TSTP Solution File: SWW473+3 by Vampire-SAT---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW473+3 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:52:22 EDT 2024
% Result : Theorem 6.59s 1.41s
% Output : Refutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2784
% Syntax : Number of formulae : 8599 (2359 unt; 0 def)
% Number of atoms : 23225 (3760 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 22710 (8084 ~;7941 |;2740 &)
% (1995 <=>;1944 =>; 0 <=; 6 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 1664 (1662 usr;1613 prp; 0-4 aty)
% Number of functors : 556 ( 556 usr; 105 con; 0-3 aty)
% Number of variables : 15605 (14750 !; 855 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29211,plain,
$false,
inference(avatar_sat_refutation,[],[f7791,f7796,f7801,f7806,f7811,f7816,f7821,f7826,f7831,f7836,f7841,f7846,f7851,f7856,f7861,f7865,f7869,f7874,f7879,f7884,f7889,f7894,f7899,f7904,f7908,f7913,f7918,f7923,f7928,f7933,f7938,f7942,f7946,f7950,f7954,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8030,f8034,f8038,f8042,f8046,f8050,f8054,f8058,f8062,f8066,f8070,f8074,f8078,f8082,f8086,f8090,f8094,f8098,f8102,f8106,f8110,f8114,f8118,f8123,f8132,f8141,f8154,f8159,f8164,f8179,f8198,f8203,f8208,f8213,f8218,f8223,f8228,f8232,f8236,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8280,f8284,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8332,f8336,f8341,f8345,f8349,f8353,f8357,f8361,f8365,f8366,f8381,f8391,f8404,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8448,f8452,f8456,f8460,f8465,f8469,f8473,f8477,f8481,f8485,f8489,f8493,f8497,f8501,f8505,f8509,f8513,f8517,f8525,f8529,f8533,f8537,f8539,f8543,f8547,f8551,f8555,f8559,f8563,f8567,f8571,f8575,f8579,f8583,f8587,f8591,f8595,f8599,f8603,f8607,f8611,f8615,f8619,f8623,f8627,f8631,f8635,f8639,f8643,f8647,f8651,f8655,f8659,f8663,f8667,f8671,f8675,f8679,f8683,f8687,f8691,f8695,f8699,f8703,f8707,f8712,f8717,f8721,f8725,f8729,f8733,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8771,f8775,f8788,f8802,f8814,f8826,f8830,f8836,f8841,f8845,f8849,f8853,f8857,f8861,f8865,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8918,f8922,f8926,f8930,f8934,f8938,f8942,f8946,f8950,f8954,f8958,f8962,f8966,f8970,f8974,f8978,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9014,f9018,f9022,f9026,f9030,f9034,f9038,f9042,f9046,f9050,f9054,f9058,f9063,f9067,f9071,f9075,f9079,f9083,f9087,f9093,f9097,f9105,f9109,f9115,f9127,f9132,f9137,f9141,f9145,f9149,f9154,f9158,f9162,f9166,f9170,f9174,f9178,f9182,f9186,f9190,f9194,f9198,f9202,f9206,f9210,f9214,f9218,f9222,f9226,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9262,f9266,f9270,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9306,f9310,f9314,f9319,f9323,f9327,f9331,f9335,f9340,f9344,f9348,f9352,f9356,f9360,f9404,f9440,f9538,f9542,f9553,f9557,f9561,f9565,f9569,f9574,f9578,f9583,f9587,f9591,f9595,f9599,f9603,f9607,f9612,f9616,f9620,f9624,f9628,f9632,f9636,f9640,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9676,f9680,f9684,f9688,f9693,f9697,f9701,f9705,f9709,f9713,f9717,f9721,f9820,f9824,f9828,f9832,f9836,f9840,f9844,f9848,f9852,f9856,f9860,f9864,f9868,f9872,f9877,f9881,f9885,f9889,f9893,f9897,f9901,f9905,f9909,f9913,f9917,f9921,f9925,f9929,f9933,f9937,f9941,f9945,f9949,f9953,f9958,f9962,f9966,f9970,f9974,f9978,f9982,f9986,f9990,f9994,f9998,f10002,f10006,f10010,f10014,f10018,f10022,f10026,f10030,f10034,f10039,f10043,f10047,f10051,f10055,f10059,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10103,f10107,f10111,f10115,f10120,f10124,f10128,f10132,f10136,f10140,f10144,f10148,f10152,f10156,f10160,f10164,f10168,f10172,f10176,f10180,f10184,f10188,f10192,f10196,f10201,f10205,f10209,f10213,f10217,f10221,f10225,f10229,f10233,f10237,f10241,f10245,f10249,f10253,f10257,f10261,f10265,f10269,f10273,f10277,f10282,f10286,f10319,f10357,f10408,f10453,f10537,f10563,f10567,f10571,f10577,f10581,f10585,f10589,f10593,f10597,f10601,f10605,f10609,f10613,f10619,f10623,f10627,f10631,f10635,f10639,f10643,f10647,f10651,f10655,f10660,f10664,f10668,f10672,f10676,f10680,f10684,f10688,f10692,f10696,f10700,f10704,f10708,f10712,f10716,f10720,f10724,f10728,f10732,f10736,f10740,f10745,f10749,f10753,f10757,f10761,f10765,f10769,f10773,f10777,f10781,f10785,f10790,f10794,f10798,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10835,f10839,f10843,f10847,f10852,f10856,f10860,f10864,f10868,f10872,f10876,f10923,f11041,f11127,f11212,f11296,f11322,f11326,f11343,f11349,f11354,f11358,f11362,f11366,f11370,f11374,f11378,f11382,f11386,f11390,f11394,f11398,f11402,f11406,f11410,f11414,f11418,f11422,f11426,f11430,f11434,f11438,f11442,f11446,f11450,f11454,f11458,f11462,f11466,f11470,f11474,f11478,f11482,f11486,f11490,f11494,f11498,f11502,f11506,f11510,f11514,f11518,f11522,f11526,f11530,f11534,f11538,f11542,f11546,f11550,f11554,f11558,f11562,f11566,f11570,f11574,f11578,f11582,f11586,f11590,f11594,f11598,f11602,f11607,f11611,f11615,f11619,f11623,f11627,f11631,f11635,f11639,f11643,f11647,f11651,f11655,f11659,f11663,f11667,f11671,f11675,f11679,f11683,f11688,f11692,f11696,f11700,f11704,f11708,f11712,f11716,f11720,f11724,f11728,f11733,f11741,f11749,f11755,f11759,f11763,f11767,f11771,f11775,f11779,f11783,f11787,f11791,f11795,f11799,f11803,f11807,f11811,f11815,f11819,f11823,f11827,f11831,f11835,f11839,f11843,f11847,f11875,f11961,f12026,f12070,f12141,f12501,f12505,f12509,f12513,f12517,f12521,f12525,f12529,f12533,f12537,f12541,f12545,f12549,f12553,f12557,f12561,f12565,f12569,f12573,f12578,f12582,f12586,f12590,f12594,f12598,f12602,f12606,f12610,f12614,f12619,f12623,f12627,f12631,f12635,f12639,f12643,f12647,f12651,f12655,f12660,f12664,f12668,f12788,f12849,f12887,f13064,f13086,f13090,f13094,f13098,f13102,f13106,f13110,f13114,f13118,f13122,f13126,f13130,f13134,f13138,f13142,f13146,f13150,f13154,f13158,f13162,f13166,f13170,f13174,f13178,f13182,f13186,f13190,f13194,f13198,f13202,f13206,f13210,f13214,f13218,f13222,f13226,f13230,f13234,f13238,f13242,f13246,f13250,f13254,f13258,f13262,f13266,f13270,f13274,f13278,f13282,f13286,f13290,f13294,f13298,f13302,f13306,f13310,f13314,f13318,f13322,f13326,f13330,f13334,f13338,f13342,f13346,f13350,f13354,f13358,f13362,f13366,f13370,f13374,f13378,f13382,f13386,f13390,f13394,f13398,f13402,f13406,f13410,f13414,f13418,f13422,f13426,f13430,f13434,f13438,f13442,f13446,f13450,f13454,f13458,f13462,f13466,f13470,f13474,f13478,f13482,f13486,f13491,f13498,f13502,f13506,f13510,f13514,f13518,f13522,f13526,f13554,f13658,f13783,f13793,f13833,f13890,f14170,f14278,f14481,f14565,f14581,f14594,f14598,f14602,f14606,f14610,f14614,f14618,f14622,f14626,f14630,f14634,f14638,f14642,f14646,f14650,f14654,f14658,f14662,f14666,f14670,f14674,f14678,f14682,f14686,f14690,f14694,f14698,f14702,f14706,f14710,f14714,f14718,f14722,f14727,f14732,f14736,f14740,f14744,f14748,f14752,f14997,f15529,f15533,f15537,f15541,f15545,f15549,f15553,f15557,f15561,f15565,f15569,f15573,f15577,f15581,f15585,f15589,f15593,f15597,f15601,f15605,f15609,f15613,f15617,f15621,f15625,f15629,f15633,f15637,f15641,f15645,f15649,f15653,f15657,f15661,f15665,f15669,f15675,f15686,f15690,f15694,f15698,f15702,f15708,f15713,f15726,f15730,f15734,f15738,f15742,f15746,f15751,f15756,f15761,f15766,f15770,f15774,f15778,f15782,f15786,f15790,f15794,f15798,f15802,f15806,f15810,f15814,f15818,f15822,f15826,f15830,f15834,f15838,f15842,f15846,f15850,f15854,f15858,f15862,f15866,f15870,f15874,f15878,f15882,f15886,f15890,f15894,f15898,f15902,f15906,f15910,f15914,f15918,f15922,f15926,f15930,f15934,f15938,f15942,f15946,f15950,f15954,f15958,f15962,f15966,f15970,f15974,f15978,f15982,f15986,f15990,f15994,f15998,f16002,f16006,f16010,f16014,f16018,f16022,f16026,f16030,f16034,f16038,f16042,f16046,f16050,f16054,f16058,f16062,f16066,f16070,f16074,f16078,f16082,f16086,f16090,f16094,f16098,f16102,f16106,f16110,f16114,f16118,f16122,f16126,f16130,f16134,f16138,f16142,f16146,f16150,f16154,f16158,f16162,f16166,f16170,f16174,f16178,f16182,f16186,f16190,f16194,f16199,f16204,f16208,f16213,f16217,f16221,f16225,f16229,f16233,f16237,f16241,f16245,f16249,f16253,f16354,f16429,f16672,f16676,f16680,f16684,f17491,f17495,f17499,f17669,f17673,f17677,f17681,f17685,f17689,f17693,f17697,f17701,f17705,f17709,f17713,f17717,f17721,f17725,f17729,f17733,f17738,f17742,f17746,f17750,f17754,f17758,f17762,f17766,f17770,f17774,f17778,f17782,f17786,f17790,f17794,f17798,f17802,f17806,f17810,f17814,f17819,f17823,f17827,f17831,f17835,f17839,f17843,f17847,f17851,f17855,f17859,f17863,f17867,f17871,f17875,f17879,f17883,f17887,f17891,f17895,f17899,f17903,f17907,f17911,f17915,f17919,f17923,f17927,f17931,f17935,f17939,f17943,f17947,f18194,f19429,f19433,f19437,f19441,f19445,f19449,f19453,f19457,f19461,f19465,f19469,f19474,f19478,f19482,f19486,f19490,f19494,f19498,f19502,f19506,f19510,f19536,f19540,f19544,f19548,f19552,f19556,f19562,f19566,f19570,f19574,f19599,f19603,f19607,f19611,f19615,f19619,f19623,f19627,f19631,f19635,f19636,f20291,f20295,f20299,f20303,f20346,f20450,f21020,f21024,f21028,f21032,f21036,f21040,f21044,f21048,f21052,f21056,f21062,f21066,f21070,f21074,f21078,f21082,f21086,f21090,f21094,f21098,f21102,f21106,f21110,f21114,f21118,f21122,f21126,f21130,f21134,f21138,f21142,f21146,f21150,f21154,f21158,f21162,f21166,f21170,f21174,f21178,f21182,f21186,f21190,f21194,f21198,f21202,f21206,f21210,f21214,f21218,f21227,f21231,f21235,f21239,f21243,f21247,f21251,f21255,f21259,f21263,f21267,f21272,f21276,f21280,f21284,f21288,f21292,f21296,f21300,f21304,f21308,f21312,f21316,f21497,f22275,f22367,f22968,f22972,f22976,f22980,f22984,f22989,f22993,f22997,f23001,f23005,f23009,f23013,f23017,f23021,f23025,f23029,f23033,f23037,f23041,f23045,f23049,f23053,f23059,f23066,f23072,f23079,f23085,f23089,f23097,f23103,f23111,f23117,f23124,f23130,f23134,f23141,f23145,f23149,f23153,f23157,f23161,f23165,f23169,f23173,f23178,f23182,f23186,f23190,f23194,f23198,f23202,f23206,f23210,f23214,f23218,f23222,f23226,f23230,f23234,f23238,f23242,f23246,f23250,f23254,f23258,f23262,f23266,f23270,f23274,f23278,f23282,f23286,f23290,f23294,f23298,f23302,f23306,f23310,f23314,f23318,f23322,f23326,f23330,f23334,f23338,f23342,f23346,f23350,f23355,f23359,f23363,f23367,f23371,f23375,f23379,f23383,f23387,f23391,f23397,f23401,f23405,f23409,f23413,f23417,f23421,f23425,f23429,f23433,f23446,f23451,f23456,f23461,f23466,f23471,f23476,f23481,f23485,f23489,f23502,f23506,f23510,f23514,f23518,f23522,f23526,f23550,f23774,f24716,f25183,f25373,f25564,f25568,f25572,f25576,f25580,f25584,f25588,f25592,f25596,f25710,f25942,f25965,f25969,f25973,f25977,f25981,f25985,f25989,f25993,f25997,f26001,f26005,f26009,f26013,f26017,f26021,f26025,f26029,f26033,f26037,f26041,f26045,f26049,f26053,f26057,f26061,f26065,f26069,f26073,f26077,f26081,f26085,f26089,f26093,f26097,f26101,f26105,f26109,f26113,f26117,f26121,f26125,f26129,f26133,f26137,f26141,f26145,f26149,f26153,f26157,f26161,f26165,f26169,f26173,f26177,f26181,f26185,f26189,f26193,f26197,f26201,f26205,f26209,f26213,f26217,f26221,f26225,f26229,f26233,f26237,f26241,f26245,f26249,f26253,f26257,f26262,f26480,f26531,f26595,f26777,f27001,f27210,f27377,f27382,f27386,f27390,f27394,f27398,f27402,f27406,f27410,f27414,f27418,f27422,f27426,f27430,f27434,f27438,f27442,f27446,f27450,f27454,f27458,f27462,f27466,f27470,f27474,f27478,f27482,f27486,f27490,f27494,f27498,f27502,f27506,f27510,f27514,f27518,f27522,f27526,f27530,f27534,f27538,f27542,f27546,f27550,f27554,f27558,f27562,f27566,f27570,f27574,f27578,f27582,f27586,f27590,f27594,f27598,f27602,f27606,f27610,f27614,f27618,f27622,f27626,f27630,f27634,f27638,f27642,f27646,f27650,f27654,f27658,f27662,f27666,f27823,f27875,f27994,f28149,f28588,f29204,f29209,f29210]) ).
fof(f29210,plain,
( ~ spl263_129
| ~ spl263_1037
| spl263_1610 ),
inference(avatar_split_clause,[],[f28934,f28585,f15964,f8412]) ).
fof(f8412,plain,
( spl263_129
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_129])]) ).
fof(f15964,plain,
( spl263_1037
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1037])]) ).
fof(f28585,plain,
( spl263_1610
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1610])]) ).
fof(f28934,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl263_1037
| spl263_1610 ),
inference(resolution,[],[f28587,f15965]) ).
fof(f15965,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl263_1037 ),
inference(avatar_component_clause,[],[f15964]) ).
fof(f28587,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| spl263_1610 ),
inference(avatar_component_clause,[],[f28585]) ).
fof(f29209,plain,
( spl263_1612
| ~ spl263_408
| ~ spl263_1462
| ~ spl263_1611 ),
inference(avatar_split_clause,[],[f29205,f29202,f26003,f9875,f29207]) ).
fof(f29207,plain,
( spl263_1612
<=> ! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1612])]) ).
fof(f9875,plain,
( spl263_408
<=> ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_408])]) ).
fof(f26003,plain,
( spl263_1462
<=> ! [X2,X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1462])]) ).
fof(f29202,plain,
( spl263_1611
<=> ! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1611])]) ).
fof(f29205,plain,
( ! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_408
| ~ spl263_1462
| ~ spl263_1611 ),
inference(forward_demodulation,[],[f29203,f26452]) ).
fof(f26452,plain,
( ! [X2,X0,X1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2))
| ~ spl263_408
| ~ spl263_1462 ),
inference(resolution,[],[f26004,f9876]) ).
fof(f9876,plain,
( ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
| ~ spl263_408 ),
inference(avatar_component_clause,[],[f9875]) ).
fof(f26004,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) )
| ~ spl263_1462 ),
inference(avatar_component_clause,[],[f26003]) ).
fof(f29203,plain,
( ! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_1611 ),
inference(avatar_component_clause,[],[f29202]) ).
fof(f29204,plain,
spl263_1611,
inference(avatar_split_clause,[],[f5389,f29202]) ).
fof(f5389,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2798]) ).
fof(f2798,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(flattening,[],[f2797]) ).
fof(f2797,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f1739]) ).
fof(f1739,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1 ) ),
inference(rectify,[],[f658]) ).
fof(f658,axiom,
! [X10,X4] :
( is_fun_pname_bool(X4)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),bot_bo844097828e_bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f28588,plain,
( ~ spl263_1610
| ~ spl263_291
| spl263_23
| ~ spl263_1583 ),
inference(avatar_split_clause,[],[f28456,f27576,f7896,f9129,f28585]) ).
fof(f9129,plain,
( spl263_291
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_291])]) ).
fof(f7896,plain,
( spl263_23
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_23])]) ).
fof(f27576,plain,
( spl263_1583
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1583])]) ).
fof(f28456,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| spl263_23
| ~ spl263_1583 ),
inference(resolution,[],[f27577,f7898]) ).
fof(f7898,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
| spl263_23 ),
inference(avatar_component_clause,[],[f7896]) ).
fof(f27577,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl263_1583 ),
inference(avatar_component_clause,[],[f27576]) ).
fof(f28149,plain,
( spl263_1609
| ~ spl263_37
| ~ spl263_194 ),
inference(avatar_split_clause,[],[f8818,f8681,f7960,f28147]) ).
fof(f28147,plain,
( spl263_1609
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP5(cOMBB_bool_bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1609])]) ).
fof(f7960,plain,
( spl263_37
<=> ! [X0] :
( sP5(X0)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_37])]) ).
fof(f8681,plain,
( spl263_194
<=> ! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_194])]) ).
fof(f8818,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP5(cOMBB_bool_bool_a(X1,X0)) )
| ~ spl263_37
| ~ spl263_194 ),
inference(resolution,[],[f8682,f7961]) ).
fof(f7961,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| sP5(X0) )
| ~ spl263_37 ),
inference(avatar_component_clause,[],[f7960]) ).
fof(f8682,plain,
( ! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl263_194 ),
inference(avatar_component_clause,[],[f8681]) ).
fof(f27994,plain,
( spl263_1608
| ~ spl263_38
| ~ spl263_194 ),
inference(avatar_split_clause,[],[f8817,f8681,f7964,f27992]) ).
fof(f27992,plain,
( spl263_1608
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP7(cOMBB_bool_bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1608])]) ).
fof(f7964,plain,
( spl263_38
<=> ! [X0] :
( sP7(X0)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_38])]) ).
fof(f8817,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP7(cOMBB_bool_bool_a(X1,X0)) )
| ~ spl263_38
| ~ spl263_194 ),
inference(resolution,[],[f8682,f7965]) ).
fof(f7965,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| sP7(X0) )
| ~ spl263_38 ),
inference(avatar_component_clause,[],[f7964]) ).
fof(f27875,plain,
( spl263_1607
| ~ spl263_35
| ~ spl263_193 ),
inference(avatar_split_clause,[],[f8816,f8677,f7952,f27873]) ).
fof(f27873,plain,
( spl263_1607
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP1(image_a_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1607])]) ).
fof(f7952,plain,
( spl263_35
<=> ! [X0] :
( sP1(X0)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_35])]) ).
fof(f8677,plain,
( spl263_193
<=> ! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_193])]) ).
fof(f8816,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP1(image_a_pname(X1,X0)) )
| ~ spl263_35
| ~ spl263_193 ),
inference(resolution,[],[f8678,f7953]) ).
fof(f7953,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP1(X0) )
| ~ spl263_35 ),
inference(avatar_component_clause,[],[f7952]) ).
fof(f8678,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl263_193 ),
inference(avatar_component_clause,[],[f8677]) ).
fof(f27823,plain,
( spl263_1606
| ~ spl263_36
| ~ spl263_193 ),
inference(avatar_split_clause,[],[f8815,f8677,f7956,f27821]) ).
fof(f27821,plain,
( spl263_1606
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP3(image_a_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1606])]) ).
fof(f7956,plain,
( spl263_36
<=> ! [X0] :
( sP3(X0)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_36])]) ).
fof(f8815,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP3(image_a_pname(X1,X0)) )
| ~ spl263_36
| ~ spl263_193 ),
inference(resolution,[],[f8678,f7957]) ).
fof(f7957,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP3(X0) )
| ~ spl263_36 ),
inference(avatar_component_clause,[],[f7956]) ).
fof(f27666,plain,
( spl263_1605
| ~ spl263_87
| ~ spl263_246
| ~ spl263_1121
| ~ spl263_1533 ),
inference(avatar_split_clause,[],[f27378,f27375,f17679,f8932,f8200,f27664]) ).
fof(f27664,plain,
( spl263_1605
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0))
| zero_zero_nat = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1605])]) ).
fof(f8200,plain,
( spl263_87
<=> one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_87])]) ).
fof(f8932,plain,
( spl263_246
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_246])]) ).
fof(f17679,plain,
( spl263_1121
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1121])]) ).
fof(f27375,plain,
( spl263_1533
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1533])]) ).
fof(f27378,plain,
( ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0))
| zero_zero_nat = X1 )
| ~ spl263_87
| ~ spl263_246
| ~ spl263_1121
| ~ spl263_1533 ),
inference(forward_demodulation,[],[f27376,f18041]) ).
fof(f18041,plain,
( ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X0)
| ~ spl263_87
| ~ spl263_246
| ~ spl263_1121 ),
inference(forward_demodulation,[],[f18036,f8202]) ).
fof(f8202,plain,
( one_one_nat = hAPP_nat_nat(suc,zero_zero_nat)
| ~ spl263_87 ),
inference(avatar_component_clause,[],[f8200]) ).
fof(f18036,plain,
( ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X0)
| ~ spl263_246
| ~ spl263_1121 ),
inference(superposition,[],[f17680,f8933]) ).
fof(f8933,plain,
( ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0
| ~ spl263_246 ),
inference(avatar_component_clause,[],[f8932]) ).
fof(f17680,plain,
( ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))
| ~ spl263_1121 ),
inference(avatar_component_clause,[],[f17679]) ).
fof(f27376,plain,
( ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 )
| ~ spl263_1533 ),
inference(avatar_component_clause,[],[f27375]) ).
fof(f27662,plain,
spl263_1604,
inference(avatar_split_clause,[],[f7747,f27660]) ).
fof(f27660,plain,
( spl263_1604
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ sP35(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1604])]) ).
fof(f7747,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ sP35(X0,X1,X2) ),
inference(forward_demodulation,[],[f6834,f7397]) ).
fof(f7397,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0),
inference(forward_demodulation,[],[f4965,f4876]) ).
fof(f4876,plain,
! [X0] : collect_nat(X0) = X0,
inference(cnf_transformation,[],[f1422]) ).
fof(f1422,plain,
! [X0] : collect_nat(X0) = X0,
inference(rectify,[],[f488]) ).
fof(f488,axiom,
! [X12] : collect_nat(X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4965,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X0)),
inference(cnf_transformation,[],[f1511]) ).
fof(f1511,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X0)),
inference(rectify,[],[f748]) ).
fof(f748,axiom,
! [X7] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6834,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f4730]) ).
fof(f4730,plain,
! [X0,X1,X2] :
( ( sP35(X0,X1,X2)
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) )
| ~ sP35(X0,X1,X2) ) ),
inference(rectify,[],[f4729]) ).
fof(f4729,plain,
! [X2,X0,X1] :
( ( sP35(X2,X0,X1)
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
| ~ sP35(X2,X0,X1) ) ),
inference(flattening,[],[f4728]) ).
fof(f4728,plain,
! [X2,X0,X1] :
( ( sP35(X2,X0,X1)
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
| ~ sP35(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3976]) ).
fof(f3976,plain,
! [X2,X0,X1] :
( sP35(X2,X0,X1)
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP35])]) ).
fof(f27658,plain,
spl263_1603,
inference(avatar_split_clause,[],[f7746,f27656]) ).
fof(f27656,plain,
( spl263_1603
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
| sP35(X0,X1,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1603])]) ).
fof(f7746,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
| sP35(X0,X1,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(forward_demodulation,[],[f6837,f7397]) ).
fof(f6837,plain,
! [X2,X0,X1] :
( sP35(X0,X1,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0)) ),
inference(cnf_transformation,[],[f4730]) ).
fof(f27654,plain,
( spl263_1602
| ~ spl263_35
| ~ spl263_187 ),
inference(avatar_split_clause,[],[f8810,f8653,f7952,f27652]) ).
fof(f27652,plain,
( spl263_1602
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(hAPP_f759274231e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1602])]) ).
fof(f8653,plain,
( spl263_187
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_187])]) ).
fof(f8810,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(hAPP_f759274231e_bool(X1,X0)) )
| ~ spl263_35
| ~ spl263_187 ),
inference(resolution,[],[f8654,f7953]) ).
fof(f8654,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_187 ),
inference(avatar_component_clause,[],[f8653]) ).
fof(f27650,plain,
spl263_1601,
inference(avatar_split_clause,[],[f7744,f27648]) ).
fof(f27648,plain,
( spl263_1601
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ sP34(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1601])]) ).
fof(f7744,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ sP34(X0,X1,X2) ),
inference(forward_demodulation,[],[f6817,f7396]) ).
