%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW470_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:29:44 PM UTC 2026
% Result : Theorem 21.64s 3.84s
% Output : CNFRefutation 21.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 51 ~; 50 |; 10 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 52 ( 50 usr; 48 prp; 0-4 aty)
% Number of functors : 135 ( 135 usr; 30 con; 0-6 aty)
% Number of variables : 163 ( 0 sgn 157 !; 6 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cOMBB_160679318_state: fun_bool_bool > fun_fu373216837e_bool ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( fun_Ho333840202iple_a * ( hoare_1927711152iple_a * ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) ) ) > $o ).
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_Ho1877127206a_bool * fun_Ho333840202iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_24,type,
finite1943414032iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a ).
tff(func_def_25,type,
finite148164294iple_a: ( fun_Ho1877127206a_bool * ( hoare_1927711152iple_a * fun_Ho333840202iple_a ) ) > fun_Ho1877127206a_bool ).
tff(func_def_26,type,
finite83514413iple_a: ( fun_fu1033095803iple_a * fun_Ho333840202iple_a ) > bool ).
tff(func_def_27,type,
finite1511031594iple_a: ( fun_fu1033095803iple_a * fun_Ho333840202iple_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: ( x_a * fun_a_fun_state_bool ) > fun_state_bool ).
tff(func_def_46,type,
hAPP_a849909144l_bool: ( x_a * fun_a_1632297036l_bool ) > fun_st2063251938l_bool ).
tff(func_def_47,type,
hAPP_a723219176e_bool: ( x_a * fun_a_998512028e_bool ) > fun_bo1936561970e_bool ).
tff(func_def_48,type,
hAPP_a1200519163e_bool: ( x_a * fun_a_2117018159e_bool ) > fun_fu373216837e_bool ).
tff(func_def_49,type,
hAPP_state_bool: ( state * fun_state_bool ) > bool ).
tff(func_def_50,type,
hAPP_s1806633685e_bool: ( state * fun_st1506752259e_bool ) > fun_state_bool ).
tff(func_def_51,type,
hAPP_s58564346l_bool: ( state * fun_st2063251938l_bool ) > fun_bool_bool ).
tff(func_def_52,type,
hAPP_bool_bool: ( bool * fun_bool_bool ) > bool ).
tff(func_def_53,type,
hAPP_b540892988e_bool: ( bool * fun_bo675861616e_bool ) > fun_a_fun_state_bool ).
tff(func_def_54,type,
hAPP_b2019457360e_bool: ( bool * fun_bo1936561970e_bool ) > fun_state_bool ).
tff(func_def_55,type,
hAPP_b589554111l_bool: ( bool * fun_bo1549164019l_bool ) > fun_bool_bool ).
tff(func_def_56,type,
hAPP_H1448631928a_bool: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > bool ).
tff(func_def_57,type,
hAPP_H963118037iple_a: ( hoare_1927711152iple_a * fun_Ho843200573iple_a ) > hoare_1927711152iple_a ).
tff(func_def_58,type,
hAPP_H1487873860l_bool: ( hoare_1927711152iple_a * fun_Ho957066028l_bool ) > fun_bool_bool ).
tff(func_def_59,type,
hAPP_H1027145665a_bool: ( hoare_1927711152iple_a * fun_Ho440810351a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_60,type,
hAPP_H1700437986iple_a: ( hoare_1927711152iple_a * fun_Ho333840202iple_a ) > fun_Ho843200573iple_a ).
tff(func_def_61,type,
hAPP_H694056973l_bool: ( hoare_1927711152iple_a * fun_Ho525994229l_bool ) > fun_fu832487784l_bool ).
tff(func_def_62,type,
hAPP_H1975128022a_bool: ( hoare_1927711152iple_a * fun_Ho1630563774a_bool ) > fun_fu1585556401a_bool ).
tff(func_def_63,type,
hAPP_f1509969235l_bool: ( fun_a_fun_state_bool * fun_fu2118559873l_bool ) > fun_a_1632297036l_bool ).
tff(func_def_64,type,
hAPP_f340725611e_bool: ( fun_a_1632297036l_bool * fun_fu1591723597e_bool ) > fun_a_998512028e_bool ).
