max,max,max,max,max]
% 0.12/0.47 TRYING [1,1,1,1,1,1,1,1]
% 0.12/0.47 TRYING [1,1,1,1,1,2,1,1]
% 0.12/0.48 TRYING [1,1,1,1,1,2,2,1]
% 0.12/0.49 TRYING [1,1,1,1,1,3,2,1]
% 0.12/0.50 TRYING [1,1,1,1,1,3,3,1]
% 0.12/0.52 TRYING [1,1,1,2,1,3,3,1]
% 0.12/0.55 % (25334)First to succeed.
% 2.04/0.58 TRYING [1,1,2,2,1,3,3,1]
% 2.04/0.59 % (25334)Refutation found. Thanks to Tanya!
% 2.04/0.59 % SZS status Theorem for theBenchmark
% 2.04/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 2.04/0.61 % (25334)------------------------------
% 2.04/0.61 % (25334)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.04/0.61 % (25334)Termination reason: Refutation
% 2.04/0.61
% 2.04/0.61 % (25334)Memory used [KB]: 5082
% 2.04/0.61 % (25334)Time elapsed: 0.296 s
% 2.04/0.61 % (25334)Instructions burned: 587 (million)
% 2.04/0.61 % (25334)------------------------------
% 2.04/0.61 % (25334)------------------------------
% 2.04/0.61 % (25329)Success in time 0.3 s
%------------------------------------------------------------------------------