fof(f7396,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0),
inference(forward_demodulation,[],[f4964,f4874]) ).
fof(f4874,plain,
! [X0] : collect_int(X0) = X0,
inference(cnf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0] : collect_int(X0) = X0,
inference(rectify,[],[f487]) ).
fof(f487,axiom,
! [X12] : collect_int(X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4964,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X0)),
inference(cnf_transformation,[],[f1510]) ).
fof(f1510,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X0)),
inference(rectify,[],[f747]) ).
fof(f747,axiom,
! [X7] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6817,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f4720]) ).
fof(f4720,plain,
! [X0,X1,X2] :
( ( sP34(X0,X1,X2)
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) )
| ~ sP34(X0,X1,X2) ) ),
inference(rectify,[],[f4719]) ).
fof(f4719,plain,
! [X2,X0,X1] :
( ( sP34(X2,X0,X1)
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
| ~ sP34(X2,X0,X1) ) ),
inference(flattening,[],[f4718]) ).
fof(f4718,plain,
! [X2,X0,X1] :
( ( sP34(X2,X0,X1)
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
| ~ sP34(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3974]) ).
fof(f3974,plain,
! [X2,X0,X1] :
( sP34(X2,X0,X1)
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f27646,plain,
spl263_1600,
inference(avatar_split_clause,[],[f7743,f27644]) ).
fof(f27644,plain,
( spl263_1600
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
| sP34(X0,X1,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1600])]) ).
fof(f7743,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
| sP34(X0,X1,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(forward_demodulation,[],[f6820,f7396]) ).
fof(f6820,plain,
! [X2,X0,X1] :
( sP34(X0,X1,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0)) ),
inference(cnf_transformation,[],[f4720]) ).
fof(f27642,plain,
spl263_1599,
inference(avatar_split_clause,[],[f7685,f27640]) ).
fof(f27640,plain,
( spl263_1599
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1599])]) ).
fof(f7685,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ),
inference(forward_demodulation,[],[f6196,f4875]) ).
fof(f4875,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(cnf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(rectify,[],[f1178]) ).
fof(f1178,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6196,plain,
! [X2,X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) ),
inference(cnf_transformation,[],[f3282]) ).
fof(f3282,plain,
! [X0,X1,X2] :
( ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))),X1)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) ) ),
inference(ennf_transformation,[],[f2261]) ).
fof(f2261,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))),X1) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X1) ) ) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ) ),
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X155,X21,X132] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X155)),X21)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X132),X155))),X21) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X155)),X21)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),X21) ) ) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X155)),X21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X155)),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27638,plain,
spl263_1598,
inference(avatar_split_clause,[],[f7679,f27636]) ).
fof(f27636,plain,
( spl263_1598
<=> ! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1)))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1598])]) ).
fof(f7679,plain,
! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1)))),X2),
inference(forward_demodulation,[],[f6183,f4966]) ).
fof(f4966,plain,
! [X0] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)),
inference(cnf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)),
inference(rectify,[],[f746]) ).
fof(f746,axiom,
! [X7] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6183,plain,
! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2),
inference(cnf_transformation,[],[f2249]) ).
fof(f2249,plain,
! [X0,X1,X2] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2),
inference(rectify,[],[f662]) ).
fof(f662,axiom,
! [X4,X7,X9] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X9)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27634,plain,
spl263_1597,
inference(avatar_split_clause,[],[f7678,f27632]) ).
fof(f27632,plain,
( spl263_1597
<=> ! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1597])]) ).
fof(f7678,plain,
! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))),
inference(forward_demodulation,[],[f6182,f4966]) ).
fof(f6182,plain,
! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)),
inference(cnf_transformation,[],[f2248]) ).
fof(f2248,plain,
! [X0,X1,X2] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)),
inference(rectify,[],[f665]) ).
fof(f665,axiom,
! [X4,X7,X9] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X9)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27630,plain,
spl263_1596,
inference(avatar_split_clause,[],[f7550,f27628]) ).
fof(f27628,plain,
( spl263_1596
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1596])]) ).
fof(f7550,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
inference(forward_demodulation,[],[f7549,f4848]) ).
fof(f4848,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7549,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(forward_demodulation,[],[f7548,f4848]) ).
fof(f7548,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(forward_demodulation,[],[f5780,f4848]) ).
fof(f5780,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(cnf_transformation,[],[f3196]) ).
fof(f3196,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(flattening,[],[f3195]) ).
fof(f3195,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(ennf_transformation,[],[f2019]) ).
fof(f2019,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
inference(rectify,[],[f1117]) ).
fof(f1117,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27626,plain,
spl263_1595,
inference(avatar_split_clause,[],[f7547,f27624]) ).
fof(f27624,plain,
( spl263_1595
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1595])]) ).
fof(f7547,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
inference(forward_demodulation,[],[f7546,f4848]) ).
fof(f7546,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(forward_demodulation,[],[f5779,f4848]) ).
fof(f5779,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(cnf_transformation,[],[f3194]) ).
fof(f3194,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(flattening,[],[f3193]) ).
fof(f3193,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(ennf_transformation,[],[f2018]) ).
fof(f2018,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
inference(rectify,[],[f1115]) ).
fof(f1115,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27622,plain,
spl263_1594,
inference(avatar_split_clause,[],[f7545,f27620]) ).
fof(f27620,plain,
( spl263_1594
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1594])]) ).
fof(f7545,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ),
inference(forward_demodulation,[],[f7544,f4848]) ).
fof(f7544,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(forward_demodulation,[],[f5778,f4848]) ).
fof(f5778,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(cnf_transformation,[],[f3192]) ).
fof(f3192,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(flattening,[],[f3191]) ).
fof(f3191,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
inference(ennf_transformation,[],[f2017]) ).
fof(f2017,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ) ),
inference(rectify,[],[f1116]) ).
fof(f1116,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27618,plain,
spl263_1593,
inference(avatar_split_clause,[],[f7474,f27616]) ).
fof(f27616,plain,
( spl263_1593
<=> ! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1593])]) ).
fof(f7474,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(forward_demodulation,[],[f5412,f4966]) ).
fof(f5412,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2815]) ).
fof(f2815,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(flattening,[],[f2814]) ).
fof(f2814,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f1745]) ).
fof(f1745,plain,
! [X0,X1] :
( is_fun_a_bool(X1)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1 ) ),
inference(rectify,[],[f655]) ).
fof(f655,axiom,
! [X10,X4] :
( is_fun_a_bool(X4)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27614,plain,
spl263_1592,
inference(avatar_split_clause,[],[f7095,f27612]) ).
fof(f27612,plain,
( spl263_1592
<=> ! [X0,X1] :
( X0 = X1
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1592])]) ).
fof(f7095,plain,
! [X0,X1] :
( X0 = X1
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) ),
inference(definition_unfolding,[],[f5886,f4973,f4973]) ).
fof(f4973,plain,
! [X0] : bit1(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0),
inference(cnf_transformation,[],[f1519]) ).
fof(f1519,plain,
! [X0] : bit1(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0),
inference(rectify,[],[f1284]) ).
fof(f1284,axiom,
! [X21] : bit1(X21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X21)),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5886,plain,
! [X0,X1] :
( X0 = X1
| bit1(X0) != bit1(X1) ),
inference(cnf_transformation,[],[f4304]) ).
fof(f4304,plain,
! [X0,X1] :
( ( bit1(X0) = bit1(X1)
| X0 != X1 )
& ( X0 = X1
| bit1(X0) != bit1(X1) ) ),
inference(nnf_transformation,[],[f2081]) ).
fof(f2081,plain,
! [X0,X1] :
( bit1(X0) = bit1(X1)
<=> X0 = X1 ),
inference(rectify,[],[f1288]) ).
fof(f1288,axiom,
! [X15,X133] :
( bit1(X15) = bit1(X133)
<=> X15 = X133 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27610,plain,
( spl263_1591
| ~ spl263_36
| ~ spl263_187 ),
inference(avatar_split_clause,[],[f8809,f8653,f7956,f27608]) ).
fof(f27608,plain,
( spl263_1591
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(hAPP_f759274231e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1591])]) ).
fof(f8809,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(hAPP_f759274231e_bool(X1,X0)) )
| ~ spl263_36
| ~ spl263_187 ),
inference(resolution,[],[f8654,f7957]) ).
fof(f27606,plain,
spl263_1590,
inference(avatar_split_clause,[],[f7090,f27604]) ).
fof(f27604,plain,
( spl263_1590
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1590])]) ).
fof(f7090,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f5710,f4830,f4830,f4830]) ).
fof(f4830,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f1287]) ).
fof(f1287,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5710,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3104]) ).
fof(f3104,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(flattening,[],[f3103]) ).
fof(f3103,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f1956]) ).
fof(f1956,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0))) ) ),
inference(rectify,[],[f1192]) ).
fof(f1192,axiom,
! [X18,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X17),X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27602,plain,
spl263_1589,
inference(avatar_split_clause,[],[f7089,f27600]) ).
fof(f27600,plain,
( spl263_1589
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1589])]) ).
fof(f7089,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f5709,f4830,f4830,f4830]) ).
fof(f5709,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3102]) ).
fof(f3102,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(flattening,[],[f3101]) ).
fof(f3101,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f1955]) ).
fof(f1955,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0))) ) ),
inference(rectify,[],[f1190]) ).
fof(f1190,axiom,
! [X18,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X17),X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27598,plain,
spl263_1588,
inference(avatar_split_clause,[],[f7088,f27596]) ).
fof(f27596,plain,
( spl263_1588
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1588])]) ).
fof(f7088,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f5708,f4830,f4830,f4830]) ).
fof(f5708,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3100]) ).
fof(f3100,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(flattening,[],[f3099]) ).
fof(f3099,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f1954]) ).
fof(f1954,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0))) ) ),
inference(rectify,[],[f1235]) ).
fof(f1235,axiom,
! [X18,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X17),X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27594,plain,
spl263_1587,
inference(avatar_split_clause,[],[f6848,f27592]) ).
fof(f27592,plain,
( spl263_1587
<=> ! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1587])]) ).
fof(f6848,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
inference(cnf_transformation,[],[f4736]) ).
fof(f4736,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
| ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) )
& ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) )
| ~ sP36(X0,X1,X2) ) ),
inference(rectify,[],[f4735]) ).
fof(f4735,plain,
! [X0,X2,X1] :
( ( sP36(X0,X2,X1)
| ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
| ~ sP36(X0,X2,X1) ) ),
inference(flattening,[],[f4734]) ).
fof(f4734,plain,
! [X0,X2,X1] :
( ( sP36(X0,X2,X1)
| ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
| ~ sP36(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3978]) ).
fof(f3978,plain,
! [X0,X2,X1] :
( sP36(X0,X2,X1)
<=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f27590,plain,
spl263_1586,
inference(avatar_split_clause,[],[f6845,f27588]) ).
fof(f27588,plain,
( spl263_1586
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1586])]) ).
fof(f6845,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f4736]) ).
fof(f27586,plain,
spl263_1585,
inference(avatar_split_clause,[],[f6844,f27584]) ).
fof(f27584,plain,
( spl263_1585
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1585])]) ).
fof(f6844,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
inference(cnf_transformation,[],[f4733]) ).
fof(f4733,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
& ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
inference(flattening,[],[f4732]) ).
fof(f4732,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
& ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f2600]) ).
fof(f2600,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
inference(rectify,[],[f562]) ).
fof(f562,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)),X9))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27582,plain,
spl263_1584,
inference(avatar_split_clause,[],[f6827,f27580]) ).
fof(f27580,plain,
( spl263_1584
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1584])]) ).
fof(f6827,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ),
inference(cnf_transformation,[],[f4723]) ).
fof(f4723,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
& ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
inference(flattening,[],[f4722]) ).
fof(f4722,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
& ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f2596]) ).
fof(f2596,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
inference(rectify,[],[f561]) ).
fof(f561,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)),X9))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27578,plain,
spl263_1583,
inference(avatar_split_clause,[],[f6810,f27576]) ).
fof(f6810,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
inference(cnf_transformation,[],[f4713]) ).
fof(f4713,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(flattening,[],[f4712]) ).
fof(f4712,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f2592]) ).
fof(f2592,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
inference(rectify,[],[f560]) ).
fof(f560,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),X9))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27574,plain,
spl263_1582,
inference(avatar_split_clause,[],[f6796,f27572]) ).
fof(f27572,plain,
( spl263_1582
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1582])]) ).
fof(f6796,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ),
inference(cnf_transformation,[],[f4705]) ).
fof(f4705,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
& ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
inference(flattening,[],[f4704]) ).
fof(f4704,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
& ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f2589]) ).
fof(f2589,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
inference(rectify,[],[f563]) ).
fof(f563,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)),X9))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27570,plain,
spl263_1581,
inference(avatar_split_clause,[],[f6635,f27568]) ).
fof(f27568,plain,
( spl263_1581
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK238(X0,X2))))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1581])]) ).
fof(f6635,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK238(X0,X2))))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4619]) ).
fof(f4619,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ( ~ hBOOL(hAPP_nat_bool(X0,sK238(X0,X2)))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK238(X0,X2))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK238(X0,X2)),X2)) )
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK238])],[f3706,f4618]) ).
fof(f4618,plain,
! [X0,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK238(X0,X2)))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK238(X0,X2))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK238(X0,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3706,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(flattening,[],[f3705]) ).
fof(f3705,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2510]) ).
fof(f2510,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> ( hBOOL(hAPP_nat_bool(X0,X2))
=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
=> ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
=> hBOOL(hAPP_nat_bool(X0,X3)) ) )
=> hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
inference(rectify,[],[f1022]) ).
fof(f1022,axiom,
! [X12,X32,X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X119))
=> ( hBOOL(hAPP_nat_bool(X12,X119))
=> ( ! [X125] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X125),X119))
=> ( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(suc,X125)))
=> hBOOL(hAPP_nat_bool(X12,X125)) ) )
=> hBOOL(hAPP_nat_bool(X12,X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27566,plain,
( spl263_1580
| ~ spl263_35
| ~ spl263_186 ),
inference(avatar_split_clause,[],[f8808,f8649,f7952,f27564]) ).
fof(f27564,plain,
( spl263_1580
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(cOMBS_568398431l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1580])]) ).
fof(f8649,plain,
( spl263_186
<=> ! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_186])]) ).
fof(f8808,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(cOMBS_568398431l_bool(X1,X0)) )
| ~ spl263_35
| ~ spl263_186 ),
inference(resolution,[],[f8650,f7953]) ).
fof(f8650,plain,
( ! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_186 ),
inference(avatar_component_clause,[],[f8649]) ).
fof(f27562,plain,
spl263_1579,
inference(avatar_split_clause,[],[f6634,f27560]) ).
fof(f27560,plain,
( spl263_1579
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK238(X0,X2)),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1579])]) ).
fof(f6634,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK238(X0,X2)),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4619]) ).
fof(f27558,plain,
spl263_1578,
inference(avatar_split_clause,[],[f6596,f27556]) ).
fof(f27556,plain,
( spl263_1578
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK237(X0,X1)))
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1578])]) ).
fof(f6596,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK237(X0,X1)))
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f4617]) ).
fof(f4617,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X2))
| ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK237(X0,X1)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK237(X0,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK237(X0,X1))) )
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK237])],[f3659,f4616]) ).
fof(f4616,plain,
! [X0,X1] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
=> ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK237(X0,X1)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK237(X0,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK237(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f3659,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X2))
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(flattening,[],[f3658]) ).
fof(f3658,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X2))
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(ennf_transformation,[],[f2474]) ).
fof(f2474,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
=> ( hBOOL(hAPP_int_bool(X0,X1))
=> ( ! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
=> ( hBOOL(hAPP_int_bool(X0,X3))
=> hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X0,X2)) ) ) ),
inference(rectify,[],[f1189]) ).
fof(f1189,axiom,
! [X12,X15,X32] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X32))
=> ( hBOOL(hAPP_int_bool(X12,X15))
=> ( ! [X125] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X125))
=> ( hBOOL(hAPP_int_bool(X12,X125))
=> hBOOL(hAPP_int_bool(X12,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X125),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X12,X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27554,plain,
spl263_1577,
inference(avatar_split_clause,[],[f6593,f27552]) ).
fof(f27552,plain,
( spl263_1577
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK236(X0,X2)),X2))
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1577])]) ).
fof(f6593,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK236(X0,X2)),X2))
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f4615]) ).
fof(f4615,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X1))
| ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK236(X0,X2)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK236(X0,X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK236(X0,X2)),X2)) )
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK236])],[f3657,f4614]) ).
fof(f4614,plain,
! [X0,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
=> ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK236(X0,X2)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK236(X0,X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK236(X0,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3657,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(flattening,[],[f3656]) ).
fof(f3656,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(ennf_transformation,[],[f2473]) ).
fof(f2473,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
=> ( hBOOL(hAPP_int_bool(X0,X2))
=> ( ! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
=> ( hBOOL(hAPP_int_bool(X0,X3))
=> hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X0,X1)) ) ) ),
inference(rectify,[],[f1187]) ).
fof(f1187,axiom,
! [X12,X32,X15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X32),X15))
=> ( hBOOL(hAPP_int_bool(X12,X15))
=> ( ! [X125] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X125),X15))
=> ( hBOOL(hAPP_int_bool(X12,X125))
=> hBOOL(hAPP_int_bool(X12,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X125),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X12,X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27550,plain,
spl263_1576,
inference(avatar_split_clause,[],[f6563,f27548]) ).
fof(f27548,plain,
( spl263_1576
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1576])]) ).
fof(f6563,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f3614,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(flattening,[],[f3613]) ).
fof(f3613,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2447]) ).
fof(f2447,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0))) ) ),
inference(rectify,[],[f816]) ).
fof(f816,axiom,
! [X9,X31,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),X4))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),X9))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27546,plain,
spl263_1575,
inference(avatar_split_clause,[],[f6543,f27544]) ).
fof(f27544,plain,
( spl263_1575
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1575])]) ).
fof(f6543,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(cnf_transformation,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(flattening,[],[f3582]) ).
fof(f3582,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(ennf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0))) ) ),
inference(rectify,[],[f815]) ).
fof(f815,axiom,
! [X9,X31,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),X4))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),X9))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27542,plain,
spl263_1574,
inference(avatar_split_clause,[],[f6527,f27540]) ).
fof(f27540,plain,
( spl263_1574
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1574])]) ).
fof(f6527,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f3557]) ).
fof(f3557,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(flattening,[],[f3556]) ).
fof(f3556,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f2411]) ).
fof(f2411,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0))) ) ),
inference(rectify,[],[f817]) ).
fof(f817,axiom,
! [X9,X31,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),X4))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),X9))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27538,plain,
spl263_1573,
inference(avatar_split_clause,[],[f6523,f27536]) ).
fof(f27536,plain,
( spl263_1573
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1573])]) ).
fof(f6523,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3551]) ).
fof(f3551,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(flattening,[],[f3550]) ).
fof(f3550,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2407]) ).
fof(f2407,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0))) ) ),
inference(rectify,[],[f818]) ).
fof(f818,axiom,
! [X9,X31,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),X4))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),X9))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27534,plain,
spl263_1572,
inference(avatar_split_clause,[],[f6488,f27532]) ).
fof(f27532,plain,
( spl263_1572
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1572])]) ).
fof(f6488,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4580]) ).
fof(f4580,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))) ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(nnf_transformation,[],[f3520]) ).
fof(f3520,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2386]) ).
fof(f2386,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
inference(rectify,[],[f566]) ).
fof(f566,axiom,
! [X9,X10,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X9)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27530,plain,
spl263_1571,
inference(avatar_split_clause,[],[f6484,f27528]) ).
fof(f27528,plain,
( spl263_1571
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1571])]) ).
fof(f6484,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(cnf_transformation,[],[f4578]) ).
fof(f4578,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))) ) )
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(nnf_transformation,[],[f3517]) ).
fof(f3517,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) )
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(ennf_transformation,[],[f2384]) ).
fof(f2384,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) ) ),
inference(rectify,[],[f565]) ).
fof(f565,axiom,
! [X9,X10,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X9)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27526,plain,
spl263_1570,
inference(avatar_split_clause,[],[f6480,f27524]) ).
fof(f27524,plain,
( spl263_1570
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1570])]) ).
fof(f6480,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f4576]) ).
fof(f4576,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(nnf_transformation,[],[f3514]) ).
fof(f3514,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
inference(rectify,[],[f564]) ).
fof(f564,axiom,
! [X9,X10,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X9)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27522,plain,
( spl263_1569
| ~ spl263_36
| ~ spl263_186 ),
inference(avatar_split_clause,[],[f8807,f8649,f7956,f27520]) ).
fof(f27520,plain,
( spl263_1569
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(cOMBS_568398431l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1569])]) ).
fof(f8807,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(cOMBS_568398431l_bool(X1,X0)) )
| ~ spl263_36
| ~ spl263_186 ),
inference(resolution,[],[f8650,f7957]) ).
fof(f27518,plain,
spl263_1568,
inference(avatar_split_clause,[],[f6479,f27516]) ).
fof(f27516,plain,
( spl263_1568
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1568])]) ).
fof(f6479,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f4575]) ).
fof(f4575,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0))) ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(nnf_transformation,[],[f3513]) ).
fof(f3513,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2381]) ).
fof(f2381,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) ) ),
inference(rectify,[],[f567]) ).
fof(f567,axiom,
! [X9,X10,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X9)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27514,plain,
spl263_1567,
inference(avatar_split_clause,[],[f6478,f27512]) ).
fof(f27512,plain,
( spl263_1567
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1567])]) ).
fof(f6478,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f4575]) ).
fof(f27510,plain,
spl263_1566,
inference(avatar_split_clause,[],[f6301,f27508]) ).
fof(f27508,plain,
( spl263_1566
<=> ! [X2,X0,X1] :
( image_pname_a(X0,sK184(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1566])]) ).
fof(f6301,plain,
! [X2,X0,X1] :
( image_pname_a(X0,sK184(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4497]) ).
fof(f4497,plain,
! [X0,X1,X2] :
( ( image_pname_a(X0,sK184(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK184(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK184(X0,X1,X2)),X1))
& is_fun_pname_bool(sK184(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK184])],[f3341,f4496]) ).
fof(f4496,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_a(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_pname_a(X0,sK184(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK184(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK184(X0,X1,X2)),X1))
& is_fun_pname_bool(sK184(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3341,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_a(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3340]) ).
fof(f3340,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_a(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2293]) ).
fof(f2293,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
=> ? [X3] :
( image_pname_a(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_pname_a(X8,X4)))
=> ? [X26] :
( image_pname_a(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27506,plain,
spl263_1565,
inference(avatar_split_clause,[],[f6297,f27504]) ).
fof(f27504,plain,
( spl263_1565
<=> ! [X2,X0,X1] :
( image_int_a(X0,sK183(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1565])]) ).
fof(f6297,plain,
! [X2,X0,X1] :
( image_int_a(X0,sK183(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4495]) ).
fof(f4495,plain,
! [X0,X1,X2] :
( ( image_int_a(X0,sK183(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK183(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK183(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f3339,f4494]) ).
fof(f4494,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_a(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_int_a(X0,sK183(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK183(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK183(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3339,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_a(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3338]) ).
fof(f3338,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_a(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2292]) ).
fof(f2292,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
=> ? [X3] :
( image_int_a(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f363]) ).
fof(f363,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_int_a(X8,X4)))
=> ? [X26] :
( image_int_a(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27502,plain,
spl263_1564,
inference(avatar_split_clause,[],[f6294,f27500]) ).
fof(f27500,plain,
( spl263_1564
<=> ! [X2,X0,X1] :
( image_nat_a(X0,sK182(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1564])]) ).
fof(f6294,plain,
! [X2,X0,X1] :
( image_nat_a(X0,sK182(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4493]) ).
fof(f4493,plain,
! [X0,X1,X2] :
( ( image_nat_a(X0,sK182(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK182(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK182(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f3337,f4492]) ).
fof(f4492,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_a(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_nat_a(X0,sK182(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK182(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK182(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3337,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_a(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3336]) ).
fof(f3336,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_a(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2291]) ).
fof(f2291,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
=> ? [X3] :
( image_nat_a(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f357]) ).
fof(f357,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_nat_a(X8,X4)))
=> ? [X26] :
( image_nat_a(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27498,plain,
spl263_1563,
inference(avatar_split_clause,[],[f6291,f27496]) ).
fof(f27496,plain,
( spl263_1563
<=> ! [X2,X0,X1] :
( image_fun_nat_bool_a(X0,sK181(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1563])]) ).
fof(f6291,plain,
! [X2,X0,X1] :
( image_fun_nat_bool_a(X0,sK181(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4491]) ).
fof(f4491,plain,
! [X0,X1,X2] :
( ( image_fun_nat_bool_a(X0,sK181(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK181(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK181(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181])],[f3335,f4490]) ).
fof(f4490,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_nat_bool_a(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
=> ( image_fun_nat_bool_a(X0,sK181(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK181(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK181(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3335,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_nat_bool_a(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3334]) ).
fof(f3334,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_nat_bool_a(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2290]) ).
fof(f2290,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
=> ? [X3] :
( image_fun_nat_bool_a(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_nat_bool_a(X8,X4)))
=> ? [X26] :
( image_fun_nat_bool_a(X8,X26) = X9
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X26))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27494,plain,
spl263_1562,
inference(avatar_split_clause,[],[f6288,f27492]) ).
fof(f27492,plain,
( spl263_1562
<=> ! [X2,X0,X1] :
( image_fun_int_bool_a(X0,sK180(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1562])]) ).
fof(f6288,plain,
! [X2,X0,X1] :
( image_fun_int_bool_a(X0,sK180(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4489]) ).
fof(f4489,plain,
! [X0,X1,X2] :
( ( image_fun_int_bool_a(X0,sK180(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK180(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK180(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f3333,f4488]) ).
fof(f4488,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_int_bool_a(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
=> ( image_fun_int_bool_a(X0,sK180(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK180(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK180(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3333,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_int_bool_a(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3332]) ).
fof(f3332,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_int_bool_a(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2289]) ).
fof(f2289,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
=> ? [X3] :
( image_fun_int_bool_a(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f326]) ).
fof(f326,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_int_bool_a(X8,X4)))
=> ? [X26] :
( image_fun_int_bool_a(X8,X26) = X9
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X26))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27490,plain,
spl263_1561,
inference(avatar_split_clause,[],[f6285,f27488]) ).