tff(func_def_65,type,
hAPP_f963367678e_bool: ( fun_a_1632297036l_bool * fun_fu2008829792e_bool ) > fun_a_2117018159e_bool ).
tff(func_def_66,type,
hAPP_f1824947087e_bool: ( fun_a_998512028e_bool * fun_fu222103665e_bool ) > fun_bo675861616e_bool ).
tff(func_def_67,type,
hAPP_f1261923407e_bool: ( fun_a_2117018159e_bool * fun_fu734682033e_bool ) > fun_fu281355805e_bool ).
tff(func_def_68,type,
hAPP_f762886889e_bool: ( fun_state_bool * fun_fu281355805e_bool ) > fun_a_fun_state_bool ).
tff(func_def_69,type,
hAPP_f1759915619e_bool: ( fun_state_bool * fun_fu373216837e_bool ) > fun_state_bool ).
tff(func_def_70,type,
hAPP_f1259673775l_bool: ( fun_state_bool * fun_fu1658206819l_bool ) > fun_st2063251938l_bool ).
tff(func_def_71,type,
hAPP_f817621513e_bool: ( fun_st1506752259e_bool * fun_fu402792811e_bool ) > fun_st1506752259e_bool ).
tff(func_def_72,type,
hAPP_f167292325e_bool: ( fun_st2063251938l_bool * fun_fu1219323149e_bool ) > fun_bo1936561970e_bool ).
tff(func_def_73,type,
hAPP_f644196280e_bool: ( fun_st2063251938l_bool * fun_fu1047394976e_bool ) > fun_fu373216837e_bool ).
tff(func_def_74,type,
hAPP_f1454306822l_bool: ( fun_Ho1877127206a_bool * fun_fu832487784l_bool ) > bool ).
tff(func_def_75,type,
hAPP_f490779847iple_a: ( fun_Ho1877127206a_bool * fun_fu1033095803iple_a ) > hoare_1927711152iple_a ).
tff(func_def_76,type,
hAPP_f16502863a_bool: ( fun_Ho1877127206a_bool * fun_fu1585556401a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_77,type,
hAPP_f749678531l_bool: ( fun_Ho1877127206a_bool * fun_fu269925879l_bool ) > fun_Ho957066028l_bool ).
tff(func_def_78,type,
hAPP_f993216280a_bool: ( fun_Ho1877127206a_bool * fun_fu276214394a_bool ) > fun_Ho440810351a_bool ).
tff(func_def_79,type,
hAPP_f625100287l_bool: ( fun_Ho1877127206a_bool * fun_fu1644852787l_bool ) > fun_fu832487784l_bool ).
tff(func_def_80,type,
hAPP_f2112551770a_bool: ( fun_Ho957066028l_bool * fun_fu1249172034a_bool ) > fun_fu1585556401a_bool ).
tff(func_def_81,type,
hAPP_f909473944a_bool: ( fun_Ho440810351a_bool * fun_fu1563903738a_bool ) > fun_Ho1877127206a_bool ).
tff(func_def_82,type,
hAPP_f1216137953a_bool: ( fun_Ho440810351a_bool * fun_fu893561155a_bool ) > fun_Ho440810351a_bool ).
tff(func_def_83,type,
hAPP_f684479953a_bool: ( fun_Ho525994229l_bool * fun_fu1192765369a_bool ) > fun_fu1585556401a_bool ).
tff(func_def_84,type,
hAPP_f1022403729a_bool: ( fun_Ho1630563774a_bool * fun_fu1905604217a_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,
sK1: ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( com * fun_Ho1877127206a_bool ) ) ) > x_a ).
tff(func_def_91,type,
sK2: ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( com * fun_Ho1877127206a_bool ) ) ) > state ).
tff(func_def_92,type,
sK3: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_93,type,
sK4: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_94,type,
sK5: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).
tff(func_def_95,type,
sK6: ( fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).
tff(func_def_96,type,
sK7: ( 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_97,type,
sK8: ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * fun_a_fun_state_bool ) ) ) > state ).
tff(func_def_98,type,
sK9: ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * fun_a_fun_state_bool ) ) ) > state ).
tff(func_def_99,type,
sK10: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_100,type,
sK11: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_101,type,
sK12: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_102,type,
sK13: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_103,type,
sK14: hoare_1927711152iple_a > fun_a_fun_state_bool ).
tff(func_def_104,type,
sK15: hoare_1927711152iple_a > com ).
tff(func_def_105,type,
sK16: hoare_1927711152iple_a > fun_a_fun_state_bool ).
tff(func_def_106,type,
sK17: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_107,type,
sK18: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(func_def_108,type,
sK19: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_109,type,
sK20: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_110,type,
sK21: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_111,type,
sK22: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_112,type,
sK23: ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(func_def_113,type,
sK24: ( fun_a_fun_state_bool * ( com * ( fun_Ho1877127206a_bool * fun_a_fun_state_bool ) ) ) > x_a ).
tff(func_def_114,type,
sK25: ( fun_a_fun_state_bool * ( com * ( fun_Ho1877127206a_bool * fun_a_fun_state_bool ) ) ) > state ).
tff(func_def_115,type,
sK26: ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( fun_a_fun_state_bool * ( com * ( fun_Ho1877127206a_bool * fun_a_fun_state_bool ) ) ) ) ) > state ).
tff(func_def_116,type,
sK27: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_117,type,
sK28: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).
tff(func_def_118,type,
sK29: fun_Ho333840202iple_a > hoare_1927711152iple_a ).
tff(func_def_119,type,
sK30: fun_Ho333840202iple_a > hoare_1927711152iple_a ).
tff(func_def_120,type,
sK31: ( hoare_1927711152iple_a * ( fun_Ho1877127206a_bool * ( hoare_1927711152iple_a * fun_Ho333840202iple_a ) ) ) > hoare_1927711152iple_a ).
tff(func_def_121,type,
sK32: ( hoare_1927711152iple_a * ( fun_Ho1877127206a_bool * ( hoare_1927711152iple_a * fun_Ho333840202iple_a ) ) ) > fun_Ho1877127206a_bool ).
tff(func_def_122,type,
sK33: ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a ) > hoare_1927711152iple_a ).
tff(func_def_123,type,
sK34: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(func_def_124,type,
sK35: fun_fu832487784l_bool > fun_Ho1877127206a_bool ).
tff(func_def_125,type,
sK36: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).
tff(func_def_126,type,
sK37: fun_Ho1877127206a_bool > hoare_1927711152iple_a ).
tff(func_def_127,type,
sK38: ( fun_Ho1877127206a_bool * ( hoare_1927711152iple_a * fun_Ho333840202iple_a ) ) > hoare_1927711152iple_a ).
tff(func_def_128,type,
sK39: ( hoare_1927711152iple_a * ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a ) ) > hoare_1927711152iple_a ).
tff(func_def_129,type,
sK40: ( hoare_1927711152iple_a * ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a ) ) > fun_Ho1877127206a_bool ).
tff(func_def_130,type,
sK41: ( hoare_1927711152iple_a * ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a ) ) > hoare_1927711152iple_a ).
tff(func_def_131,type,
sK42: ( fun_Ho333840202iple_a * ( hoare_1927711152iple_a * ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) ) ) > hoare_1927711152iple_a ).
tff(func_def_132,type,
sK43: ( fun_Ho333840202iple_a * ( hoare_1927711152iple_a * ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) ) ) > fun_Ho1877127206a_bool ).
tff(func_def_133,type,
sK44: ( fun_Ho333840202iple_a * ( hoare_1927711152iple_a * ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) ) ) > hoare_1927711152iple_a ).
tff(func_def_134,type,
sK45: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(func_def_135,type,
sK46: fun_fu832487784l_bool > fun_Ho1877127206a_bool ).
tff(func_def_136,type,
sK47: fun_fu832487784l_bool > hoare_1927711152iple_a ).
tff(f5,axiom,
! [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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant) ).
tff(f8,axiom,
! [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))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_conseq1) ).
tff(f13,axiom,
! [X0: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
tff(f22,axiom,
! [X0: fun_Ho1877127206a_bool] :
( ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
<=> ( X0 = bot_bo1208640912a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).