fof(f27488,plain,
( spl263_1561
<=> ! [X2,X0,X1] :
( image_a_a(X0,sK179(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1561])]) ).
fof(f6285,plain,
! [X2,X0,X1] :
( image_a_a(X0,sK179(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4487]) ).
fof(f4487,plain,
! [X0,X1,X2] :
( ( image_a_a(X0,sK179(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK179(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK179(X0,X1,X2)),X1))
& is_fun_a_bool(sK179(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK179])],[f3331,f4486]) ).
fof(f4486,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_a(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_a(X0,sK179(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK179(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK179(X0,X1,X2)),X1))
& is_fun_a_bool(sK179(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3331,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_a(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3330]) ).
fof(f3330,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_a(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2288]) ).
fof(f2288,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
=> ? [X3] :
( image_a_a(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ) ),
inference(rectify,[],[f330]) ).
fof(f330,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_a_a(X8,X4)))
=> ? [X26] :
( image_a_a(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27486,plain,
spl263_1560,
inference(avatar_split_clause,[],[f6281,f27484]) ).
fof(f27484,plain,
( spl263_1560
<=> ! [X2,X0,X1] :
( image_fun_a_bool_a(X0,sK178(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1560])]) ).
fof(f6281,plain,
! [X2,X0,X1] :
( image_fun_a_bool_a(X0,sK178(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4485]) ).
fof(f4485,plain,
! [X0,X1,X2] :
( ( image_fun_a_bool_a(X0,sK178(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK178(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK178(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK178(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178])],[f3329,f4484]) ).
fof(f4484,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_a(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
=> ( image_fun_a_bool_a(X0,sK178(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK178(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK178(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK178(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3329,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_a(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3328]) ).
fof(f3328,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_a(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2287]) ).
fof(f2287,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
=> ? [X3] :
( image_fun_a_bool_a(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) ) ) ) ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_a_bool_a(X8,X4)))
=> ? [X26] :
( image_fun_a_bool_a(X8,X26) = X9
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X26))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X26),X4))
& is_fun949378684l_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27482,plain,
spl263_1559,
inference(avatar_split_clause,[],[f6277,f27480]) ).
fof(f27480,plain,
( spl263_1559
<=> ! [X2,X0,X1] :
( image_876012084bool_a(X0,sK177(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1559])]) ).
fof(f6277,plain,
! [X2,X0,X1] :
( image_876012084bool_a(X0,sK177(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4483]) ).
fof(f4483,plain,
! [X0,X1,X2] :
( ( image_876012084bool_a(X0,sK177(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK177(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK177(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK177(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f3327,f4482]) ).
fof(f4482,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_876012084bool_a(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
=> ( image_876012084bool_a(X0,sK177(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK177(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK177(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK177(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3327,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_876012084bool_a(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(flattening,[],[f3326]) ).
fof(f3326,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_876012084bool_a(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(ennf_transformation,[],[f2286]) ).
fof(f2286,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
=> ? [X3] :
( image_876012084bool_a(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) ) ) ) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X8,X4,X9] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_876012084bool_a(X8,X4)))
=> ? [X26] :
( image_876012084bool_a(X8,X26) = X9
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X26))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X26),X4))
& is_fun1661590463l_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27478,plain,
( spl263_1558
| ~ spl263_35
| ~ spl263_185 ),
inference(avatar_split_clause,[],[f8806,f8645,f7952,f27476]) ).
fof(f27476,plain,
( spl263_1558
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(image_pname_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1558])]) ).
fof(f8645,plain,
( spl263_185
<=> ! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_185])]) ).
fof(f8806,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(image_pname_pname(X1,X0)) )
| ~ spl263_35
| ~ spl263_185 ),
inference(resolution,[],[f8646,f7953]) ).
fof(f8646,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_185 ),
inference(avatar_component_clause,[],[f8645]) ).
fof(f27474,plain,
spl263_1557,
inference(avatar_split_clause,[],[f6270,f27472]) ).
fof(f27472,plain,
( spl263_1557
<=> ! [X2,X0,X1] :
( image_a_pname(X0,sK174(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1557])]) ).
fof(f6270,plain,
! [X2,X0,X1] :
( image_a_pname(X0,sK174(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4479]) ).
fof(f4479,plain,
! [X0,X1,X2] :
( ( image_a_pname(X0,sK174(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK174(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK174(X0,X1,X2)),X1))
& is_fun_a_bool(sK174(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f3323,f4478]) ).
fof(f4478,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_pname(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_pname(X0,sK174(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK174(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK174(X0,X1,X2)),X1))
& is_fun_a_bool(sK174(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3323,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_pname(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3322]) ).
fof(f3322,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_pname(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2284]) ).
fof(f2284,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
=> ? [X3] :
( image_a_pname(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ) ),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_a_pname(X8,X4)))
=> ? [X26] :
( image_a_pname(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27470,plain,
spl263_1556,
inference(avatar_split_clause,[],[f6266,f27468]) ).
fof(f27468,plain,
( spl263_1556
<=> ! [X2,X0,X1] :
( image_nat_pname(X0,sK173(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1556])]) ).
fof(f6266,plain,
! [X2,X0,X1] :
( image_nat_pname(X0,sK173(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4477]) ).
fof(f4477,plain,
! [X0,X1,X2] :
( ( image_nat_pname(X0,sK173(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK173(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK173(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173])],[f3321,f4476]) ).
fof(f4476,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_pname(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_nat_pname(X0,sK173(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK173(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK173(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3321,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_pname(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3320]) ).
fof(f3320,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_pname(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2283]) ).
fof(f2283,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
=> ? [X3] :
( image_nat_pname(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f362]) ).
fof(f362,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_nat_pname(X8,X4)))
=> ? [X26] :
( image_nat_pname(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27466,plain,
spl263_1555,
inference(avatar_split_clause,[],[f6263,f27464]) ).
fof(f27464,plain,
( spl263_1555
<=> ! [X2,X0,X1] :
( image_int_pname(X0,sK172(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1555])]) ).
fof(f6263,plain,
! [X2,X0,X1] :
( image_int_pname(X0,sK172(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4475]) ).
fof(f4475,plain,
! [X0,X1,X2] :
( ( image_int_pname(X0,sK172(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK172(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK172(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f3319,f4474]) ).
fof(f4474,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_pname(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_int_pname(X0,sK172(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK172(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK172(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3319,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_pname(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3318]) ).
fof(f3318,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_pname(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2282]) ).
fof(f2282,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
=> ? [X3] :
( image_int_pname(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f368]) ).
fof(f368,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_int_pname(X8,X4)))
=> ? [X26] :
( image_int_pname(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27462,plain,
spl263_1554,
inference(avatar_split_clause,[],[f6260,f27460]) ).
fof(f27460,plain,
( spl263_1554
<=> ! [X2,X0,X1] :
( image_1921560913_pname(X0,sK171(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1554])]) ).
fof(f6260,plain,
! [X2,X0,X1] :
( image_1921560913_pname(X0,sK171(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4473]) ).
fof(f4473,plain,
! [X0,X1,X2] :
( ( image_1921560913_pname(X0,sK171(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK171(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK171(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f3317,f4472]) ).
fof(f4472,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1921560913_pname(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
=> ( image_1921560913_pname(X0,sK171(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK171(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK171(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3317,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1921560913_pname(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3316]) ).
fof(f3316,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1921560913_pname(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2281]) ).
fof(f2281,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
=> ? [X3] :
( image_1921560913_pname(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1921560913_pname(X8,X4)))
=> ? [X26] :
( image_1921560913_pname(X8,X26) = X9
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X26))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27458,plain,
spl263_1553,
inference(avatar_split_clause,[],[f6257,f27456]) ).
fof(f27456,plain,
( spl263_1553
<=> ! [X2,X0,X1] :
( image_62782965_pname(X0,sK170(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1553])]) ).
fof(f6257,plain,
! [X2,X0,X1] :
( image_62782965_pname(X0,sK170(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4471]) ).
fof(f4471,plain,
! [X0,X1,X2] :
( ( image_62782965_pname(X0,sK170(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK170(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK170(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f3315,f4470]) ).
fof(f4470,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_62782965_pname(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
=> ( image_62782965_pname(X0,sK170(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK170(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK170(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3315,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_62782965_pname(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3314]) ).
fof(f3314,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_62782965_pname(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2280]) ).
fof(f2280,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
=> ? [X3] :
( image_62782965_pname(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f336]) ).
fof(f336,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_62782965_pname(X8,X4)))
=> ? [X26] :
( image_62782965_pname(X8,X26) = X9
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X26))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27454,plain,
spl263_1552,
inference(avatar_split_clause,[],[f6254,f27452]) ).
fof(f27452,plain,
( spl263_1552
<=> ! [X2,X0,X1] :
( image_pname_pname(X0,sK169(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1552])]) ).
fof(f6254,plain,
! [X2,X0,X1] :
( image_pname_pname(X0,sK169(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4469]) ).
fof(f4469,plain,
! [X0,X1,X2] :
( ( image_pname_pname(X0,sK169(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK169(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK169(X0,X1,X2)),X1))
& is_fun_pname_bool(sK169(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f3313,f4468]) ).
fof(f4468,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_pname(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_pname_pname(X0,sK169(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK169(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK169(X0,X1,X2)),X1))
& is_fun_pname_bool(sK169(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3313,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_pname(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3312]) ).
fof(f3312,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_pname(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2279]) ).
fof(f2279,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
=> ? [X3] :
( image_pname_pname(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ) ),
inference(rectify,[],[f356]) ).
fof(f356,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_pname_pname(X8,X4)))
=> ? [X26] :
( image_pname_pname(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27450,plain,
spl263_1551,
inference(avatar_split_clause,[],[f6250,f27448]) ).
fof(f27448,plain,
( spl263_1551
<=> ! [X2,X0,X1] :
( image_1854862208_pname(X0,sK168(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1551])]) ).
fof(f6250,plain,
! [X2,X0,X1] :
( image_1854862208_pname(X0,sK168(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4467]) ).
fof(f4467,plain,
! [X0,X1,X2] :
( ( image_1854862208_pname(X0,sK168(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK168(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK168(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK168(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f3311,f4466]) ).
fof(f4466,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1854862208_pname(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
=> ( image_1854862208_pname(X0,sK168(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK168(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK168(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK168(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3311,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1854862208_pname(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3310]) ).
fof(f3310,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1854862208_pname(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2278]) ).
fof(f2278,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
=> ? [X3] :
( image_1854862208_pname(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) ) ) ) ),
inference(rectify,[],[f339]) ).
fof(f339,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1854862208_pname(X8,X4)))
=> ? [X26] :
( image_1854862208_pname(X8,X26) = X9
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X26))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X26),X4))
& is_fun949378684l_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27446,plain,
spl263_1550,
inference(avatar_split_clause,[],[f6246,f27444]) ).
fof(f27444,plain,
( spl263_1550
<=> ! [X2,X0,X1] :
( image_1283814551_pname(X0,sK167(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1550])]) ).
fof(f6246,plain,
! [X2,X0,X1] :
( image_1283814551_pname(X0,sK167(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4465]) ).
fof(f4465,plain,
! [X0,X1,X2] :
( ( image_1283814551_pname(X0,sK167(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK167(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK167(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK167(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f3309,f4464]) ).
fof(f4464,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1283814551_pname(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
=> ( image_1283814551_pname(X0,sK167(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK167(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK167(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK167(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3309,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1283814551_pname(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(flattening,[],[f3308]) ).
fof(f3308,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1283814551_pname(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(ennf_transformation,[],[f2277]) ).
fof(f2277,plain,
! [X0,X1,X2] :
( is_fun_pname_bool(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
=> ? [X3] :
( image_1283814551_pname(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) ) ) ) ),
inference(rectify,[],[f338]) ).
fof(f338,axiom,
! [X8,X4,X9] :
( is_fun_pname_bool(X9)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1283814551_pname(X8,X4)))
=> ? [X26] :
( image_1283814551_pname(X8,X26) = X9
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X26))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X26),X4))
& is_fun1661590463l_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27442,plain,
spl263_1549,
inference(avatar_split_clause,[],[f6242,f27440]) ).
fof(f27440,plain,
( spl263_1549
<=> ! [X2,X0,X1] :
( image_nat_fun_a_bool(X0,sK166(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1549])]) ).
fof(f6242,plain,
! [X2,X0,X1] :
( image_nat_fun_a_bool(X0,sK166(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4463]) ).
fof(f4463,plain,
! [X0,X1,X2] :
( ( image_nat_fun_a_bool(X0,sK166(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK166(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK166(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f3307,f4462]) ).
fof(f4462,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_nat_fun_a_bool(X0,sK166(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK166(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK166(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3307,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(flattening,[],[f3306]) ).
fof(f3306,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(ennf_transformation,[],[f2276]) ).
fof(f2276,plain,
! [X0,X1,X2] :
( is_fun949378684l_bool(X2)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
=> ? [X3] :
( image_nat_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X8,X4,X9] :
( is_fun949378684l_bool(X9)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_nat_fun_a_bool(X8,X4)))
=> ? [X26] :
( image_nat_fun_a_bool(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27438,plain,
spl263_1548,
inference(avatar_split_clause,[],[f6239,f27436]) ).
fof(f27436,plain,
( spl263_1548
<=> ! [X2,X0,X1] :
( image_int_fun_a_bool(X0,sK165(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1548])]) ).
fof(f6239,plain,
! [X2,X0,X1] :
( image_int_fun_a_bool(X0,sK165(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4461]) ).
fof(f4461,plain,
! [X0,X1,X2] :
( ( image_int_fun_a_bool(X0,sK165(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK165(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK165(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f3305,f4460]) ).
fof(f4460,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_int_fun_a_bool(X0,sK165(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK165(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK165(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3305,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(flattening,[],[f3304]) ).
fof(f3304,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_int_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(ennf_transformation,[],[f2275]) ).
fof(f2275,plain,
! [X0,X1,X2] :
( is_fun949378684l_bool(X2)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
=> ? [X3] :
( image_int_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f367]) ).
fof(f367,axiom,
! [X8,X4,X9] :
( is_fun949378684l_bool(X9)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_int_fun_a_bool(X8,X4)))
=> ? [X26] :
( image_int_fun_a_bool(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27434,plain,
( spl263_1547
| ~ spl263_36
| ~ spl263_185 ),
inference(avatar_split_clause,[],[f8805,f8645,f7956,f27432]) ).
fof(f27432,plain,
( spl263_1547
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(image_pname_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1547])]) ).
fof(f8805,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(image_pname_pname(X1,X0)) )
| ~ spl263_36
| ~ spl263_185 ),
inference(resolution,[],[f8646,f7957]) ).
fof(f27430,plain,
spl263_1546,
inference(avatar_split_clause,[],[f6236,f27428]) ).
fof(f27428,plain,
( spl263_1546
<=> ! [X2,X0,X1] :
( image_112932426a_bool(X0,sK164(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1546])]) ).
fof(f6236,plain,
! [X2,X0,X1] :
( image_112932426a_bool(X0,sK164(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4459]) ).
fof(f4459,plain,
! [X0,X1,X2] :
( ( image_112932426a_bool(X0,sK164(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK164(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK164(X0,X1,X2)),X1))
& is_fun_pname_bool(sK164(X0,X1,X2)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f3303,f4458]) ).
fof(f4458,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_112932426a_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_112932426a_bool(X0,sK164(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK164(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK164(X0,X1,X2)),X1))
& is_fun_pname_bool(sK164(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3303,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_112932426a_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(flattening,[],[f3302]) ).
fof(f3302,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_112932426a_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(ennf_transformation,[],[f2274]) ).
fof(f2274,plain,
! [X0,X1,X2] :
( is_fun949378684l_bool(X2)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
=> ? [X3] :
( image_112932426a_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ) ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X8,X4,X9] :
( is_fun949378684l_bool(X9)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_112932426a_bool(X8,X4)))
=> ? [X26] :
( image_112932426a_bool(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27426,plain,
spl263_1545,
inference(avatar_split_clause,[],[f6232,f27424]) ).
fof(f27424,plain,
( spl263_1545
<=> ! [X2,X0,X1] :
( image_a_fun_a_bool(X0,sK163(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1545])]) ).
fof(f6232,plain,
! [X2,X0,X1] :
( image_a_fun_a_bool(X0,sK163(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4457]) ).
fof(f4457,plain,
! [X0,X1,X2] :
( ( image_a_fun_a_bool(X0,sK163(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK163(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK163(X0,X1,X2)),X1))
& is_fun_a_bool(sK163(X0,X1,X2)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f3301,f4456]) ).
fof(f4456,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_fun_a_bool(X0,sK163(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK163(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK163(X0,X1,X2)),X1))
& is_fun_a_bool(sK163(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3301,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(flattening,[],[f3300]) ).
fof(f3300,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(ennf_transformation,[],[f2273]) ).
fof(f2273,plain,
! [X0,X1,X2] :
( is_fun949378684l_bool(X2)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
=> ? [X3] :
( image_a_fun_a_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ) ),
inference(rectify,[],[f334]) ).
fof(f334,axiom,
! [X8,X4,X9] :
( is_fun949378684l_bool(X9)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_a_fun_a_bool(X8,X4)))
=> ? [X26] :
( image_a_fun_a_bool(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27422,plain,
spl263_1544,
inference(avatar_split_clause,[],[f6228,f27420]) ).
fof(f27420,plain,
( spl263_1544
<=> ! [X2,X0,X1] :
( image_1655916159e_bool(X0,sK162(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1544])]) ).
fof(f6228,plain,
! [X2,X0,X1] :
( image_1655916159e_bool(X0,sK162(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4455]) ).
fof(f4455,plain,
! [X0,X1,X2] :
( ( image_1655916159e_bool(X0,sK162(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK162(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK162(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f3299,f4454]) ).
fof(f4454,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1655916159e_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_1655916159e_bool(X0,sK162(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK162(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK162(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3299,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1655916159e_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(flattening,[],[f3298]) ).
fof(f3298,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1655916159e_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(ennf_transformation,[],[f2272]) ).
fof(f2272,plain,
! [X0,X1,X2] :
( is_fun1661590463l_bool(X2)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
=> ? [X3] :
( image_1655916159e_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f360]) ).
fof(f360,axiom,
! [X8,X4,X9] :
( is_fun1661590463l_bool(X9)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_1655916159e_bool(X8,X4)))
=> ? [X26] :
( image_1655916159e_bool(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27418,plain,
spl263_1543,
inference(avatar_split_clause,[],[f6225,f27416]) ).
fof(f27416,plain,
( spl263_1543
<=> ! [X2,X0,X1] :
( image_637364955e_bool(X0,sK161(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1543])]) ).
fof(f6225,plain,
! [X2,X0,X1] :
( image_637364955e_bool(X0,sK161(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4453]) ).
fof(f4453,plain,
! [X0,X1,X2] :
( ( image_637364955e_bool(X0,sK161(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK161(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK161(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f3297,f4452]) ).
fof(f4452,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_637364955e_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_637364955e_bool(X0,sK161(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK161(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK161(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3297,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_637364955e_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(flattening,[],[f3296]) ).
fof(f3296,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_637364955e_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(ennf_transformation,[],[f2271]) ).
fof(f2271,plain,
! [X0,X1,X2] :
( is_fun1661590463l_bool(X2)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
=> ? [X3] :
( image_637364955e_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ) ),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X8,X4,X9] :
( is_fun1661590463l_bool(X9)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_637364955e_bool(X8,X4)))
=> ? [X26] :
( image_637364955e_bool(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27414,plain,
spl263_1542,
inference(avatar_split_clause,[],[f6222,f27412]) ).
fof(f27412,plain,
( spl263_1542
<=> ! [X2,X0,X1] :
( image_47868345e_bool(X0,sK160(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1542])]) ).
fof(f6222,plain,
! [X2,X0,X1] :
( image_47868345e_bool(X0,sK160(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4451]) ).
fof(f4451,plain,
! [X0,X1,X2] :
( ( image_47868345e_bool(X0,sK160(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK160(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK160(X0,X1,X2)),X1))
& is_fun_pname_bool(sK160(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f3295,f4450]) ).
fof(f4450,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_47868345e_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_47868345e_bool(X0,sK160(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK160(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK160(X0,X1,X2)),X1))
& is_fun_pname_bool(sK160(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3295,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_47868345e_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(flattening,[],[f3294]) ).
fof(f3294,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_47868345e_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(ennf_transformation,[],[f2270]) ).
fof(f2270,plain,
! [X0,X1,X2] :
( is_fun1661590463l_bool(X2)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
=> ? [X3] :
( image_47868345e_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ) ),
inference(rectify,[],[f354]) ).
fof(f354,axiom,
! [X8,X4,X9] :
( is_fun1661590463l_bool(X9)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_47868345e_bool(X8,X4)))
=> ? [X26] :
( image_47868345e_bool(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27410,plain,
spl263_1541,
inference(avatar_split_clause,[],[f6218,f27408]) ).
fof(f27408,plain,
( spl263_1541
<=> ! [X2,X0,X1] :
( image_819518260e_bool(X0,sK159(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1541])]) ).
fof(f6218,plain,
! [X2,X0,X1] :
( image_819518260e_bool(X0,sK159(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4449]) ).
fof(f4449,plain,
! [X0,X1,X2] :
( ( image_819518260e_bool(X0,sK159(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK159(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK159(X0,X1,X2)),X1))
& is_fun_a_bool(sK159(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f3293,f4448]) ).
fof(f4448,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_819518260e_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_819518260e_bool(X0,sK159(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK159(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK159(X0,X1,X2)),X1))
& is_fun_a_bool(sK159(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3293,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_819518260e_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(flattening,[],[f3292]) ).
fof(f3292,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_819518260e_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(ennf_transformation,[],[f2269]) ).
fof(f2269,plain,
! [X0,X1,X2] :
( is_fun1661590463l_bool(X2)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
=> ? [X3] :
( image_819518260e_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ) ),
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X8,X4,X9] :
( is_fun1661590463l_bool(X9)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_819518260e_bool(X8,X4)))
=> ? [X26] :
( image_819518260e_bool(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27406,plain,
spl263_1540,
inference(avatar_split_clause,[],[f6085,f27404]) ).
fof(f27404,plain,
( spl263_1540
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1540])]) ).
fof(f6085,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ),
inference(cnf_transformation,[],[f4437]) ).
fof(f4437,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
inference(flattening,[],[f4436]) ).
fof(f4436,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
inference(nnf_transformation,[],[f2157]) ).
fof(f2157,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(rectify,[],[f1058]) ).
fof(f1058,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27402,plain,
spl263_1539,
inference(avatar_split_clause,[],[f6082,f27400]) ).
fof(f27400,plain,
( spl263_1539
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1539])]) ).
fof(f6082,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f4434]) ).
fof(f4434,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
inference(flattening,[],[f4433]) ).
fof(f4433,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
inference(nnf_transformation,[],[f2155]) ).
fof(f2155,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(rectify,[],[f1109]) ).
fof(f1109,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27398,plain,
spl263_1538,
inference(avatar_split_clause,[],[f5712,f27396]) ).
fof(f27396,plain,
( spl263_1538
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1538])]) ).
fof(f5712,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f3107]) ).
fof(f3107,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(flattening,[],[f3106]) ).
fof(f3106,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(ennf_transformation,[],[f1958]) ).
fof(f1958,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)) ) ),
inference(rectify,[],[f1060]) ).
fof(f1060,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27394,plain,
spl263_1537,
inference(avatar_split_clause,[],[f5675,f27392]) ).
fof(f27392,plain,
( spl263_1537
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK128(X0)),sK129(X0))))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1537])]) ).
fof(f5675,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK128(X0)),sK129(X0))))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4234]) ).
fof(f4234,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK128(X0)),sK129(X0))))
& hBOOL(hAPP_f54304608l_bool(X0,sK129(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK128(X0)),sK129(X0)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129])],[f3063,f4233]) ).
fof(f4233,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK128(X0)),sK129(X0))))
& hBOOL(hAPP_f54304608l_bool(X0,sK129(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK128(X0)),sK129(X0)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3063,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f3062]) ).
fof(f3062,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1930]) ).
fof(f1930,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
=> ( ! [X2,X3] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
=> ( hBOOL(hAPP_f54304608l_bool(X0,X3))
=> hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ) ),
inference(rectify,[],[f796]) ).
fof(f796,axiom,
! [X12,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> ( hBOOL(hAPP_f54304608l_bool(X12,bot_bot_fun_nat_bool))
=> ( ! [X29,X78] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X78))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X78))
=> ( hBOOL(hAPP_f54304608l_bool(X12,X78))
=> hBOOL(hAPP_f54304608l_bool(X12,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),X78))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X12,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27390,plain,
( spl263_1536
| ~ spl263_35
| ~ spl263_184 ),
inference(avatar_split_clause,[],[f8804,f8641,f7952,f27388]) ).
fof(f27388,plain,
( spl263_1536
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(cOMBB_647938656_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1536])]) ).
fof(f8641,plain,
( spl263_184
<=> ! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_184])]) ).
fof(f8804,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP1(cOMBB_647938656_pname(X1,X0)) )
| ~ spl263_35
| ~ spl263_184 ),
inference(resolution,[],[f8642,f7953]) ).
fof(f8642,plain,
( ! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_184 ),
inference(avatar_component_clause,[],[f8641]) ).
fof(f27386,plain,
spl263_1535,
inference(avatar_split_clause,[],[f5632,f27384]) ).
fof(f27384,plain,
( spl263_1535
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK121(X0)),sK122(X0))))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1535])]) ).
fof(f5632,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK121(X0)),sK122(X0))))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4223]) ).
fof(f4223,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK121(X0)),sK122(X0))))
& hBOOL(hAPP_f448129468l_bool(X0,sK122(X0)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK121(X0)),sK122(X0)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK122(X0))) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121,sK122])],[f3023,f4222]) ).
fof(f4222,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK121(X0)),sK122(X0))))
& hBOOL(hAPP_f448129468l_bool(X0,sK122(X0)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK121(X0)),sK122(X0)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK122(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3023,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f3022]) ).
fof(f3022,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1901]) ).
fof(f1901,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
=> ( ! [X2,X3] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
=> ( hBOOL(hAPP_f448129468l_bool(X0,X3))
=> hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X0,X1)) ) ) ),
inference(rectify,[],[f795]) ).
fof(f795,axiom,
! [X12,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> ( hBOOL(hAPP_f448129468l_bool(X12,bot_bot_fun_int_bool))
=> ( ! [X29,X78] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X78))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X78))
=> ( hBOOL(hAPP_f448129468l_bool(X12,X78))
=> hBOOL(hAPP_f448129468l_bool(X12,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),X78))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X12,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27382,plain,
spl263_1534,
inference(avatar_split_clause,[],[f5537,f27380]) ).
fof(f27380,plain,
( spl263_1534
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1534])]) ).
fof(f5537,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2947]) ).
fof(f2947,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1845]) ).
fof(f1845,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f760]) ).
fof(f760,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27377,plain,
spl263_1533,
inference(avatar_split_clause,[],[f5303,f27375]) ).
fof(f5303,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 ),
inference(cnf_transformation,[],[f2754]) ).
fof(f2754,plain,
! [X0,X1] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 )
& ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)
| zero_zero_nat != X1 ) ),
inference(ennf_transformation,[],[f1697]) ).
fof(f1697,plain,
! [X0,X1] :
( ( zero_zero_nat != X1
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
& ( zero_zero_nat = X1
=> zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ) ),
inference(rectify,[],[f1121]) ).
fof(f1121,axiom,
! [X13,X14] :
( ( zero_zero_nat != X14
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),one_one_nat)),X13)) )
& ( zero_zero_nat = X14
=> zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f27210,plain,
( spl263_1532
| ~ spl263_36
| ~ spl263_184 ),
inference(avatar_split_clause,[],[f8803,f8641,f7956,f27208]) ).
fof(f27208,plain,
( spl263_1532
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(cOMBB_647938656_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1532])]) ).
fof(f8803,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP3(cOMBB_647938656_pname(X1,X0)) )
| ~ spl263_36
| ~ spl263_184 ),
inference(resolution,[],[f8642,f7957]) ).
fof(f27001,plain,
( spl263_1531
| ~ spl263_37
| ~ spl263_178 ),
inference(avatar_split_clause,[],[f8798,f8617,f7960,f26999]) ).
fof(f26999,plain,
( spl263_1531
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP5(image_fun_a_bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1531])]) ).
fof(f8617,plain,
( spl263_178
<=> ! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_178])]) ).
fof(f8798,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP5(image_fun_a_bool_a(X1,X0)) )
| ~ spl263_37
| ~ spl263_178 ),
inference(resolution,[],[f8618,f7961]) ).
fof(f8618,plain,
( ! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl263_178 ),
inference(avatar_component_clause,[],[f8617]) ).
fof(f26777,plain,
( spl263_1530
| ~ spl263_38
| ~ spl263_178 ),
inference(avatar_split_clause,[],[f8797,f8617,f7964,f26775]) ).
fof(f26775,plain,
( spl263_1530
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP7(image_fun_a_bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1530])]) ).
fof(f8797,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP7(image_fun_a_bool_a(X1,X0)) )
| ~ spl263_38
| ~ spl263_178 ),
inference(resolution,[],[f8618,f7965]) ).
fof(f26595,plain,
( spl263_1529
| ~ spl263_37
| ~ spl263_176 ),
inference(avatar_split_clause,[],[f8796,f8609,f7960,f26593]) ).
fof(f26593,plain,
( spl263_1529
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP5(cOMBB_1273333599bool_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1529])]) ).
fof(f8609,plain,
( spl263_176
<=> ! [X0,X1] :
( is_fun_a_bool(cOMBB_1273333599bool_a(X0,X1))
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_176])]) ).
fof(f8796,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP5(cOMBB_1273333599bool_a(X0,X1)) )
| ~ spl263_37
| ~ spl263_176 ),
inference(resolution,[],[f8610,f7961]) ).
fof(f8610,plain,
( ! [X0,X1] :
( is_fun_a_bool(cOMBB_1273333599bool_a(X0,X1))
| ~ is_fun949378684l_bool(X0) )
| ~ spl263_176 ),
inference(avatar_component_clause,[],[f8609]) ).
fof(f26531,plain,
( spl263_1528
| ~ spl263_38
| ~ spl263_176 ),
inference(avatar_split_clause,[],[f8795,f8609,f7964,f26529]) ).
fof(f26529,plain,
( spl263_1528
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP7(cOMBB_1273333599bool_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1528])]) ).
fof(f8795,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP7(cOMBB_1273333599bool_a(X0,X1)) )
| ~ spl263_38
| ~ spl263_176 ),
inference(resolution,[],[f8610,f7965]) ).
fof(f26480,plain,
( spl263_1527
| ~ spl263_35
| ~ spl263_175 ),
inference(avatar_split_clause,[],[f8794,f8605,f7952,f26478]) ).
fof(f26478,plain,
( spl263_1527
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP1(image_1854862208_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1527])]) ).
fof(f8605,plain,
( spl263_175
<=> ! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_175])]) ).
fof(f8794,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP1(image_1854862208_pname(X1,X0)) )
| ~ spl263_35
| ~ spl263_175 ),
inference(resolution,[],[f8606,f7953]) ).
fof(f8606,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl263_175 ),
inference(avatar_component_clause,[],[f8605]) ).
fof(f26262,plain,
( spl263_1526
| ~ spl263_36
| ~ spl263_175 ),
inference(avatar_split_clause,[],[f8793,f8605,f7956,f26260]) ).
fof(f26260,plain,
( spl263_1526
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP3(image_1854862208_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1526])]) ).
fof(f8793,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| sP3(image_1854862208_pname(X1,X0)) )
| ~ spl263_36
| ~ spl263_175 ),
inference(resolution,[],[f8606,f7957]) ).
fof(f26257,plain,
spl263_1525,
inference(avatar_split_clause,[],[f7677,f26255]) ).
fof(f26255,plain,
( spl263_1525
<=> ! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1525])]) ).
fof(f7677,plain,
! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1))),X2),
inference(forward_demodulation,[],[f6181,f7397]) ).
fof(f6181,plain,
! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2),
inference(cnf_transformation,[],[f2247]) ).
fof(f2247,plain,
! [X0,X1,X2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2),
inference(rectify,[],[f663]) ).
fof(f663,axiom,
! [X4,X7,X9] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26253,plain,
spl263_1524,
inference(avatar_split_clause,[],[f7676,f26251]) ).
fof(f26251,plain,
( spl263_1524
<=> ! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_n1699378549t_bool(fequal_nat,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1524])]) ).
fof(f7676,plain,
! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_n1699378549t_bool(fequal_nat,X1)),
inference(forward_demodulation,[],[f6180,f7397]) ).
fof(f6180,plain,
! [X2,X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)),
inference(cnf_transformation,[],[f2246]) ).
fof(f2246,plain,
! [X0,X1,X2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)),
inference(rectify,[],[f666]) ).
fof(f666,axiom,
! [X4,X7,X9] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26249,plain,
spl263_1523,
inference(avatar_split_clause,[],[f7675,f26247]) ).
fof(f26247,plain,
( spl263_1523
<=> ! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1523])]) ).
fof(f7675,plain,
! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1))),X2),
inference(forward_demodulation,[],[f6179,f7396]) ).
fof(f6179,plain,
! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2),
inference(cnf_transformation,[],[f2245]) ).
fof(f2245,plain,
! [X0,X1,X2] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2),
inference(rectify,[],[f664]) ).
fof(f664,axiom,
! [X4,X7,X9] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26245,plain,
spl263_1522,
inference(avatar_split_clause,[],[f7674,f26243]) ).
fof(f26243,plain,
( spl263_1522
<=> ! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_i1948725293t_bool(fequal_int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1522])]) ).
fof(f7674,plain,
! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_i1948725293t_bool(fequal_int,X1)),
inference(forward_demodulation,[],[f6178,f7396]) ).
fof(f6178,plain,
! [X2,X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)),
inference(cnf_transformation,[],[f2244]) ).
fof(f2244,plain,
! [X0,X1,X2] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)),
inference(rectify,[],[f667]) ).
fof(f667,axiom,
! [X4,X7,X9] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26241,plain,
spl263_1521,
inference(avatar_split_clause,[],[f7496,f26239]) ).
fof(f26239,plain,
( spl263_1521
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1521])]) ).
fof(f7496,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(forward_demodulation,[],[f5577,f4966]) ).
fof(f5577,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2981]) ).
fof(f2981,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1870]) ).
fof(f1870,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f757]) ).
fof(f757,axiom,
! [X10,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26237,plain,
spl263_1520,
inference(avatar_split_clause,[],[f6475,f26235]) ).
fof(f26235,plain,
( spl263_1520
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK222(X1,X2)),one_one_int)))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1520])]) ).
fof(f6475,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK222(X1,X2)),one_one_int)))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4572]) ).
fof(f4572,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X0))
| ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK222(X1,X2)),one_one_int)))
& hBOOL(hAPP_int_bool(X1,sK222(X1,X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK222(X1,X2)),X2)) )
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK222])],[f4570,f4571]) ).
fof(f4571,plain,
! [X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
=> ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK222(X1,X2)),one_one_int)))
& hBOOL(hAPP_int_bool(X1,sK222(X1,X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK222(X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4570,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X0))
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rectify,[],[f3955]) ).
fof(f3955,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X0))
| ? [X4] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(definition_folding,[],[f3510,f3954]) ).
fof(f3954,plain,
! [X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
| ~ sP24(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f3510,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X0))
| ? [X4] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(flattening,[],[f3509]) ).
fof(f3509,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X0))
| ? [X4] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
| ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(ennf_transformation,[],[f2379]) ).
fof(f2379,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X1,X2))
=> ( ! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
=> ( hBOOL(hAPP_int_bool(X1,X3))
=> hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int))) ) )
=> ( ! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2))
=> ( hBOOL(hAPP_int_bool(X1,X4))
=> hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X1,X0)) ) ) ),
inference(rectify,[],[f1199]) ).
fof(f1199,axiom,
! [X32,X12,X15] :
( hBOOL(hAPP_int_bool(X12,X15))
=> ( ! [X125] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X125))
=> ( hBOOL(hAPP_int_bool(X12,X125))
=> hBOOL(hAPP_int_bool(X12,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X125),one_one_int))) ) )
=> ( ! [X125] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X125),X15))
=> ( hBOOL(hAPP_int_bool(X12,X125))
=> hBOOL(hAPP_int_bool(X12,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X125),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X12,X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26233,plain,
spl263_1519,
inference(avatar_split_clause,[],[f6463,f26231]) ).
fof(f26231,plain,
( spl263_1519
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK216(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1519])]) ).
fof(f6463,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK216(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4561]) ).
fof(f4561,plain,
! [X0,X1,X2] :
( ( image_496248727ol_nat(X0,sK216(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK216(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK216(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK216])],[f3502,f4560]) ).
fof(f4560,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_496248727ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
=> ( image_496248727ol_nat(X0,sK216(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK216(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK216(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3502,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_496248727ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3501]) ).
fof(f3501,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_496248727ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
=> ? [X3] :
( image_496248727ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_496248727ol_nat(X8,X4)))
=> ? [X26] :
( image_496248727ol_nat(X8,X26) = X9
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X26))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26229,plain,
spl263_1518,
inference(avatar_split_clause,[],[f6460,f26227]) ).
fof(f26227,plain,
( spl263_1518
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK215(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1518])]) ).
fof(f6460,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK215(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4559]) ).
fof(f4559,plain,
! [X0,X1,X2] :
( ( image_1431733819ol_nat(X0,sK215(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK215(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK215(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK215])],[f3500,f4558]) ).
fof(f4558,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1431733819ol_nat(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
=> ( image_1431733819ol_nat(X0,sK215(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK215(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK215(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3500,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1431733819ol_nat(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3499]) ).
fof(f3499,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1431733819ol_nat(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2373]) ).
fof(f2373,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
=> ? [X3] :
( image_1431733819ol_nat(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_1431733819ol_nat(X8,X4)))
=> ? [X26] :
( image_1431733819ol_nat(X8,X26) = X9
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X26))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26225,plain,
spl263_1517,
inference(avatar_split_clause,[],[f6457,f26223]) ).
fof(f26223,plain,
( spl263_1517
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK214(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1517])]) ).
fof(f6457,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK214(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f4557,plain,
! [X0,X1,X2] :
( ( image_a_nat(X0,sK214(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK214(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK214(X0,X1,X2)),X1))
& is_fun_a_bool(sK214(X0,X1,X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK214])],[f3498,f4556]) ).
fof(f4556,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_nat(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_nat(X0,sK214(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK214(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK214(X0,X1,X2)),X1))
& is_fun_a_bool(sK214(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3498,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_nat(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3497]) ).
fof(f3497,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_nat(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2372]) ).
fof(f2372,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
=> ? [X3] :
( image_a_nat(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_a_nat(X8,X4)))
=> ? [X26] :
( image_a_nat(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26221,plain,
( spl263_1516
| ~ spl263_37
| ~ spl263_171 ),
inference(avatar_split_clause,[],[f8792,f8589,f7960,f26219]) ).
fof(f26219,plain,
( spl263_1516
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP5(image_876012084bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1516])]) ).
fof(f8589,plain,
( spl263_171
<=> ! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_171])]) ).
fof(f8792,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP5(image_876012084bool_a(X1,X0)) )
| ~ spl263_37
| ~ spl263_171 ),
inference(resolution,[],[f8590,f7961]) ).
fof(f8590,plain,
( ! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl263_171 ),
inference(avatar_component_clause,[],[f8589]) ).
fof(f26217,plain,
spl263_1515,
inference(avatar_split_clause,[],[f6453,f26215]) ).
fof(f26215,plain,
( spl263_1515
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK213(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1515])]) ).
fof(f6453,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK213(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4555]) ).
fof(f4555,plain,
! [X0,X1,X2] :
( ( image_fun_a_bool_nat(X0,sK213(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK213(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK213(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK213(X0,X1,X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK213])],[f3496,f4554]) ).
fof(f4554,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_nat(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
=> ( image_fun_a_bool_nat(X0,sK213(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK213(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK213(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK213(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3496,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_nat(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3495]) ).
fof(f3495,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_nat(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2371]) ).
fof(f2371,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
=> ? [X3] :
( image_fun_a_bool_nat(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) ) ) ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_fun_a_bool_nat(X8,X4)))
=> ? [X26] :
( image_fun_a_bool_nat(X8,X26) = X9
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X26))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X26),X4))
& is_fun949378684l_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26213,plain,
spl263_1514,
inference(avatar_split_clause,[],[f6449,f26211]) ).
fof(f26211,plain,
( spl263_1514
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK212(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1514])]) ).
fof(f6449,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK212(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4553]) ).
fof(f4553,plain,
! [X0,X1,X2] :
( ( image_1551609309ol_nat(X0,sK212(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK212(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK212(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK212(X0,X1,X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK212])],[f3494,f4552]) ).
fof(f4552,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1551609309ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
=> ( image_1551609309ol_nat(X0,sK212(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK212(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK212(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK212(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3494,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1551609309ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3493]) ).
fof(f3493,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1551609309ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2370]) ).
fof(f2370,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
=> ? [X3] :
( image_1551609309ol_nat(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) ) ) ),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_1551609309ol_nat(X8,X4)))
=> ? [X26] :
( image_1551609309ol_nat(X8,X26) = X9
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X26))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X26),X4))
& is_fun1661590463l_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26209,plain,
spl263_1513,
inference(avatar_split_clause,[],[f6445,f26207]) ).
fof(f26207,plain,
( spl263_1513
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK211(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1513])]) ).
fof(f6445,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK211(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4551]) ).
fof(f4551,plain,
! [X0,X1,X2] :
( ( image_pname_nat(X0,sK211(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK211(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK211(X0,X1,X2)),X1))
& is_fun_pname_bool(sK211(X0,X1,X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK211])],[f3492,f4550]) ).
fof(f4550,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_nat(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_pname_nat(X0,sK211(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK211(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK211(X0,X1,X2)),X1))
& is_fun_pname_bool(sK211(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3492,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_nat(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3491]) ).
fof(f3491,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_nat(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2369]) ).
fof(f2369,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
=> ? [X3] :
( image_pname_nat(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_pname_nat(X8,X4)))
=> ? [X26] :
( image_pname_nat(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26205,plain,
spl263_1512,
inference(avatar_split_clause,[],[f6436,f26203]) ).
fof(f26203,plain,
( spl263_1512
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X2))
| sP23(X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1512])]) ).
fof(f6436,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X2))
| sP23(X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3953]) ).
fof(f3953,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(X0,X2))
| sP23(X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(definition_folding,[],[f3476,f3952]) ).
fof(f3952,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ sP23(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f3476,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3475]) ).
fof(f3475,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
=> ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
=> ( ! [X3,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
=> ( hBOOL(hAPP_f54304608l_bool(X0,X4))
=> hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X0,X2)) ) ) ) ),
inference(rectify,[],[f787]) ).
fof(f787,axiom,
! [X12,X4,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6),X4))
=> ( hBOOL(hAPP_f54304608l_bool(X12,bot_bot_fun_nat_bool))
=> ( ! [X77,X78] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X78))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X77),X4))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X77),X78))
=> ( hBOOL(hAPP_f54304608l_bool(X12,X78))
=> hBOOL(hAPP_f54304608l_bool(X12,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X77),X78))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26201,plain,
spl263_1511,
inference(avatar_split_clause,[],[f6427,f26199]) ).
fof(f26199,plain,
( spl263_1511
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK208(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1511])]) ).
fof(f6427,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK208(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4545]) ).
fof(f4545,plain,
! [X0,X1,X2] :
( ( image_nat_int(X0,sK208(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK208(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK208(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK208])],[f3472,f4544]) ).
fof(f4544,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_int(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_nat_int(X0,sK208(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK208(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK208(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3472,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_int(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3471]) ).
fof(f3471,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_nat_int(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2359]) ).
fof(f2359,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
=> ? [X3] :
( image_nat_int(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_nat_int(X8,X4)))
=> ? [X26] :
( image_nat_int(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26197,plain,
spl263_1510,
inference(avatar_split_clause,[],[f6424,f26195]) ).
fof(f26195,plain,
( spl263_1510
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK207(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1510])]) ).
fof(f6424,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK207(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4543]) ).
fof(f4543,plain,
! [X0,X1,X2] :
( ( image_2069007511ol_int(X0,sK207(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK207(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK207(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK207])],[f3470,f4542]) ).
fof(f4542,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2069007511ol_int(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
=> ( image_2069007511ol_int(X0,sK207(X0,X1,X2)) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK207(X0,X1,X2)))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK207(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3470,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2069007511ol_int(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3469]) ).
fof(f3469,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2069007511ol_int(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2358]) ).
fof(f2358,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
=> ? [X3] :
( image_2069007511ol_int(X0,X3) = X2
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_2069007511ol_int(X8,X4)))
=> ? [X26] :
( image_2069007511ol_int(X8,X26) = X9
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X26))
& hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26193,plain,
spl263_1509,
inference(avatar_split_clause,[],[f6421,f26191]) ).
fof(f26191,plain,
( spl263_1509
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK206(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1509])]) ).
fof(f6421,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK206(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4541]) ).
fof(f4541,plain,
! [X0,X1,X2] :
( ( image_1133522419ol_int(X0,sK206(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK206(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK206(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK206])],[f3468,f4540]) ).
fof(f4540,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1133522419ol_int(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
=> ( image_1133522419ol_int(X0,sK206(X0,X1,X2)) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK206(X0,X1,X2)))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK206(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3468,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1133522419ol_int(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3467]) ).
fof(f3467,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1133522419ol_int(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2357]) ).
fof(f2357,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
=> ? [X3] :
( image_1133522419ol_int(X0,X3) = X2
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
inference(rectify,[],[f348]) ).
fof(f348,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_1133522419ol_int(X8,X4)))
=> ? [X26] :
( image_1133522419ol_int(X8,X26) = X9
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X26))
& hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26189,plain,
spl263_1508,
inference(avatar_split_clause,[],[f6418,f26187]) ).
fof(f26187,plain,
( spl263_1508
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK205(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1508])]) ).
fof(f6418,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK205(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4539]) ).
fof(f4539,plain,
! [X0,X1,X2] :
( ( image_a_int(X0,sK205(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK205(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK205(X0,X1,X2)),X1))
& is_fun_a_bool(sK205(X0,X1,X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK205])],[f3466,f4538]) ).
fof(f4538,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_int(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_int(X0,sK205(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK205(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK205(X0,X1,X2)),X1))
& is_fun_a_bool(sK205(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3466,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_int(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3465]) ).
fof(f3465,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_int(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2356]) ).
fof(f2356,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
=> ? [X3] :
( image_a_int(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ),
inference(rectify,[],[f346]) ).
fof(f346,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_a_int(X8,X4)))
=> ? [X26] :
( image_a_int(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26185,plain,
spl263_1507,
inference(avatar_split_clause,[],[f6414,f26183]) ).
fof(f26183,plain,
( spl263_1507
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK204(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1507])]) ).
fof(f6414,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK204(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4537]) ).
fof(f4537,plain,
! [X0,X1,X2] :
( ( image_fun_a_bool_int(X0,sK204(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK204(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK204(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK204(X0,X1,X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK204])],[f3464,f4536]) ).
fof(f4536,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_int(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
=> ( image_fun_a_bool_int(X0,sK204(X0,X1,X2)) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK204(X0,X1,X2)))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK204(X0,X1,X2)),X1))
& is_fun949378684l_bool(sK204(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3464,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_int(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3463]) ).
fof(f3463,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_fun_a_bool_int(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2355]) ).
fof(f2355,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
=> ? [X3] :
( image_fun_a_bool_int(X0,X3) = X2
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1))
& is_fun949378684l_bool(X3) ) ) ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_fun_a_bool_int(X8,X4)))
=> ? [X26] :
( image_fun_a_bool_int(X8,X26) = X9
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X26))
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X26),X4))
& is_fun949378684l_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26181,plain,
spl263_1506,
inference(avatar_split_clause,[],[f6410,f26179]) ).
fof(f26179,plain,
( spl263_1506
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK203(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1506])]) ).
fof(f6410,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK203(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4535]) ).
fof(f4535,plain,
! [X0,X1,X2] :
( ( image_41399353ol_int(X0,sK203(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK203(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK203(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK203(X0,X1,X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK203])],[f3462,f4534]) ).
fof(f4534,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_41399353ol_int(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
=> ( image_41399353ol_int(X0,sK203(X0,X1,X2)) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK203(X0,X1,X2)))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK203(X0,X1,X2)),X1))
& is_fun1661590463l_bool(sK203(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3462,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_41399353ol_int(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3461]) ).
fof(f3461,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_41399353ol_int(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
=> ? [X3] :
( image_41399353ol_int(X0,X3) = X2
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1))
& is_fun1661590463l_bool(X3) ) ) ),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_41399353ol_int(X8,X4)))
=> ? [X26] :
( image_41399353ol_int(X8,X26) = X9
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X26))
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X26),X4))
& is_fun1661590463l_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26177,plain,
( spl263_1505
| ~ spl263_38
| ~ spl263_171 ),
inference(avatar_split_clause,[],[f8791,f8589,f7964,f26175]) ).
fof(f26175,plain,
( spl263_1505
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP7(image_876012084bool_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1505])]) ).
fof(f8791,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP7(image_876012084bool_a(X1,X0)) )
| ~ spl263_38
| ~ spl263_171 ),
inference(resolution,[],[f8590,f7965]) ).
fof(f26173,plain,
spl263_1504,
inference(avatar_split_clause,[],[f6406,f26171]) ).
fof(f26171,plain,
( spl263_1504
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK202(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1504])]) ).
fof(f6406,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK202(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4533]) ).
fof(f4533,plain,
! [X0,X1,X2] :
( ( image_pname_int(X0,sK202(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK202(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK202(X0,X1,X2)),X1))
& is_fun_pname_bool(sK202(X0,X1,X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202])],[f3460,f4532]) ).
fof(f4532,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_int(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_pname_int(X0,sK202(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK202(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK202(X0,X1,X2)),X1))
& is_fun_pname_bool(sK202(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3460,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_int(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3459]) ).
fof(f3459,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_pname_int(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
=> ? [X3] :
( image_pname_int(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_pname_int(X8,X4)))
=> ? [X26] :
( image_pname_int(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26169,plain,
spl263_1503,
inference(avatar_split_clause,[],[f6398,f26167]) ).
fof(f26167,plain,
( spl263_1503
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X2))
| sP22(X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1503])]) ).
fof(f6398,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X2))
| sP22(X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3951]) ).
fof(f3951,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(X0,X2))
| sP22(X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(definition_folding,[],[f3446,f3950]) ).
fof(f3950,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ sP22(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f3446,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3445]) ).
fof(f3445,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2346]) ).
fof(f2346,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
=> ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
=> ( ! [X3,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
=> ( hBOOL(hAPP_f448129468l_bool(X0,X4))
=> hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X0,X2)) ) ) ) ),
inference(rectify,[],[f786]) ).
fof(f786,axiom,
! [X12,X4,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X6),X4))
=> ( hBOOL(hAPP_f448129468l_bool(X12,bot_bot_fun_int_bool))
=> ( ! [X77,X78] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X78))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X77),X4))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X77),X78))
=> ( hBOOL(hAPP_f448129468l_bool(X12,X78))
=> hBOOL(hAPP_f448129468l_bool(X12,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X77),X78))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26165,plain,
spl263_1502,
inference(avatar_split_clause,[],[f6387,f26163]) ).
fof(f26163,plain,
( spl263_1502
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
| sP21(X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1502])]) ).
fof(f6387,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
| sP21(X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f3949]) ).
fof(f3949,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
| sP21(X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(definition_folding,[],[f3434,f3948]) ).
fof(f3948,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ sP21(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f3434,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f3433]) ).
fof(f3433,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
=> ( ! [X3,X4] :
( ( is_fun_a_bool(X4)
& is_a(X3) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,X4))
=> hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X0,X2)) ) ) ) ),
inference(rectify,[],[f785]) ).
fof(f785,axiom,
! [X12,X4,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X6),X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,bot_bot_fun_a_bool))
=> ( ! [X77,X78] :
( ( is_fun_a_bool(X78)
& is_a(X77) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X78))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X77),X4))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X77),X78))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,X78))
=> hBOOL(hAPP_fun_a_bool_bool(X12,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X77),X78))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26161,plain,
spl263_1501,
inference(avatar_split_clause,[],[f6371,f26159]) ).
fof(f26159,plain,
( spl263_1501
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X2))
| sP20(X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1501])]) ).
fof(f6371,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X2))
| sP20(X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3947]) ).
fof(f3947,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(X0,X2))
| sP20(X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(definition_folding,[],[f3416,f3946]) ).