tff(f43,axiom,
! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
tff(f65,axiom,
! [X0: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
<=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).
tff(f74,axiom,
! [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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mem__def) ).
tff(f75,axiom,
! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Collect__def) ).
tff(f104,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(f111,axiom,
! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
tff(f112,axiom,
! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
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,[status(cth)],[f135]) ).
tff(f138,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(f143,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(ennf_transformation,[],[f5]) ).
tff(f147,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(ennf_transformation,[],[f8]) ).
tff(f148,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(flattening,[],[f147]) ).
tff(f214,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)))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK5(X0,X2)),sK6(X0,X2)))
& ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK5(X0,X2)),sK6(X0,X2))) )
| 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(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X5,sK5(X0,X2)),skolemize(X6,sK6(X0,X2))],[f148]) ).
tff(f225,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0))
| ( X0 = bot_bo1208640912a_bool ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f226,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( ? [X2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X2),X0))
| ( X0 = bot_bo1208640912a_bool ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ) ),
inference(rectify,[],[f225]) ).
tff(f227,plain,
! [X0: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,sK13(X0)),X0))
| ( X0 = bot_bo1208640912a_bool ) )
& ( ( bot_bo1208640912a_bool != X0 )
| ! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0))],[f226]) ).
tff(f237,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,[],[f43]) ).
tff(f253,plain,
! [X0: hoare_1927711152iple_a] :
( ( ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)) )
& ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool))
| hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ) ),
inference(nnf_transformation,[],[f65]) ).
tff(f254,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,[],[f74]) ).
tff(f284,plain,
! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho1877127206a_bool,X1: 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(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(cnf_transformation,[],[f143]) ).
tff(f290,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,X4)),bot_bo1208640912a_bool)))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK5(X0,X2)),sK6(X0,X2)))
| 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(cnf_transformation,[],[f214]) ).
tff(f299,plain,
! [X0: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0),bot_bo1208640912a_bool) ),
inference(cnf_transformation,[],[f13]) ).
tff(f314,plain,
! [X0: fun_Ho1877127206a_bool,X1: hoare_1927711152iple_a] :
( ( bot_bo1208640912a_bool != X0 )
| ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),X0)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f347,plain,
! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f237]) ).
tff(f348,plain,
! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0)) ),
inference(cnf_transformation,[],[f237]) ).
tff(f384,plain,
! [X0: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0))
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0),bot_bo1208640912a_bool)) ),
inference(cnf_transformation,[],[f253]) ).
tff(f396,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,[],[f254]) ).
tff(f397,plain,
! [X0: fun_Ho1877127206a_bool] : ( collec829051333iple_a(X0) = X0 ),
inference(cnf_transformation,[],[f75]) ).
tff(f456,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f104]) ).
tff(f463,plain,
! [X0: bool,X1: state] : ( hAPP_state_bool(cOMBK_bool_state(X0),X1) = X0 ),
inference(cnf_transformation,[],[f111]) ).
tff(f464,plain,
! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0),X1) = X0 ),
inference(cnf_transformation,[],[f112]) ).
tff(f487,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,[],[f138]) ).
tff(f494,plain,
! [X1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X1),bot_bo1208640912a_bool)),
inference(equality_resolution,[],[f314]) ).
tcf(c_56,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_62,plain,
! [X0_com: com,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool,X2_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_fun_a_fun_state_bool,sK5(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)),sK6(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)))
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X2_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool)),bot_bo1208640912a_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(X0_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool)),bot_bo1208640912a_bool))) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_70,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0_hoare_1927711152iple_a),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,X0_hoare_1927711152iple_a)),
inference(cnf_transformation,[],[f299]) ).
tcf(c_84,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0_hoare_1927711152iple_a),bot_bo1208640912a_bool)),
inference(cnf_transformation,[],[f494]) ).
tcf(c_117,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0_hoare_1927711152iple_a))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_118,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] :
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0_hoare_1927711152iple_a)) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_154,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0_hoare_1927711152iple_a),bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0_hoare_1927711152iple_a)) ),
inference(cnf_transformation,[],[f384]) ).