fof(f3946,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ sP20(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f3416,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3415]) ).
fof(f3415,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(X0,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2331]) ).
fof(f2331,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
=> ( ! [X3,X4] :
( ( is_fun_pname_bool(X4)
& is_pname(X3) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,X4))
=> hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X0,X2)) ) ) ) ),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X12,X4,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X6),X4))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,bot_bo844097828e_bool))
=> ( ! [X77,X78] :
( ( is_fun_pname_bool(X78)
& is_pname(X77) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X78))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X77),X4))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X77),X78))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,X78))
=> hBOOL(hAPP_f1664156314l_bool(X12,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X77),X78))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26157,plain,
spl263_1500,
inference(avatar_split_clause,[],[f6345,f26155]) ).
fof(f26155,plain,
( spl263_1500
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK195(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1500])]) ).
fof(f6345,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK195(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4519]) ).
fof(f4519,plain,
! [X0,X1,X2] :
( ( image_26036933t_bool(X0,sK195(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK195(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK195(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK195])],[f3382,f4518]) ).
fof(f4518,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_26036933t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_26036933t_bool(X0,sK195(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK195(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK195(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3382,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_26036933t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3381]) ).
fof(f3381,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_26036933t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2314]) ).
fof(f2314,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
=> ? [X3] :
( image_26036933t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
inference(rectify,[],[f359]) ).
fof(f359,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_26036933t_bool(X8,X4)))
=> ? [X26] :
( image_26036933t_bool(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26153,plain,
spl263_1499,
inference(avatar_split_clause,[],[f6342,f26151]) ).
fof(f26151,plain,
( spl263_1499
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK194(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1499])]) ).
fof(f6342,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK194(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4517]) ).
fof(f4517,plain,
! [X0,X1,X2] :
( ( image_1556378401t_bool(X0,sK194(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK194(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK194(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194])],[f3380,f4516]) ).
fof(f4516,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1556378401t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
=> ( image_1556378401t_bool(X0,sK194(X0,X1,X2)) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK194(X0,X1,X2)))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK194(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3380,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1556378401t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3379]) ).
fof(f3379,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1556378401t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2313]) ).
fof(f2313,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
=> ? [X3] :
( image_1556378401t_bool(X0,X3) = X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_1556378401t_bool(X8,X4)))
=> ? [X26] :
( image_1556378401t_bool(X8,X26) = X9
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X26))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26149,plain,
spl263_1498,
inference(avatar_split_clause,[],[f6339,f26147]) ).
fof(f26147,plain,
( spl263_1498
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK193(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1498])]) ).
fof(f6339,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK193(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4515]) ).
fof(f4515,plain,
! [X0,X1,X2] :
( ( image_275383677t_bool(X0,sK193(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK193(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK193(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK193])],[f3378,f4514]) ).
fof(f4514,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_275383677t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_275383677t_bool(X0,sK193(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK193(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK193(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3378,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_275383677t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3377]) ).
fof(f3377,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_275383677t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2312]) ).
fof(f2312,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
=> ? [X3] :
( image_275383677t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
inference(rectify,[],[f364]) ).
fof(f364,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_275383677t_bool(X8,X4)))
=> ? [X26] :
( image_275383677t_bool(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26145,plain,
spl263_1497,
inference(avatar_split_clause,[],[f6336,f26143]) ).
fof(f26143,plain,
( spl263_1497
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK192(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1497])]) ).
fof(f6336,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK192(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4513]) ).
fof(f4513,plain,
! [X0,X1,X2] :
( ( image_892525857t_bool(X0,sK192(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK192(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK192(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192])],[f3376,f4512]) ).
fof(f4512,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_892525857t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
=> ( image_892525857t_bool(X0,sK192(X0,X1,X2)) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK192(X0,X1,X2)))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK192(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3376,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_892525857t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3375]) ).
fof(f3375,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_892525857t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2311]) ).
fof(f2311,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
=> ? [X3] :
( image_892525857t_bool(X0,X3) = X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_892525857t_bool(X8,X4)))
=> ? [X26] :
( image_892525857t_bool(X8,X26) = X9
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X26))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X26),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26141,plain,
spl263_1496,
inference(avatar_split_clause,[],[f6333,f26139]) ).
fof(f26139,plain,
( spl263_1496
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1496])]) ).
fof(f6333,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4511]) ).
fof(f4511,plain,
! [X0,X1,X2] :
( ( image_1512837979t_bool(X0,sK191(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
& is_fun_pname_bool(sK191(X0,X1,X2)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK191])],[f3374,f4510]) ).
fof(f4510,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1512837979t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_1512837979t_bool(X0,sK191(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
& is_fun_pname_bool(sK191(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3374,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1512837979t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3373]) ).
fof(f3373,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_1512837979t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2310]) ).
fof(f2310,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
=> ? [X3] :
( image_1512837979t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_1512837979t_bool(X8,X4)))
=> ? [X26] :
( image_1512837979t_bool(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26137,plain,
spl263_1495,
inference(avatar_split_clause,[],[f6329,f26135]) ).
fof(f26135,plain,
( spl263_1495
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK190(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1495])]) ).
fof(f6329,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK190(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4509]) ).
fof(f4509,plain,
! [X0,X1,X2] :
( ( image_2129980159t_bool(X0,sK190(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK190(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK190(X0,X1,X2)),X1))
& is_fun_pname_bool(sK190(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190])],[f3372,f4508]) ).
fof(f4508,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2129980159t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
=> ( image_2129980159t_bool(X0,sK190(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK190(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK190(X0,X1,X2)),X1))
& is_fun_pname_bool(sK190(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3372,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2129980159t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3371]) ).
fof(f3371,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_2129980159t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2309]) ).
fof(f2309,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
=> ? [X3] :
( image_2129980159t_bool(X0,X3) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
& is_fun_pname_bool(X3) ) ) ),
inference(rectify,[],[f353]) ).
fof(f353,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_2129980159t_bool(X8,X4)))
=> ? [X26] :
( image_2129980159t_bool(X8,X26) = X9
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X26))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X26),X4))
& is_fun_pname_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26133,plain,
( spl263_1494
| ~ spl263_35
| ~ spl263_170 ),
inference(avatar_split_clause,[],[f8790,f8585,f7952,f26131]) ).
fof(f26131,plain,
( spl263_1494
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP1(image_1283814551_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1494])]) ).
fof(f8585,plain,
( spl263_170
<=> ! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_170])]) ).
fof(f8790,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP1(image_1283814551_pname(X1,X0)) )
| ~ spl263_35
| ~ spl263_170 ),
inference(resolution,[],[f8586,f7953]) ).
fof(f8586,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl263_170 ),
inference(avatar_component_clause,[],[f8585]) ).
fof(f26129,plain,
spl263_1493,
inference(avatar_split_clause,[],[f6325,f26127]) ).
fof(f26127,plain,
( spl263_1493
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK189(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1493])]) ).
fof(f6325,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK189(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4507]) ).
fof(f4507,plain,
! [X0,X1,X2] :
( ( image_a_fun_nat_bool(X0,sK189(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK189(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK189(X0,X1,X2)),X1))
& is_fun_a_bool(sK189(X0,X1,X2)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK189])],[f3370,f4506]) ).
fof(f4506,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_nat_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_fun_nat_bool(X0,sK189(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK189(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK189(X0,X1,X2)),X1))
& is_fun_a_bool(sK189(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3370,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_nat_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3369]) ).
fof(f3369,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_nat_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2308]) ).
fof(f2308,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
=> ? [X3] :
( image_a_fun_nat_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ),
inference(rectify,[],[f332]) ).
fof(f332,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_a_fun_nat_bool(X8,X4)))
=> ? [X26] :
( image_a_fun_nat_bool(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26125,plain,
spl263_1492,
inference(avatar_split_clause,[],[f6321,f26123]) ).
fof(f26123,plain,
( spl263_1492
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK188(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1492])]) ).
fof(f6321,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK188(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4505]) ).
fof(f4505,plain,
! [X0,X1,X2] :
( ( image_a_fun_int_bool(X0,sK188(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK188(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK188(X0,X1,X2)),X1))
& is_fun_a_bool(sK188(X0,X1,X2)) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188])],[f3368,f4504]) ).
fof(f4504,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_int_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
=> ( image_a_fun_int_bool(X0,sK188(X0,X1,X2)) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK188(X0,X1,X2)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK188(X0,X1,X2)),X1))
& is_fun_a_bool(sK188(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3368,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_int_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3367]) ).
fof(f3367,plain,
! [X0,X1,X2] :
( ? [X3] :
( image_a_fun_int_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) )
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2307]) ).
fof(f2307,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
=> ? [X3] :
( image_a_fun_int_bool(X0,X3) = X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1))
& is_fun_a_bool(X3) ) ) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_a_fun_int_bool(X8,X4)))
=> ? [X26] :
( image_a_fun_int_bool(X8,X26) = X9
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X26))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X26),X4))
& is_fun_a_bool(X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26121,plain,
spl263_1491,
inference(avatar_split_clause,[],[f6300,f26119]) ).
fof(f26119,plain,
( spl263_1491
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK184(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1491])]) ).
fof(f6300,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK184(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4497]) ).
fof(f26117,plain,
spl263_1490,
inference(avatar_split_clause,[],[f6296,f26115]) ).
fof(f26115,plain,
( spl263_1490
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK183(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1490])]) ).
fof(f6296,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK183(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4495]) ).
fof(f26113,plain,
spl263_1489,
inference(avatar_split_clause,[],[f6293,f26111]) ).
fof(f26111,plain,
( spl263_1489
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK182(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1489])]) ).
fof(f6293,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK182(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4493]) ).
fof(f26109,plain,
spl263_1488,
inference(avatar_split_clause,[],[f6290,f26107]) ).
fof(f26107,plain,
( spl263_1488
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK181(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1488])]) ).
fof(f6290,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK181(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4491]) ).
fof(f26105,plain,
spl263_1487,
inference(avatar_split_clause,[],[f6287,f26103]) ).
fof(f26103,plain,
( spl263_1487
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK180(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1487])]) ).
fof(f6287,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK180(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4489]) ).
fof(f26101,plain,
spl263_1486,
inference(avatar_split_clause,[],[f6284,f26099]) ).
fof(f26099,plain,
( spl263_1486
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK179(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1486])]) ).
fof(f6284,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK179(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4487]) ).
fof(f26097,plain,
spl263_1485,
inference(avatar_split_clause,[],[f6280,f26095]) ).
fof(f26095,plain,
( spl263_1485
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK178(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1485])]) ).
fof(f6280,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK178(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4485]) ).
fof(f26093,plain,
spl263_1484,
inference(avatar_split_clause,[],[f6276,f26091]) ).
fof(f26091,plain,
( spl263_1484
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK177(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1484])]) ).
fof(f6276,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK177(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4483]) ).
fof(f26089,plain,
( spl263_1483
| ~ spl263_36
| ~ spl263_170 ),
inference(avatar_split_clause,[],[f8789,f8585,f7956,f26087]) ).
fof(f26087,plain,
( spl263_1483
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP3(image_1283814551_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1483])]) ).
fof(f8789,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| sP3(image_1283814551_pname(X1,X0)) )
| ~ spl263_36
| ~ spl263_170 ),
inference(resolution,[],[f8586,f7957]) ).
fof(f26085,plain,
spl263_1482,
inference(avatar_split_clause,[],[f6269,f26083]) ).
fof(f26083,plain,
( spl263_1482
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK174(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1482])]) ).
fof(f6269,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK174(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4479]) ).
fof(f26081,plain,
spl263_1481,
inference(avatar_split_clause,[],[f6265,f26079]) ).
fof(f26079,plain,
( spl263_1481
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK173(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1481])]) ).
fof(f6265,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK173(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4477]) ).
fof(f26077,plain,
spl263_1480,
inference(avatar_split_clause,[],[f6262,f26075]) ).
fof(f26075,plain,
( spl263_1480
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK172(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1480])]) ).
fof(f6262,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK172(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4475]) ).
fof(f26073,plain,
spl263_1479,
inference(avatar_split_clause,[],[f6259,f26071]) ).
fof(f26071,plain,
( spl263_1479
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK171(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1479])]) ).
fof(f6259,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK171(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4473]) ).
fof(f26069,plain,
spl263_1478,
inference(avatar_split_clause,[],[f6256,f26067]) ).
fof(f26067,plain,
( spl263_1478
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK170(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1478])]) ).
fof(f6256,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK170(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4471]) ).
fof(f26065,plain,
spl263_1477,
inference(avatar_split_clause,[],[f6253,f26063]) ).
fof(f26063,plain,
( spl263_1477
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK169(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1477])]) ).
fof(f6253,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK169(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4469]) ).
fof(f26061,plain,
spl263_1476,
inference(avatar_split_clause,[],[f6249,f26059]) ).
fof(f26059,plain,
( spl263_1476
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK168(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1476])]) ).
fof(f6249,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK168(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4467]) ).
fof(f26057,plain,
spl263_1475,
inference(avatar_split_clause,[],[f6245,f26055]) ).
fof(f26055,plain,
( spl263_1475
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK167(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1475])]) ).
fof(f6245,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK167(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4465]) ).
fof(f26053,plain,
spl263_1474,
inference(avatar_split_clause,[],[f6241,f26051]) ).
fof(f26051,plain,
( spl263_1474
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK166(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1474])]) ).
fof(f6241,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK166(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4463]) ).
fof(f26049,plain,
spl263_1473,
inference(avatar_split_clause,[],[f6238,f26047]) ).
fof(f26047,plain,
( spl263_1473
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK165(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1473])]) ).
fof(f6238,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK165(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4461]) ).
fof(f26045,plain,
( spl263_1472
| ~ spl263_37
| ~ spl263_165 ),
inference(avatar_split_clause,[],[f8784,f8565,f7960,f26043]) ).
fof(f26043,plain,
( spl263_1472
<=> ! [X0,X1] :
( ~ is_pname(X0)
| sP5(hAPP_p1534023578a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1472])]) ).
fof(f8565,plain,
( spl263_165
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_165])]) ).
fof(f8784,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| sP5(hAPP_p1534023578a_bool(X1,X0)) )
| ~ spl263_37
| ~ spl263_165 ),
inference(resolution,[],[f8566,f7961]) ).
fof(f8566,plain,
( ! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) )
| ~ spl263_165 ),
inference(avatar_component_clause,[],[f8565]) ).
fof(f26041,plain,
spl263_1471,
inference(avatar_split_clause,[],[f6235,f26039]) ).
fof(f26039,plain,
( spl263_1471
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK164(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1471])]) ).
fof(f6235,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK164(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4459]) ).
fof(f26037,plain,
spl263_1470,
inference(avatar_split_clause,[],[f6231,f26035]) ).
fof(f26035,plain,
( spl263_1470
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK163(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1470])]) ).
fof(f6231,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK163(X0,X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4457]) ).
fof(f26033,plain,
spl263_1469,
inference(avatar_split_clause,[],[f6227,f26031]) ).
fof(f26031,plain,
( spl263_1469
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK162(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1469])]) ).
fof(f6227,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK162(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4455]) ).
fof(f26029,plain,
spl263_1468,
inference(avatar_split_clause,[],[f6224,f26027]) ).
fof(f26027,plain,
( spl263_1468
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK161(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1468])]) ).
fof(f6224,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK161(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4453]) ).
fof(f26025,plain,
spl263_1467,
inference(avatar_split_clause,[],[f6221,f26023]) ).
fof(f26023,plain,
( spl263_1467
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK160(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1467])]) ).
fof(f6221,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK160(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4451]) ).
fof(f26021,plain,
spl263_1466,
inference(avatar_split_clause,[],[f6217,f26019]) ).
fof(f26019,plain,
( spl263_1466
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK159(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1466])]) ).
fof(f6217,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK159(X0,X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4449]) ).
fof(f26017,plain,
spl263_1465,
inference(avatar_split_clause,[],[f6205,f26015]) ).
fof(f26015,plain,
( spl263_1465
<=> ! [X2,X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1465])]) ).
fof(f6205,plain,
! [X2,X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3286]) ).
fof(f3286,plain,
! [X0,X1,X2] :
( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f2265]) ).
fof(f2265,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) ) ),
inference(rectify,[],[f685]) ).
fof(f685,axiom,
! [X4,X10,X9] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X9))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)),X9) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X9))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26013,plain,
spl263_1464,
inference(avatar_split_clause,[],[f6203,f26011]) ).
fof(f26011,plain,
( spl263_1464
<=> ! [X2,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1464])]) ).
fof(f6203,plain,
! [X2,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(cnf_transformation,[],[f3285]) ).
fof(f3285,plain,
! [X0,X1,X2] :
( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
inference(ennf_transformation,[],[f2264]) ).
fof(f2264,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) ) ),
inference(rectify,[],[f684]) ).
fof(f684,axiom,
! [X4,X10,X9] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X9))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)),X9) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X9))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26009,plain,
spl263_1463,
inference(avatar_split_clause,[],[f6201,f26007]) ).
fof(f26007,plain,
( spl263_1463
<=> ! [X2,X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1463])]) ).
fof(f6201,plain,
! [X2,X0,X1] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f3284]) ).
fof(f3284,plain,
! [X0,X1,X2] :
( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) )
& ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
inference(ennf_transformation,[],[f2263]) ).
fof(f2263,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) ) ),
inference(rectify,[],[f683]) ).
fof(f683,axiom,
! [X4,X10,X9] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X9))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),X9) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X9))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26005,plain,
spl263_1462,
inference(avatar_split_clause,[],[f6199,f26003]) ).
fof(f6199,plain,
! [X2,X0,X1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3283]) ).
fof(f3283,plain,
! [X0,X1,X2] :
( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
inference(ennf_transformation,[],[f2262]) ).
fof(f2262,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) ) ),
inference(rectify,[],[f686]) ).
fof(f686,axiom,
! [X4,X10,X9] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)),X9) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f26001,plain,
( spl263_1461
| ~ spl263_38
| ~ spl263_165 ),
inference(avatar_split_clause,[],[f8783,f8565,f7964,f25999]) ).
fof(f25999,plain,
( spl263_1461
<=> ! [X0,X1] :
( ~ is_pname(X0)
| sP7(hAPP_p1534023578a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1461])]) ).
fof(f8783,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| sP7(hAPP_p1534023578a_bool(X1,X0)) )
| ~ spl263_38
| ~ spl263_165 ),
inference(resolution,[],[f8566,f7965]) ).
fof(f25997,plain,
spl263_1460,
inference(avatar_split_clause,[],[f5763,f25995]) ).
fof(f25995,plain,
( spl263_1460
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1460])]) ).
fof(f5763,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3172]) ).
fof(f3172,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2004]) ).
fof(f2004,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) ),
inference(rectify,[],[f226]) ).
fof(f226,axiom,
! [X13,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X14)),X13) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25993,plain,
spl263_1459,
inference(avatar_split_clause,[],[f5662,f25991]) ).
fof(f25991,plain,
( spl263_1459
<=> ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1459])]) ).
fof(f5662,plain,
! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3058]) ).
fof(f3058,plain,
! [X0,X1] :
( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
& ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1927]) ).
fof(f1927,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) ) ) ),
inference(rectify,[],[f207]) ).
fof(f207,axiom,
! [X10,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X4)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hAPP_f22106695ol_nat(finite_card_nat,X4) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25989,plain,
spl263_1458,
inference(avatar_split_clause,[],[f5619,f25987]) ).
fof(f25987,plain,
( spl263_1458
<=> ! [X0,X1] :
( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1458])]) ).
fof(f5619,plain,
! [X0,X1] :
( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3018]) ).
fof(f3018,plain,
! [X0,X1] :
( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X1))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) )
& ( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1898]) ).
fof(f1898,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X1)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
=> hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) ) ) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X10,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X4)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> hAPP_f957591787ol_nat(finite_card_int,X4) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25985,plain,
spl263_1457,
inference(avatar_split_clause,[],[f5581,f25983]) ).
fof(f25983,plain,
( spl263_1457
<=> ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1457])]) ).
fof(f5581,plain,
! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2985]) ).
fof(f2985,plain,
! [X0,X1] :
( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) )
& ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1874]) ).
fof(f1874,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ) ) ),
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X10,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X4)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> hAPP_fun_a_bool_nat(finite_card_a,X4) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25981,plain,
spl263_1456,
inference(avatar_split_clause,[],[f5541,f25979]) ).
fof(f25979,plain,
( spl263_1456
<=> ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1456])]) ).
fof(f5541,plain,
! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2951]) ).
fof(f2951,plain,
! [X0,X1] :
( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) )
& ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1849]) ).
fof(f1849,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) ) ) ),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X4)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hAPP_f921600141ol_nat(finite_card_pname,X4) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25977,plain,
spl263_1455,
inference(avatar_split_clause,[],[f5509,f25975]) ).
fof(f25975,plain,
( spl263_1455
<=> ! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1455])]) ).
fof(f5509,plain,
! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2906]) ).
fof(f2906,plain,
! [X0,X1] :
( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) )
& ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1818]) ).
fof(f1818,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) ) ) ),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X10,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X10),X4))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X10),X4)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X4)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X10),X4))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,X4) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25973,plain,
spl263_1454,
inference(avatar_split_clause,[],[f5507,f25971]) ).
fof(f25971,plain,
( spl263_1454
<=> ! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1454])]) ).
fof(f5507,plain,
! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2905]) ).
fof(f2905,plain,
! [X0,X1] :
( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) )
& ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1817]) ).
fof(f1817,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) ) ) ),
inference(rectify,[],[f204]) ).
fof(f204,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X10),X4))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X10),X4)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X4)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X10),X4))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,X4) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25969,plain,
spl263_1453,
inference(avatar_split_clause,[],[f5505,f25967]) ).
fof(f25967,plain,
( spl263_1453
<=> ! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1453])]) ).
fof(f5505,plain,
! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2904]) ).
fof(f2904,plain,
! [X0,X1] :
( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) )
& ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1816]) ).
fof(f1816,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
=> hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) ) ) ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X10),X4))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X10),X4)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X4)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X10),X4))
=> hAPP_f696928925ol_nat(finite346522414t_bool,X4) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25965,plain,
spl263_1452,
inference(avatar_split_clause,[],[f5503,f25963]) ).
fof(f25963,plain,
( spl263_1452
<=> ! [X0,X1] :
( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1452])]) ).
fof(f5503,plain,
! [X0,X1] :
( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2903]) ).
fof(f2903,plain,
! [X0,X1] :
( ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1))
| hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1)) )
& ( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1815]) ).
fof(f1815,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> ( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)) )
& ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) ) ) ),
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X10,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> ( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X10),X4))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X10),X4)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X4)) )
& ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X10),X4))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,X4) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X10),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f25942,plain,
( spl263_1451
| ~ spl263_35
| ~ spl263_164 ),
inference(avatar_split_clause,[],[f8782,f8561,f7952,f25940]) ).
fof(f25940,plain,
( spl263_1451
<=> ! [X0,X1] :
( ~ is_pname(X0)
| sP1(hAPP_p61793385e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1451])]) ).
fof(f8561,plain,
( spl263_164
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_164])]) ).
fof(f8782,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| sP1(hAPP_p61793385e_bool(X1,X0)) )
| ~ spl263_35
| ~ spl263_164 ),
inference(resolution,[],[f8562,f7953]) ).
fof(f8562,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) )
| ~ spl263_164 ),
inference(avatar_component_clause,[],[f8561]) ).
fof(f25710,plain,
( spl263_1450
| ~ spl263_36
| ~ spl263_164 ),
inference(avatar_split_clause,[],[f8781,f8561,f7956,f25708]) ).
fof(f25708,plain,
( spl263_1450
<=> ! [X0,X1] :
( ~ is_pname(X0)
| sP3(hAPP_p61793385e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1450])]) ).
fof(f8781,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| sP3(hAPP_p61793385e_bool(X1,X0)) )
| ~ spl263_36
| ~ spl263_164 ),
inference(resolution,[],[f8562,f7957]) ).
fof(f25596,plain,
( spl263_1449
| ~ spl263_1252
| ~ spl263_1425 ),
inference(avatar_split_clause,[],[f23477,f23474,f21092,f25594]) ).
fof(f25594,plain,
( spl263_1449
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1449])]) ).
fof(f21092,plain,
( spl263_1252
<=> ! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1252])]) ).
fof(f23474,plain,
( spl263_1425
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1425])]) ).
fof(f23477,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1252
| ~ spl263_1425 ),
inference(forward_demodulation,[],[f23475,f21093]) ).
fof(f21093,plain,
( ! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2)
| ~ spl263_1252 ),
inference(avatar_component_clause,[],[f21092]) ).
fof(f23475,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) )
| ~ spl263_1425 ),
inference(avatar_component_clause,[],[f23474]) ).
fof(f25592,plain,
( spl263_1448
| ~ spl263_1252
| ~ spl263_1424 ),
inference(avatar_split_clause,[],[f23472,f23469,f21092,f25590]) ).
fof(f25590,plain,
( spl263_1448
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1448])]) ).
fof(f23469,plain,
( spl263_1424
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1424])]) ).
fof(f23472,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1252
| ~ spl263_1424 ),
inference(forward_demodulation,[],[f23470,f21093]) ).
fof(f23470,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1424 ),
inference(avatar_component_clause,[],[f23469]) ).
fof(f25588,plain,
( spl263_1447
| ~ spl263_37
| ~ spl263_162 ),
inference(avatar_split_clause,[],[f8780,f8553,f7960,f25586]) ).
fof(f25586,plain,
( spl263_1447
<=> ! [X0,X1] :
( ~ is_a(X0)
| sP5(hAPP_a_fun_a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1447])]) ).
fof(f8553,plain,
( spl263_162
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_162])]) ).
fof(f8780,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| sP5(hAPP_a_fun_a_bool(X1,X0)) )
| ~ spl263_37
| ~ spl263_162 ),
inference(resolution,[],[f8554,f7961]) ).
fof(f8554,plain,
( ! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl263_162 ),
inference(avatar_component_clause,[],[f8553]) ).
fof(f25584,plain,
( spl263_1446
| ~ spl263_1252
| ~ spl263_1423 ),
inference(avatar_split_clause,[],[f23467,f23464,f21092,f25582]) ).
fof(f25582,plain,
( spl263_1446
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1446])]) ).
fof(f23464,plain,
( spl263_1423
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1423])]) ).
fof(f23467,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1252
| ~ spl263_1423 ),
inference(forward_demodulation,[],[f23465,f21093]) ).