tcf(c_164,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X0_hoare_1927711152iple_a),X0_fun_Ho1877127206a_bool))
| ~ hBOOL(hAPP_H1448631928a_bool(X0_fun_Ho1877127206a_bool,X0_hoare_1927711152iple_a)) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_166,plain,
! [X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool] : collec829051333iple_a(X0_fun_Ho1877127206a_bool) = X0_fun_Ho1877127206a_bool,
inference(cnf_transformation,[],[f397]) ).
tcf(c_225,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f456]) ).
tcf(c_232,plain,
! [X0_state: state,X0_bool: bool] : hAPP_state_bool(cOMBK_bool_state(X0_bool),X0_state) = X0_bool,
inference(cnf_transformation,[],[f463]) ).
tcf(c_233,plain,
! [X0_x_a: x_a,X0_fun_state_bool: fun_state_bool] : hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0_fun_state_bool),X0_x_a) = X0_fun_state_bool,
inference(cnf_transformation,[],[f464]) ).
tcf(c_256,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(cnf_transformation,[],[f487]) ).
tcf(c_271,plain,
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,iProver_bot))
| ~ hBOOL(bot_bot_bool) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_272,plain,
~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,iProver_bot),bot_bo1208640912a_bool)),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_292,plain,
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,iProver_bot),bot_bo1208640912a_bool))
| ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_390,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0_hoare_1927711152iple_a)),
inference(global_subsumption_just,[status(thm)],[c_154,c_118,c_271,c_272,c_292]) ).
tcf(c_478,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)),bot_bo1208640912a_bool)))
| hBOOL(X0_bool) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_479,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)),bot_bo1208640912a_bool))) ),
inference(renaming,[status(thm)],[c_478]) ).
tcf(c_1721,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X0_hoare_1927711152iple_a),bot_bo1208640912a_bool) = hAPP_H1027145665a_bool(fequal1440857775iple_a,X0_hoare_1927711152iple_a),
inference(demodulation,[status(thm)],[c_70,c_166]) ).
tcf(c_1925,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)))) ),
inference(demodulation,[status(thm)],[c_479,c_1721]) ).
tcf(c_1994,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)))))),
inference(demodulation,[status(thm)],[c_256,c_1721]) ).
tcf(c_2078,plain,
! [X0_com: com,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool,X2_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_fun_a_fun_state_bool,sK5(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)),sK6(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool)))) ),
inference(demodulation,[status(thm)],[c_62,c_1721]) ).
tcf(c_4526,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool))))
| hBOOL(X0_bool) ),
inference(prop_impl_just,[status(thm)],[c_1925]) ).
tcf(c_4527,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)))) ),
inference(renaming,[status(thm)],[c_4526]) ).
tcf(c_6371,plain,
! [X0_com: com,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool,X2_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X2_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_fun_a_fun_state_bool,sK5(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)),sK6(X2_fun_a_fun_state_bool,X0_fun_a_fun_state_bool)))
| ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0_fun_a_fun_state_bool,X0_com,X1_fun_a_fun_state_bool)))) ),
inference(subtyping,[status(esa)],[c_2078]) ).
tcf(c_6380,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)))))),
inference(subtyping,[status(esa)],[c_1994]) ).
tcf(c_6386,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),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)),X0_fun_a_fun_state_bool))),X0_bool),X0_com,X1_fun_a_fun_state_bool)))) ),
inference(subtyping,[status(esa)],[c_4527]) ).
tcf(c_6418,plain,
! [X0_hoare_1927711152iple_a: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X0_hoare_1927711152iple_a)),
inference(subtyping,[status(esa)],[c_390]) ).
tcf(c_6441,plain,
! [X0_fun_state_bool: fun_state_bool,X0_iProver_hAPP_a2036067514e_bool_2_x_a: iProver_hAPP_a2036067514e_bool_2_x_a] : hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(X0_fun_state_bool),X0_iProver_hAPP_a2036067514e_bool_2_x_a) = X0_fun_state_bool,
inference(subtyping,[status(esa)],[c_233]) ).
tcf(c_6442,plain,
! [X0_state: state,X0_bool: bool] : hAPP_state_bool(cOMBK_bool_state(X0_bool),X0_state) = X0_bool,
inference(subtyping,[status(esa)],[c_232]) ).
tcf(c_6449,plain,
~ hBOOL(fFalse),
inference(subtyping,[status(esa)],[c_225]) ).
tcf(c_10391,plain,
! [X0_com: com,X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool,X0_fun_Ho1877127206a_bool: fun_Ho1877127206a_bool,X1_fun_a_fun_state_bool: fun_a_fun_state_bool,X2_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(X0_fun_Ho1877127206a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(X0_fun_a_fun_state_bool,X0_com,X2_fun_a_fun_state_bool))))
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0_fun_a_fun_state_bool,sK5(X0_fun_a_fun_state_bool,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_fun_a_fun_state_bool))),X0_bool))),sK6(X0_fun_a_fun_state_bool,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_fun_a_fun_state_bool))),X0_bool)))) ),
inference(superposition,[status(thm)],[c_6386,c_6371]) ).
tcf(c_10544,plain,
! [X0_bool: bool,X0_fun_a_fun_state_bool: fun_a_fun_state_bool] :
( hBOOL(X0_bool)
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),sK5(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),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)),X0_fun_a_fun_state_bool))),X0_bool))),sK6(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),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)),X0_fun_a_fun_state_bool))),X0_bool)))) ),
inference(superposition,[status(thm)],[c_10391,c_6380]) ).
tcf(c_10550,plain,
! [X0_bool: bool] :
( hBOOL(fFalse)
| hBOOL(X0_bool) ),
inference(demodulation,[status(thm)],[c_10544,c_6442,c_6441]) ).
tcf(c_10551,plain,
! [X0_bool: bool] : hBOOL(X0_bool),
inference(forward_subsumption_resolution,[status(thm)],[c_10550,c_6449]) ).
tcf(c_10600,plain,
$false,
inference(superposition,[status(thm)],[c_10551,c_6418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 22:31:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 21.64/3.84 % SZS status Started for theBenchmark.p
% 21.64/3.84 % SZS status Theorem for theBenchmark.p
% 21.64/3.84
% 21.64/3.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.64/3.84
% 21.64/3.84 % ------ iProver source info
% 21.64/3.84
% 21.64/3.84 % git: date: 2026-07-19 20:42:38 +0200
% 21.64/3.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.64/3.84 % git: non_committed_changes: false
% 21.64/3.84
% 21.64/3.84 % ------ Parsing...
% 21.64/3.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.64/3.84
% 21.64/3.84 % ------ Preprocessing... sup_sim: 51 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 21.64/3.84
% 21.64/3.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.64/3.84
% 21.64/3.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.64/3.84 % ------ Proving...
% 21.64/3.84 % ------ Problem Properties
% 21.64/3.84
% 21.64/3.84 %
% 21.64/3.84 % clauses 176
% 21.64/3.84 % conjectures 0
% 21.64/3.84 % EPR 4
% 21.64/3.84 % Horn 123
% 21.64/3.84 % unary 53
% 21.64/3.84 % binary 64
% 21.64/3.84 % lits 383
% 21.64/3.84 % lits eq 129
% 21.64/3.84 % fd_pure 1
% 21.64/3.84 % fd_pseudo 0
% 21.64/3.84 % fd_cond 18
% 21.64/3.84 % fd_pseudo_cond 25
% 21.64/3.84 % AC symbols 0
% 21.64/3.84
% 21.64/3.84 % ------ Input Options Time Limit: Unbounded
% 21.64/3.84
% 21.64/3.84
% 21.64/3.84 % ------
% 21.64/3.84 % Current options:
% 21.64/3.84 % ------
% 21.64/3.84
% 21.64/3.84
% 21.64/3.84 %
% 21.64/3.84
% 21.64/3.84 % ------ Proving...
% 21.64/3.84 %
% 21.64/3.84
% 21.64/3.84 % SZS status Theorem for theBenchmark.p
% 21.64/3.84
% 21.64/3.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.64/3.84
% 21.64/3.84
%------------------------------------------------------------------------------