fof(f23465,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) )
| ~ spl263_1423 ),
inference(avatar_component_clause,[],[f23464]) ).
fof(f25580,plain,
( spl263_1445
| ~ spl263_1252
| ~ spl263_1422 ),
inference(avatar_split_clause,[],[f23462,f23459,f21092,f25578]) ).
fof(f25578,plain,
( spl263_1445
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1445])]) ).
fof(f23459,plain,
( spl263_1422
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1422])]) ).
fof(f23462,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1252
| ~ spl263_1422 ),
inference(forward_demodulation,[],[f23460,f21093]) ).
fof(f23460,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
| ~ spl263_1422 ),
inference(avatar_component_clause,[],[f23459]) ).
fof(f25576,plain,
( spl263_1444
| ~ spl263_1252
| ~ spl263_1421 ),
inference(avatar_split_clause,[],[f23457,f23454,f21092,f25574]) ).
fof(f25574,plain,
( spl263_1444
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1444])]) ).
fof(f23454,plain,
( spl263_1421
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1421])]) ).
fof(f23457,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1252
| ~ spl263_1421 ),
inference(forward_demodulation,[],[f23455,f21093]) ).
fof(f23455,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
| ~ spl263_1421 ),
inference(avatar_component_clause,[],[f23454]) ).
fof(f25572,plain,
( spl263_1443
| ~ spl263_1252
| ~ spl263_1420 ),
inference(avatar_split_clause,[],[f23452,f23449,f21092,f25570]) ).
fof(f25570,plain,
( spl263_1443
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1443])]) ).
fof(f23449,plain,
( spl263_1420
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1420])]) ).
fof(f23452,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1252
| ~ spl263_1420 ),
inference(forward_demodulation,[],[f23450,f21093]) ).
fof(f23450,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1420 ),
inference(avatar_component_clause,[],[f23449]) ).
fof(f25568,plain,
( spl263_1442
| ~ spl263_1252
| ~ spl263_1419 ),
inference(avatar_split_clause,[],[f23447,f23444,f21092,f25566]) ).
fof(f25566,plain,
( spl263_1442
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1442])]) ).
fof(f23444,plain,
( spl263_1419
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1419])]) ).
fof(f23447,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1252
| ~ spl263_1419 ),
inference(forward_demodulation,[],[f23445,f21093]) ).
fof(f23445,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
| ~ spl263_1419 ),
inference(avatar_component_clause,[],[f23444]) ).
fof(f25564,plain,
( spl263_1441
| ~ spl263_1252
| ~ spl263_1418 ),
inference(avatar_split_clause,[],[f23434,f23431,f21092,f25562]) ).
fof(f25562,plain,
( spl263_1441
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1441])]) ).
fof(f23431,plain,
( spl263_1418
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1418])]) ).
fof(f23434,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1252
| ~ spl263_1418 ),
inference(forward_demodulation,[],[f23432,f21093]) ).
fof(f23432,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
| ~ spl263_1418 ),
inference(avatar_component_clause,[],[f23431]) ).
fof(f25373,plain,
( spl263_1440
| ~ spl263_38
| ~ spl263_162 ),
inference(avatar_split_clause,[],[f8779,f8553,f7964,f25371]) ).
fof(f25371,plain,
( spl263_1440
<=> ! [X0,X1] :
( ~ is_a(X0)
| sP7(hAPP_a_fun_a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1440])]) ).
fof(f8779,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| sP7(hAPP_a_fun_a_bool(X1,X0)) )
| ~ spl263_38
| ~ spl263_162 ),
inference(resolution,[],[f8554,f7965]) ).
fof(f25183,plain,
( spl263_1439
| ~ spl263_35
| ~ spl263_161 ),
inference(avatar_split_clause,[],[f8778,f8549,f7952,f25181]) ).
fof(f25181,plain,
( spl263_1439
<=> ! [X0,X1] :
( ~ is_a(X0)
| sP1(hAPP_a93125764e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1439])]) ).
fof(f8549,plain,
( spl263_161
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_161])]) ).
fof(f8778,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| sP1(hAPP_a93125764e_bool(X1,X0)) )
| ~ spl263_35
| ~ spl263_161 ),
inference(resolution,[],[f8550,f7953]) ).
fof(f8550,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl263_161 ),
inference(avatar_component_clause,[],[f8549]) ).
fof(f24716,plain,
( spl263_1438
| ~ spl263_36
| ~ spl263_161 ),
inference(avatar_split_clause,[],[f8777,f8549,f7956,f24714]) ).
fof(f24714,plain,
( spl263_1438
<=> ! [X0,X1] :
( ~ is_a(X0)
| sP3(hAPP_a93125764e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1438])]) ).
fof(f8777,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| sP3(hAPP_a93125764e_bool(X1,X0)) )
| ~ spl263_36
| ~ spl263_161 ),
inference(resolution,[],[f8550,f7957]) ).
fof(f23774,plain,
( spl263_1437
| ~ spl263_1085
| ~ spl263_1366 ),
inference(avatar_split_clause,[],[f23657,f23220,f16156,f23772]) ).
fof(f23772,plain,
( spl263_1437
<=> ! [X1] : is_bool(hAPP_bool_bool(X1,fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1437])]) ).
fof(f16156,plain,
( spl263_1085
<=> ! [X0] : fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1085])]) ).
fof(f23220,plain,
( spl263_1366
<=> ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1366])]) ).
fof(f23657,plain,
( ! [X1] : is_bool(hAPP_bool_bool(X1,fFalse))
| ~ spl263_1085
| ~ spl263_1366 ),
inference(superposition,[],[f23221,f16157]) ).
fof(f16157,plain,
( ! [X0] : fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0)
| ~ spl263_1085 ),
inference(avatar_component_clause,[],[f16156]) ).
fof(f23221,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl263_1366 ),
inference(avatar_component_clause,[],[f23220]) ).
fof(f23550,plain,
( spl263_1436
| ~ spl263_87
| ~ spl263_246
| ~ spl263_1121
| ~ spl263_1315 ),
inference(avatar_split_clause,[],[f22985,f22982,f17679,f8932,f8200,f23548]) ).
fof(f23548,plain,
( spl263_1436
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0))
| zero_zero_nat = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1436])]) ).
fof(f22982,plain,
( spl263_1315
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1315])]) ).
fof(f22985,plain,
( ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0))
| zero_zero_nat = X1 )
| ~ spl263_87
| ~ spl263_246
| ~ spl263_1121
| ~ spl263_1315 ),
inference(forward_demodulation,[],[f22983,f18041]) ).
fof(f22983,plain,
( ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 )
| ~ spl263_1315 ),
inference(avatar_component_clause,[],[f22982]) ).
fof(f23526,plain,
spl263_1435,
inference(avatar_split_clause,[],[f7784,f23524]) ).
fof(f23524,plain,
( spl263_1435
<=> ! [X0,X3,X2,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1))
| sP41(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1435])]) ).
fof(f7784,plain,
! [X2,X3,X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1))
| sP41(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f7783,f7397]) ).
fof(f7783,plain,
! [X2,X3,X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3))
| sP41(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f6992,f7397]) ).
fof(f6992,plain,
! [X2,X3,X0,X1] :
( sP41(X2,X1,X3,X0)
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) ),
inference(cnf_transformation,[],[f4794]) ).
fof(f4794,plain,
! [X0,X1,X2,X3] :
( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool))
| ~ sP41(X2,X1,X3,X0) )
& ( sP41(X2,X1,X3,X0)
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) ) ),
inference(nnf_transformation,[],[f3988]) ).
fof(f3988,plain,
! [X0,X1,X2,X3] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool))
<=> sP41(X2,X1,X3,X0) ),
inference(definition_folding,[],[f2670,f3987]) ).
fof(f3987,plain,
! [X2,X1,X3,X0] :
( sP41(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f2670,plain,
! [X0,X1,X2,X3] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X7,X30,X31,X72] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X72),bot_bot_fun_nat_bool))
<=> ( ( X30 = X31
& X7 = X72 )
| ( X30 = X72
& X7 = X31 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23522,plain,
spl263_1434,
inference(avatar_split_clause,[],[f7782,f23520]) ).
fof(f23520,plain,
( spl263_1434
<=> ! [X0,X3,X2,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1))
| ~ sP41(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1434])]) ).
fof(f7782,plain,
! [X2,X3,X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1))
| ~ sP41(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f7781,f7397]) ).
fof(f7781,plain,
! [X2,X3,X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3))
| ~ sP41(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f6993,f7397]) ).
fof(f6993,plain,
! [X2,X3,X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool))
| ~ sP41(X2,X1,X3,X0) ),
inference(cnf_transformation,[],[f4794]) ).
fof(f23518,plain,
spl263_1433,
inference(avatar_split_clause,[],[f7780,f23516]) ).
fof(f23516,plain,
( spl263_1433
<=> ! [X0,X3,X2,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1))
| sP40(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1433])]) ).
fof(f7780,plain,
! [X2,X3,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1))
| sP40(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f7779,f7396]) ).
fof(f7779,plain,
! [X2,X3,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3))
| sP40(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f6984,f7396]) ).
fof(f6984,plain,
! [X2,X3,X0,X1] :
( sP40(X2,X1,X3,X0)
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) ),
inference(cnf_transformation,[],[f4790]) ).
fof(f4790,plain,
! [X0,X1,X2,X3] :
( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool))
| ~ sP40(X2,X1,X3,X0) )
& ( sP40(X2,X1,X3,X0)
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) ) ),
inference(nnf_transformation,[],[f3986]) ).
fof(f3986,plain,
! [X0,X1,X2,X3] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool))
<=> sP40(X2,X1,X3,X0) ),
inference(definition_folding,[],[f2669,f3985]) ).
fof(f3985,plain,
! [X2,X1,X3,X0] :
( sP40(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
fof(f2669,plain,
! [X0,X1,X2,X3] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f705]) ).
fof(f705,axiom,
! [X7,X30,X31,X72] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X72),bot_bot_fun_int_bool))
<=> ( ( X30 = X31
& X7 = X72 )
| ( X30 = X72
& X7 = X31 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23514,plain,
spl263_1432,
inference(avatar_split_clause,[],[f7778,f23512]) ).
fof(f23512,plain,
( spl263_1432
<=> ! [X0,X3,X2,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1))
| ~ sP40(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1432])]) ).
fof(f7778,plain,
! [X2,X3,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1))
| ~ sP40(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f7777,f7396]) ).
fof(f7777,plain,
! [X2,X3,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3))
| ~ sP40(X2,X1,X3,X0) ),
inference(forward_demodulation,[],[f6985,f7396]) ).
fof(f6985,plain,
! [X2,X3,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool))
| ~ sP40(X2,X1,X3,X0) ),
inference(cnf_transformation,[],[f4790]) ).
fof(f23510,plain,
spl263_1431,
inference(avatar_split_clause,[],[f7525,f23508]) ).
fof(f23508,plain,
( spl263_1431
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(fequal_nat,sK127(X0))))
| hBOOL(hAPP_f54304608l_bool(X0,X1))
| sP15(X0)
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1431])]) ).
fof(f7525,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(fequal_nat,sK127(X0))))
| hBOOL(hAPP_f54304608l_bool(X0,X1))
| sP15(X0)
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f5671,f7397]) ).
fof(f5671,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| sP15(X0)
| ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK127(X0)),bot_bot_fun_nat_bool)))
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4232]) ).
fof(f4232,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| sP15(X0)
| ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK127(X0)),bot_bot_fun_nat_bool)))
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK127])],[f3938,f4231]) ).
fof(f4231,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
=> ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK127(X0)),bot_bot_fun_nat_bool))) ),
introduced(choice_axiom,[]) ).
fof(f3938,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| sP15(X0)
| ? [X2] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(definition_folding,[],[f3061,f3937]) ).
fof(f3937,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& bot_bot_fun_nat_bool != X4
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f3061,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& bot_bot_fun_nat_bool != X4
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ? [X2] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f3060]) ).
fof(f3060,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& bot_bot_fun_nat_bool != X4
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ? [X2] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
| bot_bot_fun_nat_bool = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1929]) ).
fof(f1929,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( bot_bot_fun_nat_bool != X1
=> ( ! [X2] : hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
=> ( ! [X3,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( bot_bot_fun_nat_bool != X4
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
=> ( hBOOL(hAPP_f54304608l_bool(X0,X4))
=> hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f888]) ).
fof(f888,axiom,
! [X12,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> ( bot_bot_fun_nat_bool != X6
=> ( ! [X29] : hBOOL(hAPP_f54304608l_bool(X12,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),bot_bot_fun_nat_bool)))
=> ( ! [X29,X78] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X78))
=> ( bot_bot_fun_nat_bool != X78
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X78))
=> ( hBOOL(hAPP_f54304608l_bool(X12,X78))
=> hBOOL(hAPP_f54304608l_bool(X12,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),X78))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23506,plain,
spl263_1430,
inference(avatar_split_clause,[],[f7519,f23504]) ).
fof(f23504,plain,
( spl263_1430
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1430])]) ).
fof(f7519,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f5658,f7397]) ).
fof(f5658,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3054]) ).
fof(f3054,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1923]) ).
fof(f1923,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f759]) ).
fof(f759,axiom,
! [X10,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23502,plain,
spl263_1429,
inference(avatar_split_clause,[],[f7513,f23500]) ).
fof(f23500,plain,
( spl263_1429
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(fequal_int,sK120(X0))))
| hBOOL(hAPP_f448129468l_bool(X0,X1))
| sP14(X0)
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1429])]) ).
fof(f7513,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(fequal_int,sK120(X0))))
| hBOOL(hAPP_f448129468l_bool(X0,X1))
| sP14(X0)
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(forward_demodulation,[],[f5628,f7396]) ).
fof(f5628,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| sP14(X0)
| ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK120(X0)),bot_bot_fun_int_bool)))
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4221]) ).
fof(f4221,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| sP14(X0)
| ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK120(X0)),bot_bot_fun_int_bool)))
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120])],[f3936,f4220]) ).
fof(f4220,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
=> ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK120(X0)),bot_bot_fun_int_bool))) ),
introduced(choice_axiom,[]) ).
fof(f3936,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| sP14(X0)
| ? [X2] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(definition_folding,[],[f3021,f3935]) ).
fof(f3935,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& bot_bot_fun_int_bool != X4
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f3021,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& bot_bot_fun_int_bool != X4
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ? [X2] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f3020]) ).
fof(f3020,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& bot_bot_fun_int_bool != X4
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ? [X2] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
| bot_bot_fun_int_bool = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1900]) ).
fof(f1900,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( bot_bot_fun_int_bool != X1
=> ( ! [X2] : hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
=> ( ! [X3,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( bot_bot_fun_int_bool != X4
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
=> ( hBOOL(hAPP_f448129468l_bool(X0,X4))
=> hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f887]) ).
fof(f887,axiom,
! [X12,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> ( bot_bot_fun_int_bool != X6
=> ( ! [X29] : hBOOL(hAPP_f448129468l_bool(X12,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),bot_bot_fun_int_bool)))
=> ( ! [X29,X78] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X78))
=> ( bot_bot_fun_int_bool != X78
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X78))
=> ( hBOOL(hAPP_f448129468l_bool(X12,X78))
=> hBOOL(hAPP_f448129468l_bool(X12,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),X78))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X12,X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23489,plain,
spl263_1428,
inference(avatar_split_clause,[],[f7507,f23487]) ).
fof(f23487,plain,
( spl263_1428
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1428])]) ).
fof(f7507,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(forward_demodulation,[],[f5615,f7396]) ).
fof(f5615,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3014]) ).
fof(f3014,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1894]) ).
fof(f1894,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1))) ),
inference(rectify,[],[f758]) ).
fof(f758,axiom,
! [X10,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23485,plain,
spl263_1427,
inference(avatar_split_clause,[],[f7478,f23483]) ).
fof(f23483,plain,
( spl263_1427
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
| collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1427])]) ).
fof(f7478,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
| collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ),
inference(forward_demodulation,[],[f7477,f4966]) ).
fof(f7477,plain,
! [X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0
| bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_fun_a_bool(X0) ),
inference(forward_demodulation,[],[f5415,f4966]) ).
fof(f5415,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0
| bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f2821]) ).
fof(f2821,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0
| bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f2820]) ).
fof(f2820,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0
| bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1748]) ).
fof(f1748,plain,
! [X0,X1] :
( is_fun_a_bool(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0
| bot_bot_fun_a_bool = X0 ) ) ),
inference(rectify,[],[f767]) ).
fof(f767,axiom,
! [X4,X10] :
( is_fun_a_bool(X4)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool)))
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool) = X4
| bot_bot_fun_a_bool = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23481,plain,
spl263_1426,
inference(avatar_split_clause,[],[f7137,f23479]) ).
fof(f23479,plain,
( spl263_1426
<=> ! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,pls))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1426])]) ).
fof(f7137,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,pls))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
inference(definition_unfolding,[],[f6850,f4830]) ).
fof(f6850,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
inference(cnf_transformation,[],[f4736]) ).
fof(f23476,plain,
spl263_1425,
inference(avatar_split_clause,[],[f7072,f23474]) ).
fof(f7072,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ),
inference(definition_unfolding,[],[f5165,f4973]) ).
fof(f5165,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ),
inference(cnf_transformation,[],[f4124]) ).
fof(f4124,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ) ),
inference(nnf_transformation,[],[f1612]) ).
fof(f1612,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(rectify,[],[f1304]) ).
fof(f1304,axiom,
! [X15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X15)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23471,plain,
spl263_1424,
inference(avatar_split_clause,[],[f7071,f23469]) ).
fof(f7071,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f5166,f4973]) ).
fof(f5166,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f4124]) ).
fof(f23466,plain,
spl263_1423,
inference(avatar_split_clause,[],[f7070,f23464]) ).
fof(f7070,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ),
inference(definition_unfolding,[],[f5163,f4973]) ).
fof(f5163,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls)) ),
inference(cnf_transformation,[],[f4123]) ).
fof(f4123,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls)) ) ),
inference(nnf_transformation,[],[f1611]) ).
fof(f1611,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(rectify,[],[f1301]) ).
fof(f1301,axiom,
! [X15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X15)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23461,plain,
spl263_1422,
inference(avatar_split_clause,[],[f7069,f23459]) ).
fof(f7069,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f5164,f4973]) ).
fof(f5164,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f4123]) ).
fof(f23456,plain,
spl263_1421,
inference(avatar_split_clause,[],[f7066,f23454]) ).
fof(f7066,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
inference(definition_unfolding,[],[f5159,f4973]) ).
fof(f5159,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ),
inference(cnf_transformation,[],[f4121]) ).
fof(f4121,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ) ),
inference(nnf_transformation,[],[f1609]) ).
fof(f1609,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(rectify,[],[f1297]) ).
fof(f1297,axiom,
! [X15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X15)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23451,plain,
spl263_1420,
inference(avatar_split_clause,[],[f7065,f23449]) ).
fof(f7065,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5160,f4973]) ).
fof(f5160,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(cnf_transformation,[],[f4121]) ).
fof(f23446,plain,
spl263_1419,
inference(avatar_split_clause,[],[f7064,f23444]) ).
fof(f7064,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
inference(definition_unfolding,[],[f5157,f4973]) ).
fof(f5157,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ),
inference(cnf_transformation,[],[f4120]) ).
fof(f4120,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ) ),
inference(nnf_transformation,[],[f1608]) ).
fof(f1608,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(rectify,[],[f1305]) ).
fof(f1305,axiom,
! [X15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X15)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23433,plain,
spl263_1418,
inference(avatar_split_clause,[],[f7063,f23431]) ).
fof(f7063,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5158,f4973]) ).
fof(f5158,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(cnf_transformation,[],[f4120]) ).
fof(f23429,plain,
spl263_1417,
inference(avatar_split_clause,[],[f6902,f23427]) ).
fof(f23427,plain,
( spl263_1417
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1417])]) ).
fof(f6902,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f4766]) ).
fof(f4766,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
inference(flattening,[],[f4765]) ).
fof(f4765,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
inference(nnf_transformation,[],[f3820]) ).
fof(f3820,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(ennf_transformation,[],[f2623]) ).
fof(f2623,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
inference(rectify,[],[f1119]) ).
fof(f1119,axiom,
! [X15,X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23425,plain,
spl263_1416,
inference(avatar_split_clause,[],[f6899,f23423]) ).
fof(f23423,plain,
( spl263_1416
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1416])]) ).
fof(f6899,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f4764]) ).
fof(f4764,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
inference(flattening,[],[f4763]) ).
fof(f4763,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
inference(nnf_transformation,[],[f3819]) ).
fof(f3819,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
inference(ennf_transformation,[],[f2622]) ).
fof(f2622,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
inference(rectify,[],[f1120]) ).
fof(f1120,axiom,
! [X24,X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X15)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23421,plain,
spl263_1415,
inference(avatar_split_clause,[],[f6897,f23419]) ).
fof(f23419,plain,
( spl263_1415
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1415])]) ).
fof(f6897,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4762]) ).
fof(f4762,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
inference(nnf_transformation,[],[f2621]) ).
fof(f2621,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rectify,[],[f985]) ).
fof(f985,axiom,
! [X15,X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23417,plain,
spl263_1414,
inference(avatar_split_clause,[],[f6896,f23415]) ).
fof(f23415,plain,
( spl263_1414
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1414])]) ).
fof(f6896,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(cnf_transformation,[],[f4762]) ).
fof(f23413,plain,
spl263_1413,
inference(avatar_split_clause,[],[f6894,f23411]) ).
fof(f23411,plain,
( spl263_1413
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1413])]) ).
fof(f6894,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
inference(cnf_transformation,[],[f4761]) ).
fof(f4761,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
inference(flattening,[],[f4760]) ).
fof(f4760,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
inference(nnf_transformation,[],[f2620]) ).
fof(f2620,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
inference(rectify,[],[f1107]) ).
fof(f1107,axiom,
! [X24,X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X15)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23409,plain,
spl263_1412,
inference(avatar_split_clause,[],[f6893,f23407]) ).
fof(f23407,plain,
( spl263_1412
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1412])]) ).
fof(f6893,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
inference(cnf_transformation,[],[f4761]) ).
fof(f23405,plain,
spl263_1411,
inference(avatar_split_clause,[],[f6891,f23403]) ).
fof(f23403,plain,
( spl263_1411
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1411])]) ).
fof(f6891,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
inference(cnf_transformation,[],[f4759]) ).
fof(f4759,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
inference(flattening,[],[f4758]) ).
fof(f4758,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
inference(nnf_transformation,[],[f2619]) ).
fof(f2619,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(rectify,[],[f1108]) ).
fof(f1108,axiom,
! [X15,X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23401,plain,
spl263_1410,
inference(avatar_split_clause,[],[f6890,f23399]) ).
fof(f23399,plain,
( spl263_1410
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1410])]) ).
fof(f6890,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
inference(cnf_transformation,[],[f4759]) ).
fof(f23397,plain,
spl263_1409,
inference(avatar_split_clause,[],[f6885,f23395]) ).
fof(f23395,plain,
( spl263_1409
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1409])]) ).
fof(f6885,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ),
inference(cnf_transformation,[],[f4755]) ).
fof(f4755,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ) ),
inference(nnf_transformation,[],[f2616]) ).
fof(f2616,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ),
inference(rectify,[],[f763]) ).
fof(f763,axiom,
! [X4,X7,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9))))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23391,plain,
spl263_1408,
inference(avatar_split_clause,[],[f6884,f23389]) ).
fof(f23389,plain,
( spl263_1408
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1408])]) ).
fof(f6884,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ),
inference(cnf_transformation,[],[f4755]) ).
fof(f23387,plain,
spl263_1407,
inference(avatar_split_clause,[],[f6883,f23385]) ).
fof(f23385,plain,
( spl263_1407
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1407])]) ).
fof(f6883,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ),
inference(cnf_transformation,[],[f4754]) ).
fof(f4754,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ) ),
inference(nnf_transformation,[],[f2615]) ).
fof(f2615,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ),
inference(rectify,[],[f762]) ).
fof(f762,axiom,
! [X4,X7,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9))))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23383,plain,
spl263_1406,
inference(avatar_split_clause,[],[f6882,f23381]) ).
fof(f23381,plain,
( spl263_1406
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1406])]) ).
fof(f6882,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ),
inference(cnf_transformation,[],[f4754]) ).
fof(f23379,plain,
spl263_1405,
inference(avatar_split_clause,[],[f6881,f23377]) ).
fof(f23377,plain,
( spl263_1405
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1405])]) ).
fof(f6881,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ),
inference(cnf_transformation,[],[f4753]) ).
fof(f4753,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ) ),
inference(nnf_transformation,[],[f2614]) ).
fof(f2614,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ),
inference(rectify,[],[f761]) ).
fof(f761,axiom,
! [X4,X7,X9] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X9))))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23375,plain,
spl263_1404,
inference(avatar_split_clause,[],[f6880,f23373]) ).
fof(f23373,plain,
( spl263_1404
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1404])]) ).
fof(f6880,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ),
inference(cnf_transformation,[],[f4753]) ).
fof(f23371,plain,
spl263_1403,
inference(avatar_split_clause,[],[f6879,f23369]) ).
fof(f23369,plain,
( spl263_1403
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1403])]) ).
fof(f6879,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ),
inference(cnf_transformation,[],[f4752]) ).
fof(f4752,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ) ),
inference(nnf_transformation,[],[f2613]) ).
fof(f2613,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ),
inference(rectify,[],[f764]) ).
fof(f764,axiom,
! [X4,X7,X9] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X9))))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23367,plain,
spl263_1402,
inference(avatar_split_clause,[],[f6878,f23365]) ).
fof(f23365,plain,
( spl263_1402
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1402])]) ).
fof(f6878,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ),
inference(cnf_transformation,[],[f4752]) ).
fof(f23363,plain,
spl263_1401,
inference(avatar_split_clause,[],[f6856,f23361]) ).
fof(f23361,plain,
( spl263_1401
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1401])]) ).
fof(f6856,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
inference(cnf_transformation,[],[f4739]) ).
fof(f4739,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f2603]) ).
fof(f2603,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
inference(rectify,[],[f946]) ).
fof(f946,axiom,
! [X119,X15,X32] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X119),X15)),X32))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X119),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X32),X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23359,plain,
spl263_1400,
inference(avatar_split_clause,[],[f6855,f23357]) ).
fof(f23357,plain,
( spl263_1400
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1400])]) ).
fof(f6855,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4739]) ).
fof(f23355,plain,
spl263_1399,
inference(avatar_split_clause,[],[f6854,f23353]) ).
fof(f23353,plain,
( spl263_1399
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1399])]) ).
fof(f6854,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ),
inference(cnf_transformation,[],[f4738]) ).
fof(f4738,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
inference(nnf_transformation,[],[f2602]) ).
fof(f2602,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ),
inference(rectify,[],[f1016]) ).
fof(f1016,axiom,
! [X32,X119,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X119),X15)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X32),X15)),X119)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23350,plain,
spl263_1398,
inference(avatar_split_clause,[],[f6853,f23348]) ).
fof(f23348,plain,
( spl263_1398
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1398])]) ).
fof(f6853,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(cnf_transformation,[],[f4738]) ).
fof(f23346,plain,
spl263_1397,
inference(avatar_split_clause,[],[f6775,f23344]) ).
fof(f23344,plain,
( spl263_1397
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1397])]) ).
fof(f6775,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f4695,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ( ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK260])],[f4693,f4694]) ).
fof(f4694,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f4693,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f4692]) ).
fof(f4692,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(flattening,[],[f4691]) ).
fof(f4691,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3968]) ).
fof(f3968,plain,
! [X0,X1,X2] :
( sP31(X0,X1,X2)
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f23342,plain,
spl263_1396,
inference(avatar_split_clause,[],[f6767,f23340]) ).
fof(f23340,plain,
( spl263_1396
<=> ! [X2,X0,X1] :
( sP30(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1396])]) ).
fof(f6767,plain,
! [X2,X0,X1] :
( sP30(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f4689,plain,
! [X0,X1,X2] :
( ( sP30(X0,X1,X2)
| ( ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK259])],[f4687,f4688]) ).
fof(f4688,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f4687,plain,
! [X0,X1,X2] :
( ( sP30(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(rectify,[],[f4686]) ).
fof(f4686,plain,
! [X0,X1,X2] :
( ( sP30(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(flattening,[],[f4685]) ).
fof(f4685,plain,
! [X0,X1,X2] :
( ( sP30(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3966]) ).
fof(f3966,plain,
! [X0,X1,X2] :
( sP30(X0,X1,X2)
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f23338,plain,
spl263_1395,
inference(avatar_split_clause,[],[f6691,f23336]) ).
fof(f23336,plain,
( spl263_1395
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1395])]) ).
fof(f6691,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
inference(cnf_transformation,[],[f3765]) ).
fof(f3765,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
inference(ennf_transformation,[],[f2554]) ).
fof(f2554,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
inference(rectify,[],[f921]) ).
fof(f921,axiom,
! [X108,X109,X110] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X108),X109)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X110),X109)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X108),X110)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23334,plain,
spl263_1394,
inference(avatar_split_clause,[],[f6690,f23332]) ).
fof(f23332,plain,
( spl263_1394
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1394])]) ).
fof(f6690,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(cnf_transformation,[],[f3764]) ).
fof(f3764,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(ennf_transformation,[],[f2553]) ).
fof(f2553,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X111,X112,X113] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X111),X112)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X111),X113)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X112),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23330,plain,
spl263_1393,
inference(avatar_split_clause,[],[f6689,f23328]) ).
fof(f23328,plain,
( spl263_1393
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1393])]) ).
fof(f6689,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ),
inference(cnf_transformation,[],[f3763]) ).
fof(f3763,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ),
inference(ennf_transformation,[],[f2552]) ).
fof(f2552,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2)) ),
inference(rectify,[],[f920]) ).
fof(f920,axiom,
! [X108,X109,X110] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X108),X109)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X110),X109)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X108),X110)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23326,plain,
spl263_1392,
inference(avatar_split_clause,[],[f6688,f23324]) ).
fof(f23324,plain,
( spl263_1392
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1392])]) ).
fof(f6688,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
inference(cnf_transformation,[],[f3762]) ).
fof(f3762,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
inference(ennf_transformation,[],[f2551]) ).
fof(f2551,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X111,X112,X113] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X111),X112)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X111),X113)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X112),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23322,plain,
spl263_1391,
inference(avatar_split_clause,[],[f6636,f23320]) ).
fof(f23320,plain,
( spl263_1391
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,sK238(X0,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1391])]) ).
fof(f6636,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,sK238(X0,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4619]) ).
fof(f23318,plain,
spl263_1390,
inference(avatar_split_clause,[],[f6624,f23316]) ).
fof(f23316,plain,
( spl263_1390
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1390])]) ).
fof(f6624,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3693]) ).
fof(f3693,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2500]) ).
fof(f2500,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(rectify,[],[f917]) ).
fof(f917,axiom,
! [X101,X102,X103] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X102),X103))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X101),X102)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X101),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23314,plain,
spl263_1389,
inference(avatar_split_clause,[],[f6622,f23312]) ).
fof(f23312,plain,
( spl263_1389
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1389])]) ).
fof(f6622,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f3691,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2498]) ).
fof(f2498,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
inference(rectify,[],[f915]) ).
fof(f915,axiom,
! [X98,X99,X100] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X99),X100))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X99),X98)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X100),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23310,plain,
( spl263_1388
| ~ spl263_25
| ~ spl263_680 ),
inference(avatar_split_clause,[],[f12194,f11673,f7906,f23308]) ).
fof(f23308,plain,
( spl263_1388
<=> ! [X2,X0,X1] : is_bool(hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1388])]) ).
fof(f7906,plain,
( spl263_25
<=> ! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_25])]) ).
fof(f11673,plain,
( spl263_680
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_680])]) ).
fof(f12194,plain,
( ! [X2,X0,X1] : is_bool(hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1))
| ~ spl263_25
| ~ spl263_680 ),
inference(superposition,[],[f7907,f11674]) ).
fof(f11674,plain,
( ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1)
| ~ spl263_680 ),
inference(avatar_component_clause,[],[f11673]) ).
fof(f7907,plain,
( ! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1))
| ~ spl263_25 ),
inference(avatar_component_clause,[],[f7906]) ).
fof(f23306,plain,
spl263_1387,
inference(avatar_split_clause,[],[f6621,f23304]) ).
fof(f23304,plain,
( spl263_1387
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1387])]) ).
fof(f6621,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3690]) ).
fof(f3690,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2497]) ).
fof(f2497,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X25,X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23302,plain,
spl263_1386,
inference(avatar_split_clause,[],[f6620,f23300]) ).
fof(f23300,plain,
( spl263_1386
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1386])]) ).
fof(f6620,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3689]) ).
fof(f3689,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2496]) ).
fof(f2496,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0))) ),
inference(rectify,[],[f284]) ).
fof(f284,axiom,
! [X25,X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23298,plain,
spl263_1385,
inference(avatar_split_clause,[],[f6619,f23296]) ).
fof(f23296,plain,
( spl263_1385
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1385])]) ).
fof(f6619,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3688]) ).
fof(f3688,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2495]) ).
fof(f2495,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0))) ),
inference(rectify,[],[f1095]) ).
fof(f1095,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X21)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23294,plain,
spl263_1384,
inference(avatar_split_clause,[],[f6618,f23292]) ).
fof(f23292,plain,
( spl263_1384
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1384])]) ).
fof(f6618,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3687]) ).
fof(f3687,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2494]) ).
fof(f2494,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
inference(rectify,[],[f1094]) ).
fof(f1094,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X21),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X21),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23290,plain,
spl263_1383,
inference(avatar_split_clause,[],[f6617,f23288]) ).
fof(f23288,plain,
( spl263_1383
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1383])]) ).
fof(f6617,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f3686,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2493]) ).
fof(f2493,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1))) ),
inference(rectify,[],[f947]) ).
fof(f947,axiom,
! [X14,X21,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14)),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23286,plain,
spl263_1382,
inference(avatar_split_clause,[],[f6610,f23284]) ).
fof(f23284,plain,
( spl263_1382
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1382])]) ).
fof(f6610,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3677]) ).
fof(f3677,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(flattening,[],[f3676]) ).
fof(f3676,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2486]) ).
fof(f2486,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0)) ) ),
inference(rectify,[],[f979]) ).
fof(f979,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X22)),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23282,plain,
spl263_1381,
inference(avatar_split_clause,[],[f6607,f23280]) ).
fof(f23280,plain,
( spl263_1381
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1381])]) ).
fof(f6607,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3671]) ).
fof(f3671,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2483]) ).
fof(f2483,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
inference(rectify,[],[f988]) ).
fof(f988,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X21)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23278,plain,
spl263_1380,
inference(avatar_split_clause,[],[f6597,f23276]) ).
fof(f23276,plain,
( spl263_1380
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X2))
| hBOOL(hAPP_int_bool(X0,sK237(X0,X1)))
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1380])]) ).
fof(f6597,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X2))
| hBOOL(hAPP_int_bool(X0,sK237(X0,X1)))
| ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f4617]) ).
fof(f23274,plain,
spl263_1379,
inference(avatar_split_clause,[],[f6594,f23272]) ).
fof(f23272,plain,
( spl263_1379
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| hBOOL(hAPP_int_bool(X0,sK236(X0,X2)))
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1379])]) ).
fof(f6594,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| hBOOL(hAPP_int_bool(X0,sK236(X0,X2)))
| ~ hBOOL(hAPP_int_bool(X0,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f4615]) ).
fof(f23270,plain,
spl263_1378,
inference(avatar_split_clause,[],[f6589,f23268]) ).
fof(f23268,plain,
( spl263_1378
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1378])]) ).
fof(f6589,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f3650]) ).
fof(f3650,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(ennf_transformation,[],[f2469]) ).
fof(f2469,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
inference(rectify,[],[f1147]) ).
fof(f1147,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),X22)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23266,plain,
( spl263_1377
| ~ spl263_25
| ~ spl263_679 ),
inference(avatar_split_clause,[],[f12189,f11669,f7906,f23264]) ).
fof(f23264,plain,
( spl263_1377
<=> ! [X2,X0,X1] : is_bool(hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1377])]) ).
fof(f11669,plain,
( spl263_679
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_679])]) ).
fof(f12189,plain,
( ! [X2,X0,X1] : is_bool(hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1))
| ~ spl263_25
| ~ spl263_679 ),
inference(superposition,[],[f7907,f11670]) ).
fof(f11670,plain,
( ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1)
| ~ spl263_679 ),
inference(avatar_component_clause,[],[f11669]) ).
fof(f23262,plain,
spl263_1376,
inference(avatar_split_clause,[],[f6588,f23260]) ).
fof(f23260,plain,
( spl263_1376
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1376])]) ).
fof(f6588,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f3649]) ).
fof(f3649,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(ennf_transformation,[],[f2468]) ).
fof(f2468,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))) ),
inference(rectify,[],[f914]) ).
fof(f914,axiom,
! [X98,X99,X100] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X99),X100))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X99),X98)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X100),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23258,plain,
spl263_1375,
inference(avatar_split_clause,[],[f6579,f23256]) ).
fof(f23256,plain,
( spl263_1375
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1375])]) ).
fof(f6579,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f3640,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(ennf_transformation,[],[f2463]) ).
fof(f2463,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))) ),
inference(rectify,[],[f1158]) ).
fof(f1158,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),X21)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X23),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23254,plain,
spl263_1374,
inference(avatar_split_clause,[],[f6569,f23252]) ).
fof(f23252,plain,
( spl263_1374
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1374])]) ).
fof(f6569,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3621]) ).
fof(f3621,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2453]) ).
fof(f2453,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
inference(rectify,[],[f573]) ).
fof(f573,axiom,
! [X7,X66,X69] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X66),X69))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X66)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X69))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23250,plain,
spl263_1373,
inference(avatar_split_clause,[],[f6548,f23248]) ).
fof(f23248,plain,
( spl263_1373
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1373])]) ).
fof(f6548,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3589]) ).
fof(f3589,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2432]) ).
fof(f2432,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
inference(rectify,[],[f572]) ).
fof(f572,axiom,
! [X7,X66,X69] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X66),X69))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X66)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X69))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23246,plain,
spl263_1372,
inference(avatar_split_clause,[],[f6532,f23244]) ).
fof(f23244,plain,
( spl263_1372
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1372])]) ).
fof(f6532,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3563]) ).
fof(f3563,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2416]) ).
fof(f2416,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
inference(rectify,[],[f571]) ).
fof(f571,axiom,
! [X7,X66,X69] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X66),X69))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X66)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X69))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23242,plain,
spl263_1371,
inference(avatar_split_clause,[],[f6508,f23240]) ).
fof(f23240,plain,
( spl263_1371
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1371])]) ).
fof(f6508,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(cnf_transformation,[],[f4607]) ).
fof(f4607,plain,
! [X0,X1,X2] :
( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(nnf_transformation,[],[f3535]) ).
fof(f3535,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
<=> X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(ennf_transformation,[],[f2395]) ).
fof(f2395,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f1166]) ).
fof(f1166,axiom,
! [X24,X16,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X16)
<=> X16 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23238,plain,
spl263_1370,
inference(avatar_split_clause,[],[f6465,f23236]) ).
fof(f23236,plain,
( spl263_1370
<=> ! [X2,X0,X1] :
( image_496248727ol_nat(X0,sK216(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1370])]) ).
fof(f6465,plain,
! [X2,X0,X1] :
( image_496248727ol_nat(X0,sK216(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4561]) ).
fof(f23234,plain,
spl263_1369,
inference(avatar_split_clause,[],[f6462,f23232]) ).
fof(f23232,plain,
( spl263_1369
<=> ! [X2,X0,X1] :
( image_1431733819ol_nat(X0,sK215(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1369])]) ).
fof(f6462,plain,
! [X2,X0,X1] :
( image_1431733819ol_nat(X0,sK215(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4559]) ).
fof(f23230,plain,
spl263_1368,
inference(avatar_split_clause,[],[f6459,f23228]) ).
fof(f23228,plain,
( spl263_1368
<=> ! [X2,X0,X1] :
( image_a_nat(X0,sK214(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1368])]) ).
fof(f6459,plain,
! [X2,X0,X1] :
( image_a_nat(X0,sK214(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f23226,plain,
spl263_1367,
inference(avatar_split_clause,[],[f6455,f23224]) ).
fof(f23224,plain,
( spl263_1367
<=> ! [X2,X0,X1] :
( image_fun_a_bool_nat(X0,sK213(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1367])]) ).
fof(f6455,plain,
! [X2,X0,X1] :
( image_fun_a_bool_nat(X0,sK213(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4555]) ).
fof(f23222,plain,
( spl263_1366
| ~ spl263_25
| ~ spl263_563 ),
inference(avatar_split_clause,[],[f11264,f10759,f7906,f23220]) ).
fof(f10759,plain,
( spl263_563
<=> ! [X2,X0,X1] : hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_563])]) ).
fof(f11264,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl263_25
| ~ spl263_563 ),
inference(superposition,[],[f7907,f10760]) ).
fof(f10760,plain,
( ! [X2,X0,X1] : hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))
| ~ spl263_563 ),
inference(avatar_component_clause,[],[f10759]) ).
fof(f23218,plain,
spl263_1365,
inference(avatar_split_clause,[],[f6451,f23216]) ).
fof(f23216,plain,
( spl263_1365
<=> ! [X2,X0,X1] :
( image_1551609309ol_nat(X0,sK212(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1365])]) ).
fof(f6451,plain,
! [X2,X0,X1] :
( image_1551609309ol_nat(X0,sK212(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4553]) ).
fof(f23214,plain,
spl263_1364,
inference(avatar_split_clause,[],[f6447,f23212]) ).
fof(f23212,plain,
( spl263_1364
<=> ! [X2,X0,X1] :
( image_pname_nat(X0,sK211(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1364])]) ).
fof(f6447,plain,
! [X2,X0,X1] :
( image_pname_nat(X0,sK211(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4551]) ).
fof(f23210,plain,
spl263_1363,
inference(avatar_split_clause,[],[f6429,f23208]) ).
fof(f23208,plain,
( spl263_1363
<=> ! [X2,X0,X1] :
( image_nat_int(X0,sK208(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1363])]) ).
fof(f6429,plain,
! [X2,X0,X1] :
( image_nat_int(X0,sK208(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4545]) ).
fof(f23206,plain,
spl263_1362,
inference(avatar_split_clause,[],[f6426,f23204]) ).
fof(f23204,plain,
( spl263_1362
<=> ! [X2,X0,X1] :
( image_2069007511ol_int(X0,sK207(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1362])]) ).
fof(f6426,plain,
! [X2,X0,X1] :
( image_2069007511ol_int(X0,sK207(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4543]) ).
fof(f23202,plain,
spl263_1361,
inference(avatar_split_clause,[],[f6423,f23200]) ).
fof(f23200,plain,
( spl263_1361
<=> ! [X2,X0,X1] :
( image_1133522419ol_int(X0,sK206(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1361])]) ).
fof(f6423,plain,
! [X2,X0,X1] :
( image_1133522419ol_int(X0,sK206(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4541]) ).
fof(f23198,plain,
spl263_1360,
inference(avatar_split_clause,[],[f6420,f23196]) ).
fof(f23196,plain,
( spl263_1360
<=> ! [X2,X0,X1] :
( image_a_int(X0,sK205(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1360])]) ).
fof(f6420,plain,
! [X2,X0,X1] :
( image_a_int(X0,sK205(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4539]) ).
fof(f23194,plain,
spl263_1359,
inference(avatar_split_clause,[],[f6416,f23192]) ).
fof(f23192,plain,
( spl263_1359
<=> ! [X2,X0,X1] :
( image_fun_a_bool_int(X0,sK204(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1359])]) ).
fof(f6416,plain,
! [X2,X0,X1] :
( image_fun_a_bool_int(X0,sK204(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4537]) ).
fof(f23190,plain,
spl263_1358,
inference(avatar_split_clause,[],[f6412,f23188]) ).
fof(f23188,plain,
( spl263_1358
<=> ! [X2,X0,X1] :
( image_41399353ol_int(X0,sK203(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1358])]) ).
fof(f6412,plain,
! [X2,X0,X1] :
( image_41399353ol_int(X0,sK203(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4535]) ).
fof(f23186,plain,
spl263_1357,
inference(avatar_split_clause,[],[f6408,f23184]) ).
fof(f23184,plain,
( spl263_1357
<=> ! [X2,X0,X1] :
( image_pname_int(X0,sK202(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1357])]) ).
fof(f6408,plain,
! [X2,X0,X1] :
( image_pname_int(X0,sK202(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4533]) ).
fof(f23182,plain,
spl263_1356,
inference(avatar_split_clause,[],[f6347,f23180]) ).
fof(f23180,plain,
( spl263_1356
<=> ! [X2,X0,X1] :
( image_26036933t_bool(X0,sK195(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1356])]) ).
fof(f6347,plain,
! [X2,X0,X1] :
( image_26036933t_bool(X0,sK195(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4519]) ).
fof(f23178,plain,
( ~ spl263_1355
| spl263_290
| ~ spl263_473 ),
inference(avatar_split_clause,[],[f10417,f10138,f9124,f23175]) ).
fof(f23175,plain,
( spl263_1355
<=> hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1355])]) ).
fof(f9124,plain,
( spl263_290
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_290])]) ).
fof(f10138,plain,
( spl263_473
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_473])]) ).
fof(f10417,plain,
( ~ hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn)))
| spl263_290
| ~ spl263_473 ),
inference(resolution,[],[f10139,f9126]) ).
fof(f9126,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g))
| spl263_290 ),
inference(avatar_component_clause,[],[f9124]) ).
fof(f10139,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
| ~ spl263_473 ),
inference(avatar_component_clause,[],[f10138]) ).
fof(f23173,plain,
spl263_1354,
inference(avatar_split_clause,[],[f6344,f23171]) ).
fof(f23171,plain,
( spl263_1354
<=> ! [X2,X0,X1] :
( image_1556378401t_bool(X0,sK194(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1354])]) ).
fof(f6344,plain,
! [X2,X0,X1] :
( image_1556378401t_bool(X0,sK194(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4517]) ).
fof(f23169,plain,
spl263_1353,
inference(avatar_split_clause,[],[f6341,f23167]) ).
fof(f23167,plain,
( spl263_1353
<=> ! [X2,X0,X1] :
( image_275383677t_bool(X0,sK193(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1353])]) ).
fof(f6341,plain,
! [X2,X0,X1] :
( image_275383677t_bool(X0,sK193(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4515]) ).
fof(f23165,plain,
spl263_1352,
inference(avatar_split_clause,[],[f6338,f23163]) ).
fof(f23163,plain,
( spl263_1352
<=> ! [X2,X0,X1] :
( image_892525857t_bool(X0,sK192(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1352])]) ).
fof(f6338,plain,
! [X2,X0,X1] :
( image_892525857t_bool(X0,sK192(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4513]) ).
fof(f23161,plain,
spl263_1351,
inference(avatar_split_clause,[],[f6335,f23159]) ).
fof(f23159,plain,
( spl263_1351
<=> ! [X2,X0,X1] :
( image_1512837979t_bool(X0,sK191(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1351])]) ).
fof(f6335,plain,
! [X2,X0,X1] :
( image_1512837979t_bool(X0,sK191(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4511]) ).
fof(f23157,plain,
spl263_1350,
inference(avatar_split_clause,[],[f6331,f23155]) ).
fof(f23155,plain,
( spl263_1350
<=> ! [X2,X0,X1] :
( image_2129980159t_bool(X0,sK190(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1350])]) ).
fof(f6331,plain,
! [X2,X0,X1] :
( image_2129980159t_bool(X0,sK190(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4509]) ).
fof(f23153,plain,
spl263_1349,
inference(avatar_split_clause,[],[f6327,f23151]) ).
fof(f23151,plain,
( spl263_1349
<=> ! [X2,X0,X1] :
( image_a_fun_nat_bool(X0,sK189(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1349])]) ).
fof(f6327,plain,
! [X2,X0,X1] :
( image_a_fun_nat_bool(X0,sK189(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4507]) ).
fof(f23149,plain,
spl263_1348,
inference(avatar_split_clause,[],[f6323,f23147]) ).
fof(f23147,plain,
( spl263_1348
<=> ! [X2,X0,X1] :
( image_a_fun_int_bool(X0,sK188(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1348])]) ).
fof(f6323,plain,
! [X2,X0,X1] :
( image_a_fun_int_bool(X0,sK188(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4505]) ).
fof(f23145,plain,
spl263_1347,
inference(avatar_split_clause,[],[f6177,f23143]) ).
fof(f23143,plain,
( spl263_1347
<=> ! [X2,X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1347])]) ).
fof(f6177,plain,
! [X2,X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))),
inference(cnf_transformation,[],[f2243]) ).
fof(f2243,plain,
! [X0,X1,X2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))),
inference(rectify,[],[f765]) ).
fof(f765,axiom,
! [X8,X4,X9] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X8,X4)),image_nat_int(X8,X9))),image_nat_int(X8,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23141,plain,
spl263_1346,
inference(avatar_split_clause,[],[f6176,f23139]) ).
fof(f23139,plain,
( spl263_1346
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1346])]) ).
fof(f6176,plain,
! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))),
inference(cnf_transformation,[],[f2242]) ).
fof(f2242,plain,
! [X0,X1,X2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))),
inference(rectify,[],[f766]) ).
fof(f766,axiom,
! [X8,X4,X9] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X8,X4)),image_pname_a(X8,X9))),image_pname_a(X8,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23134,plain,
( spl263_1345
| ~ spl263_37
| ~ spl263_135 ),
inference(avatar_split_clause,[],[f8444,f8437,f7960,f23132]) ).
fof(f23132,plain,
( spl263_1345
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP5(hAPP_f2050579477a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1345])]) ).
fof(f8437,plain,
( spl263_135
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_135])]) ).
fof(f8444,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP5(hAPP_f2050579477a_bool(X1,X0)) )
| ~ spl263_37
| ~ spl263_135 ),
inference(resolution,[],[f8438,f7961]) ).
fof(f8438,plain,
( ! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl263_135 ),
inference(avatar_component_clause,[],[f8437]) ).
fof(f23130,plain,
( spl263_1344
| ~ spl263_543
| ~ spl263_749
| ~ spl263_1343 ),
inference(avatar_split_clause,[],[f23126,f23122,f12592,f10678,f23128]) ).
fof(f23128,plain,
( spl263_1344
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK151(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1344])]) ).
fof(f10678,plain,
( spl263_543
<=> ! [X2,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_543])]) ).
fof(f12592,plain,
( spl263_749
<=> ! [X2,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_749])]) ).
fof(f23122,plain,
( spl263_1343
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK151(X0,X1))),hAPP_nat_bool(X1,sK151(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1343])]) ).
fof(f23126,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK151(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_749
| ~ spl263_1343 ),
inference(forward_demodulation,[],[f23125,f12593]) ).
fof(f12593,plain,
( ! [X2,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2))
| ~ spl263_749 ),
inference(avatar_component_clause,[],[f12592]) ).
fof(f23125,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),sK151(X0,X1)),hAPP_nat_bool(X1,sK151(X0,X1))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_1343 ),
inference(forward_demodulation,[],[f23123,f10679]) ).
fof(f10679,plain,
( ! [X2,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2))
| ~ spl263_543 ),
inference(avatar_component_clause,[],[f10678]) ).
fof(f23123,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK151(X0,X1))),hAPP_nat_bool(X1,sK151(X0,X1)))) )
| ~ spl263_1343 ),
inference(avatar_component_clause,[],[f23122]) ).
fof(f23124,plain,
spl263_1343,
inference(avatar_split_clause,[],[f5930,f23122]) ).
fof(f5930,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK151(X0,X1))),hAPP_nat_bool(X1,sK151(X0,X1)))) ),
inference(cnf_transformation,[],[f4333]) ).
fof(f4333,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK151(X0,X1))),hAPP_nat_bool(X1,sK151(X0,X1)))) )
& ( ! [X3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f4331,f4332]) ).
fof(f4332,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK151(X0,X1))),hAPP_nat_bool(X1,sK151(X0,X1)))) ),
introduced(choice_axiom,[]) ).
fof(f4331,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) )
& ( ! [X3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
inference(rectify,[],[f4330]) ).
fof(f4330,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) )
& ( ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
inference(nnf_transformation,[],[f2096]) ).
fof(f2096,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
<=> ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) ),
inference(rectify,[],[f549]) ).
fof(f549,axiom,
! [X8,X68] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X8),X68))
<=> ! [X29] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X8,X29)),hAPP_nat_bool(X68,X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23117,plain,
( spl263_1342
| ~ spl263_542
| ~ spl263_748
| ~ spl263_1341 ),
inference(avatar_split_clause,[],[f23113,f23109,f12588,f10674,f23115]) ).
fof(f23115,plain,
( spl263_1342
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK150(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1342])]) ).
fof(f10674,plain,
( spl263_542
<=> ! [X2,X0,X1] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_542])]) ).
fof(f12588,plain,
( spl263_748
<=> ! [X2,X0,X1] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_748])]) ).
fof(f23109,plain,
( spl263_1341
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK150(X0,X1))),hAPP_int_bool(X1,sK150(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1341])]) ).
fof(f23113,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK150(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_748
| ~ spl263_1341 ),
inference(forward_demodulation,[],[f23112,f12589]) ).
fof(f12589,plain,
( ! [X2,X0,X1] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2))
| ~ spl263_748 ),
inference(avatar_component_clause,[],[f12588]) ).
fof(f23112,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),sK150(X0,X1)),hAPP_int_bool(X1,sK150(X0,X1))))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_1341 ),
inference(forward_demodulation,[],[f23110,f10675]) ).
fof(f10675,plain,
( ! [X2,X0,X1] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2))
| ~ spl263_542 ),
inference(avatar_component_clause,[],[f10674]) ).
fof(f23110,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK150(X0,X1))),hAPP_int_bool(X1,sK150(X0,X1)))) )
| ~ spl263_1341 ),
inference(avatar_component_clause,[],[f23109]) ).
fof(f23111,plain,
spl263_1341,
inference(avatar_split_clause,[],[f5920,f23109]) ).
fof(f5920,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK150(X0,X1))),hAPP_int_bool(X1,sK150(X0,X1)))) ),
inference(cnf_transformation,[],[f4325]) ).
fof(f4325,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK150(X0,X1))),hAPP_int_bool(X1,sK150(X0,X1)))) )
& ( ! [X3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150])],[f4323,f4324]) ).
fof(f4324,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK150(X0,X1))),hAPP_int_bool(X1,sK150(X0,X1)))) ),
introduced(choice_axiom,[]) ).
fof(f4323,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) )
& ( ! [X3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
inference(rectify,[],[f4322]) ).
fof(f4322,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) )
& ( ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
inference(nnf_transformation,[],[f2091]) ).
fof(f2091,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
<=> ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) ),
inference(rectify,[],[f548]) ).
fof(f548,axiom,
! [X8,X68] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),X68))
<=> ! [X29] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X8,X29)),hAPP_int_bool(X68,X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23103,plain,
( spl263_1340
| ~ spl263_541
| ~ spl263_743
| ~ spl263_1339 ),
inference(avatar_split_clause,[],[f23099,f23095,f12567,f10670,f23101]) ).
fof(f23101,plain,
( spl263_1340
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK149(X0,X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1340])]) ).
fof(f10670,plain,
( spl263_541
<=> ! [X2,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_541])]) ).
fof(f12567,plain,
( spl263_743
<=> ! [X2,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_743])]) ).
fof(f23095,plain,
( spl263_1339
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK149(X0,X1))),hAPP_a_bool(X1,sK149(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1339])]) ).
fof(f23099,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK149(X0,X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
| ~ spl263_541
| ~ spl263_743
| ~ spl263_1339 ),
inference(forward_demodulation,[],[f23098,f12568]) ).
fof(f12568,plain,
( ! [X2,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2))
| ~ spl263_743 ),
inference(avatar_component_clause,[],[f12567]) ).
fof(f23098,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),sK149(X0,X1)),hAPP_a_bool(X1,sK149(X0,X1))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
| ~ spl263_541
| ~ spl263_1339 ),
inference(forward_demodulation,[],[f23096,f10671]) ).
fof(f10671,plain,
( ! [X2,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2))
| ~ spl263_541 ),
inference(avatar_component_clause,[],[f10670]) ).
fof(f23096,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK149(X0,X1))),hAPP_a_bool(X1,sK149(X0,X1)))) )
| ~ spl263_1339 ),
inference(avatar_component_clause,[],[f23095]) ).
fof(f23097,plain,
spl263_1339,
inference(avatar_split_clause,[],[f5916,f23095]) ).
fof(f5916,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK149(X0,X1))),hAPP_a_bool(X1,sK149(X0,X1)))) ),
inference(cnf_transformation,[],[f4320]) ).
fof(f4320,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK149(X0,X1))),hAPP_a_bool(X1,sK149(X0,X1))))
& is_a(sK149(X0,X1)) ) )
& ( ! [X3] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
| ~ is_a(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f4318,f4319]) ).
fof(f4319,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
& is_a(X2) )
=> ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK149(X0,X1))),hAPP_a_bool(X1,sK149(X0,X1))))
& is_a(sK149(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f4318,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ? [X2] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
& is_a(X2) ) )
& ( ! [X3] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
| ~ is_a(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
inference(rectify,[],[f4317]) ).
fof(f4317,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ? [X2] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
& is_a(X2) ) )
& ( ! [X2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
| ~ is_a(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
inference(nnf_transformation,[],[f3280]) ).
fof(f3280,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
<=> ! [X2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
| ~ is_a(X2) ) ),
inference(ennf_transformation,[],[f2089]) ).
fof(f2089,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
<=> ! [X2] :
( is_a(X2)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) ) ),
inference(rectify,[],[f550]) ).
fof(f550,axiom,
! [X8,X68] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),X68))
<=> ! [X29] :
( is_a(X29)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X8,X29)),hAPP_a_bool(X68,X29))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23089,plain,
( spl263_1338
| ~ spl263_541
| ~ spl263_743
| ~ spl263_1336 ),
inference(avatar_split_clause,[],[f23081,f23077,f12567,f10670,f23087]) ).
fof(f23087,plain,
( spl263_1338
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK142(X0,X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1338])]) ).
fof(f23077,plain,
( spl263_1336
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK142(X0,X1))),hAPP_a_bool(X1,sK142(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1336])]) ).
fof(f23081,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK142(X0,X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
| ~ spl263_541
| ~ spl263_743
| ~ spl263_1336 ),
inference(forward_demodulation,[],[f23080,f12568]) ).
fof(f23080,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),sK142(X0,X1)),hAPP_a_bool(X1,sK142(X0,X1))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
| ~ spl263_541
| ~ spl263_1336 ),
inference(forward_demodulation,[],[f23078,f10671]) ).
fof(f23078,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK142(X0,X1))),hAPP_a_bool(X1,sK142(X0,X1)))) )
| ~ spl263_1336 ),
inference(avatar_component_clause,[],[f23077]) ).
fof(f23085,plain,
( spl263_1337
| ~ spl263_38
| ~ spl263_135 ),
inference(avatar_split_clause,[],[f8443,f8437,f7964,f23083]) ).
fof(f23083,plain,
( spl263_1337
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP7(hAPP_f2050579477a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1337])]) ).
fof(f8443,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| sP7(hAPP_f2050579477a_bool(X1,X0)) )
| ~ spl263_38
| ~ spl263_135 ),
inference(resolution,[],[f8438,f7965]) ).
fof(f23079,plain,
spl263_1336,
inference(avatar_split_clause,[],[f5847,f23077]) ).
fof(f5847,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK142(X0,X1))),hAPP_a_bool(X1,sK142(X0,X1)))) ),
inference(cnf_transformation,[],[f4274]) ).
fof(f4274,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK142(X0,X1))),hAPP_a_bool(X1,sK142(X0,X1))))
& is_a(sK142(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142])],[f3270,f4273]) ).
fof(f4273,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
& is_a(X2) )
=> ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK142(X0,X1))),hAPP_a_bool(X1,sK142(X0,X1))))
& is_a(sK142(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3270,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ? [X2] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
& is_a(X2) ) ),
inference(ennf_transformation,[],[f2066]) ).
fof(f2066,plain,
! [X0,X1] :
( ! [X2] :
( is_a(X2)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(rectify,[],[f592]) ).
fof(f592,axiom,
! [X8,X68] :
( ! [X29] :
( is_a(X29)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X8,X29)),hAPP_a_bool(X68,X29))) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23072,plain,
( spl263_1335
| ~ spl263_543
| ~ spl263_749
| ~ spl263_1334 ),
inference(avatar_split_clause,[],[f23068,f23064,f12592,f10678,f23070]) ).
fof(f23070,plain,
( spl263_1335
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK141(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1335])]) ).
fof(f23064,plain,
( spl263_1334
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK141(X0,X1))),hAPP_nat_bool(X1,sK141(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1334])]) ).
fof(f23068,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK141(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_749
| ~ spl263_1334 ),
inference(forward_demodulation,[],[f23067,f12593]) ).
fof(f23067,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),sK141(X0,X1)),hAPP_nat_bool(X1,sK141(X0,X1))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_1334 ),
inference(forward_demodulation,[],[f23065,f10679]) ).
fof(f23065,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK141(X0,X1))),hAPP_nat_bool(X1,sK141(X0,X1)))) )
| ~ spl263_1334 ),
inference(avatar_component_clause,[],[f23064]) ).
fof(f23066,plain,
spl263_1334,
inference(avatar_split_clause,[],[f5845,f23064]) ).
fof(f5845,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK141(X0,X1))),hAPP_nat_bool(X1,sK141(X0,X1)))) ),
inference(cnf_transformation,[],[f4272]) ).
fof(f4272,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK141(X0,X1))),hAPP_nat_bool(X1,sK141(X0,X1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141])],[f3269,f4271]) ).
fof(f4271,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK141(X0,X1))),hAPP_nat_bool(X1,sK141(X0,X1)))) ),
introduced(choice_axiom,[]) ).
fof(f3269,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) ),
inference(ennf_transformation,[],[f2065]) ).
fof(f2065,plain,
! [X0,X1] :
( ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(rectify,[],[f591]) ).
fof(f591,axiom,
! [X8,X68] :
( ! [X29] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X8,X29)),hAPP_nat_bool(X68,X29)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X8),X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23059,plain,
( spl263_1333
| ~ spl263_542
| ~ spl263_748
| ~ spl263_1332 ),
inference(avatar_split_clause,[],[f23055,f23051,f12588,f10674,f23057]) ).
fof(f23057,plain,
( spl263_1333
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK140(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1333])]) ).
fof(f23051,plain,
( spl263_1332
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK140(X0,X1))),hAPP_int_bool(X1,sK140(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1332])]) ).
fof(f23055,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK140(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_748
| ~ spl263_1332 ),
inference(forward_demodulation,[],[f23054,f12589]) ).
fof(f23054,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),sK140(X0,X1)),hAPP_int_bool(X1,sK140(X0,X1))))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_1332 ),
inference(forward_demodulation,[],[f23052,f10675]) ).
fof(f23052,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK140(X0,X1))),hAPP_int_bool(X1,sK140(X0,X1)))) )
| ~ spl263_1332 ),
inference(avatar_component_clause,[],[f23051]) ).
fof(f23053,plain,
spl263_1332,
inference(avatar_split_clause,[],[f5844,f23051]) ).
fof(f5844,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK140(X0,X1))),hAPP_int_bool(X1,sK140(X0,X1)))) ),
inference(cnf_transformation,[],[f4270]) ).
fof(f4270,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK140(X0,X1))),hAPP_int_bool(X1,sK140(X0,X1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK140])],[f3268,f4269]) ).
fof(f4269,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK140(X0,X1))),hAPP_int_bool(X1,sK140(X0,X1)))) ),
introduced(choice_axiom,[]) ).
fof(f3268,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ? [X2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) ),
inference(ennf_transformation,[],[f2064]) ).
fof(f2064,plain,
! [X0,X1] :
( ! [X2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
inference(rectify,[],[f590]) ).
fof(f590,axiom,
! [X8,X68] :
( ! [X29] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X8,X29)),hAPP_int_bool(X68,X29)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23049,plain,
spl263_1331,
inference(avatar_split_clause,[],[f5685,f23047]) ).
fof(f23047,plain,
( spl263_1331
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1331])]) ).
fof(f5685,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3077]) ).
fof(f3077,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f3076]) ).
fof(f3076,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1937]) ).
fof(f1937,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1))) ) ),
inference(rectify,[],[f184]) ).
fof(f184,axiom,
! [X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X4)),hAPP_f22106695ol_nat(finite_card_nat,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23045,plain,
spl263_1330,
inference(avatar_split_clause,[],[f5677,f23043]) ).
fof(f23043,plain,
( spl263_1330
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(X0)),sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1330])]) ).
fof(f5677,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(X0)),sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4236]) ).
fof(f4236,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK131(X0)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK130(X0)),bot_bot_fun_nat_bool))))
& hBOOL(hAPP_f54304608l_bool(X0,sK131(X0)))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(X0)),sK131(X0)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK131(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130,sK131])],[f3065,f4235]) ).
fof(f4235,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK131(X0)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK130(X0)),bot_bot_fun_nat_bool))))
& hBOOL(hAPP_f54304608l_bool(X0,sK131(X0)))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(X0)),sK131(X0)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK131(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3065,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f3064]) ).
fof(f3064,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1931]) ).
fof(f1931,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(X0,X1))
=> ( ! [X2,X3] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
=> ( hBOOL(hAPP_f54304608l_bool(X0,X3))
=> hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool)) ) ) ),
inference(rectify,[],[f792]) ).
fof(f792,axiom,
! [X12,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f54304608l_bool(X12,X4))
=> ( ! [X77,X80] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X80))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X77),X80))
=> ( hBOOL(hAPP_f54304608l_bool(X12,X80))
=> hBOOL(hAPP_f54304608l_bool(X12,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X80),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X77),bot_bot_fun_nat_bool)))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X12,bot_bot_fun_nat_bool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23041,plain,
spl263_1329,
inference(avatar_split_clause,[],[f5673,f23039]) ).
fof(f23039,plain,
( spl263_1329
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK128(X0)),sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1329])]) ).
fof(f5673,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK128(X0)),sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4234]) ).
fof(f23037,plain,
( spl263_1328
| ~ spl263_37
| ~ spl263_133 ),
inference(avatar_split_clause,[],[f8441,f8429,f7960,f23035]) ).
fof(f23035,plain,
( spl263_1328
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP5(image_pname_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1328])]) ).
fof(f8429,plain,
( spl263_133
<=> ! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_133])]) ).
fof(f8441,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP5(image_pname_a(X1,X0)) )
| ~ spl263_37
| ~ spl263_133 ),
inference(resolution,[],[f8430,f7961]) ).
fof(f8430,plain,
( ! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl263_133 ),
inference(avatar_component_clause,[],[f8429]) ).
fof(f23033,plain,
spl263_1327,
inference(avatar_split_clause,[],[f5642,f23031]) ).
fof(f23031,plain,
( spl263_1327
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1327])]) ).
fof(f5642,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3037]) ).
fof(f3037,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f3036]) ).
fof(f3036,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1908]) ).
fof(f1908,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1))) ) ),
inference(rectify,[],[f185]) ).
fof(f185,axiom,
! [X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X4)),hAPP_f957591787ol_nat(finite_card_int,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23029,plain,
spl263_1326,
inference(avatar_split_clause,[],[f5634,f23027]) ).
fof(f23027,plain,
( spl263_1326
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK123(X0)),sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1326])]) ).
fof(f5634,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK123(X0)),sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4225]) ).
fof(f4225,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK124(X0)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK123(X0)),bot_bot_fun_int_bool))))
& hBOOL(hAPP_f448129468l_bool(X0,sK124(X0)))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK123(X0)),sK124(X0)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK124(X0))) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK123,sK124])],[f3025,f4224]) ).
fof(f4224,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK124(X0)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK123(X0)),bot_bot_fun_int_bool))))
& hBOOL(hAPP_f448129468l_bool(X0,sK124(X0)))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK123(X0)),sK124(X0)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK124(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3025,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f3024]) ).
fof(f3024,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1902]) ).
fof(f1902,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f448129468l_bool(X0,X1))
=> ( ! [X2,X3] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
=> ( hBOOL(hAPP_f448129468l_bool(X0,X3))
=> hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool)) ) ) ),
inference(rectify,[],[f791]) ).
fof(f791,axiom,
! [X12,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f448129468l_bool(X12,X4))
=> ( ! [X77,X80] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X80))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X77),X80))
=> ( hBOOL(hAPP_f448129468l_bool(X12,X80))
=> hBOOL(hAPP_f448129468l_bool(X12,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X80),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X77),bot_bot_fun_int_bool)))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X12,bot_bot_fun_int_bool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23025,plain,
spl263_1325,
inference(avatar_split_clause,[],[f5630,f23023]) ).
fof(f23023,plain,
( spl263_1325
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK121(X0)),sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1325])]) ).
fof(f5630,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK121(X0)),sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4223]) ).
fof(f23021,plain,
spl263_1324,
inference(avatar_split_clause,[],[f5604,f23019]) ).
fof(f23019,plain,
( spl263_1324
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1324])]) ).
fof(f5604,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f3002]) ).
fof(f3002,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f3001]) ).
fof(f3001,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1883]) ).
fof(f1883,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1))) ) ),
inference(rectify,[],[f183]) ).
fof(f183,axiom,
! [X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X4)),hAPP_fun_a_bool_nat(finite_card_a,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23017,plain,
spl263_1323,
inference(avatar_split_clause,[],[f5561,f23015]) ).
fof(f23015,plain,
( spl263_1323
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1323])]) ).
fof(f5561,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2962]) ).
fof(f2962,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f2961]) ).
fof(f2961,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1855]) ).
fof(f1855,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1))) ) ),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X4)),hAPP_f921600141ol_nat(finite_card_pname,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23013,plain,
spl263_1322,
inference(avatar_split_clause,[],[f5522,f23011]) ).
fof(f23011,plain,
( spl263_1322
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1322])]) ).
fof(f5522,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2930]) ).
fof(f2930,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(flattening,[],[f2929]) ).
fof(f2929,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1830]) ).
fof(f1830,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ) ),
inference(rectify,[],[f180]) ).
fof(f180,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X4)),hAPP_f55526627ol_nat(finite1340463720e_bool,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23009,plain,
spl263_1321,
inference(avatar_split_clause,[],[f5521,f23007]) ).
fof(f23007,plain,
( spl263_1321
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1321])]) ).
fof(f5521,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2928]) ).
fof(f2928,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(flattening,[],[f2927]) ).
fof(f2927,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1829]) ).
fof(f1829,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ) ),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X4,X9] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X4)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23005,plain,
spl263_1320,
inference(avatar_split_clause,[],[f5520,f23003]) ).
fof(f23003,plain,
( spl263_1320
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1320])]) ).
fof(f5520,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2926]) ).
fof(f2926,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(flattening,[],[f2925]) ).
fof(f2925,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1828]) ).
fof(f1828,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ) ),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X4)),hAPP_f696928925ol_nat(finite346522414t_bool,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f23001,plain,
spl263_1319,
inference(avatar_split_clause,[],[f5519,f22999]) ).
fof(f22999,plain,
( spl263_1319
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1319])]) ).
fof(f5519,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2924]) ).
fof(f2924,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(flattening,[],[f2923]) ).
fof(f2923,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1827]) ).
fof(f1827,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ) ),
inference(rectify,[],[f178]) ).
fof(f178,axiom,
! [X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4),X9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X4)),hAPP_f521865025ol_nat(finite1876863882t_bool,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22997,plain,
spl263_1318,
inference(avatar_split_clause,[],[f5469,f22995]) ).
fof(f22995,plain,
( spl263_1318
<=> ! [X0,X1,X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK109(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1318])]) ).
fof(f5469,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK109(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4198]) ).
fof(f4198,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(X1,sK109(X0,X1)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK109(X0,X1))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(X0,X1)),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f2870,f4197]) ).
fof(f4197,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
=> ( hBOOL(hAPP_nat_bool(X1,sK109(X0,X1)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK109(X0,X1))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2870,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(flattening,[],[f2869]) ).
fof(f2869,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(ennf_transformation,[],[f1782]) ).
fof(f1782,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X1,X0))
=> ? [X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
& ! [X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
=> ~ hBOOL(hAPP_nat_bool(X1,X3)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ) ),
inference(rectify,[],[f1077]) ).
fof(f1077,axiom,
! [X16,X12] :
( ~ hBOOL(hAPP_nat_bool(X12,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X12,X16))
=> ? [X118] :
( hBOOL(hAPP_nat_bool(X12,X118))
& ! [X125] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X125),X118))
=> ~ hBOOL(hAPP_nat_bool(X12,X125)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X118),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22993,plain,
( spl263_1317
| ~ spl263_38
| ~ spl263_133 ),
inference(avatar_split_clause,[],[f8440,f8429,f7964,f22991]) ).
fof(f22991,plain,
( spl263_1317
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP7(image_pname_a(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1317])]) ).
fof(f8440,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| sP7(image_pname_a(X1,X0)) )
| ~ spl263_38
| ~ spl263_133 ),
inference(resolution,[],[f8430,f7965]) ).
fof(f22989,plain,
spl263_1316,
inference(avatar_split_clause,[],[f5466,f22987]) ).
fof(f22987,plain,
( spl263_1316
<=> ! [X0,X1,X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK108(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1316])]) ).
fof(f5466,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK108(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4196]) ).
fof(f4196,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK108(X0,X1)),one_one_nat)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK108(X0,X1))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK108(X0,X1)),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f2868,f4195]) ).
fof(f4195,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
=> ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK108(X0,X1)),one_one_nat)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK108(X0,X1))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK108(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2868,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(flattening,[],[f2867]) ).
fof(f2867,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
& ! [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(ennf_transformation,[],[f1781]) ).
fof(f1781,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X1,X0))
=> ? [X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
& ! [X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
=> ~ hBOOL(hAPP_nat_bool(X1,X3)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ) ),
inference(rectify,[],[f1076]) ).
fof(f1076,axiom,
! [X16,X12] :
( ~ hBOOL(hAPP_nat_bool(X12,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X12,X16))
=> ? [X118] :
( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X118),one_one_nat)))
& ! [X125] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X125),X118))
=> ~ hBOOL(hAPP_nat_bool(X12,X125)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X118),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22984,plain,
spl263_1315,
inference(avatar_split_clause,[],[f5305,f22982]) ).
fof(f5305,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 ),
inference(cnf_transformation,[],[f2755]) ).
fof(f2755,plain,
! [X0,X1] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0))
| zero_zero_nat = X1 )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = X0
| zero_zero_nat != X1 ) ),
inference(ennf_transformation,[],[f1698]) ).
fof(f1698,plain,
! [X0,X1] :
( ( zero_zero_nat != X1
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
& ( zero_zero_nat = X1
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = X0 ) ),
inference(rectify,[],[f1075]) ).
fof(f1075,axiom,
! [X13,X14] :
( ( zero_zero_nat != X14
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),one_one_nat)),X13)) )
& ( zero_zero_nat = X14
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22980,plain,
spl263_1314,
inference(avatar_split_clause,[],[f5299,f22978]) ).
fof(f22978,plain,
( spl263_1314
<=> ! [X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1314])]) ).
fof(f5299,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),
inference(cnf_transformation,[],[f1695]) ).
fof(f1695,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),
inference(rectify,[],[f833]) ).
fof(f833,axiom,
! [X4,X9] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X4)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22976,plain,
spl263_1313,
inference(avatar_split_clause,[],[f5298,f22974]) ).
fof(f22974,plain,
( spl263_1313
<=> ! [X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1313])]) ).
fof(f5298,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))),
inference(cnf_transformation,[],[f1694]) ).
fof(f1694,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))),
inference(rectify,[],[f832]) ).
fof(f832,axiom,
! [X4,X9] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22972,plain,
spl263_1312,
inference(avatar_split_clause,[],[f5297,f22970]) ).
fof(f22970,plain,
( spl263_1312
<=> ! [X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1312])]) ).
fof(f5297,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))),
inference(cnf_transformation,[],[f1693]) ).
fof(f1693,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))),
inference(rectify,[],[f831]) ).
fof(f831,axiom,
! [X4,X9] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22968,plain,
spl263_1311,
inference(avatar_split_clause,[],[f5296,f22966]) ).
fof(f22966,plain,
( spl263_1311
<=> ! [X0,X1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1311])]) ).
fof(f5296,plain,
! [X0,X1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))),
inference(cnf_transformation,[],[f1692]) ).
fof(f1692,plain,
! [X0,X1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))),
inference(rectify,[],[f834]) ).
fof(f834,axiom,
! [X4,X9] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X4)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f22367,plain,
( spl263_1310
| spl263_23
| ~ spl263_841 ),
inference(avatar_split_clause,[],[f20119,f13360,f7896,f22365]) ).
fof(f22365,plain,
( spl263_1310
<=> ! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1310])]) ).
fof(f13360,plain,
( spl263_841
<=> ! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_841])]) ).
fof(f20119,plain,
( ! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),X1),X0))
| spl263_23
| ~ spl263_841 ),
inference(resolution,[],[f13361,f7898]) ).
fof(f13361,plain,
( ! [X2,X0,X1] :
( hBOOL(X2)
| hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
| ~ spl263_841 ),
inference(avatar_component_clause,[],[f13360]) ).
fof(f22275,plain,
( spl263_781
| spl263_5
| ~ spl263_383
| ~ spl263_1074 ),
inference(avatar_split_clause,[],[f19526,f16112,f9678,f7808,f13120]) ).
fof(f13120,plain,
( spl263_781
<=> ! [X0] : ~ sP24(bot_bot_fun_int_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_781])]) ).
fof(f7808,plain,
( spl263_5
<=> hBOOL(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_5])]) ).
fof(f9678,plain,
( spl263_383
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_383])]) ).
fof(f16112,plain,
( spl263_1074
<=> ! [X0] : fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1074])]) ).
fof(f19526,plain,
( ! [X0] :
( hBOOL(fFalse)
| ~ sP24(bot_bot_fun_int_bool,X0) )
| ~ spl263_383
| ~ spl263_1074 ),
inference(superposition,[],[f9679,f16113]) ).
fof(f16113,plain,
( ! [X0] : fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0)
| ~ spl263_1074 ),
inference(avatar_component_clause,[],[f16112]) ).
fof(f9679,plain,
( ! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
| ~ sP24(X0,X1) )
| ~ spl263_383 ),
inference(avatar_component_clause,[],[f9678]) ).
fof(f21497,plain,
( spl263_1308
| spl263_1309
| ~ spl263_84
| ~ spl263_249 ),
inference(avatar_split_clause,[],[f9100,f8944,f8161,f21494,f21490]) ).
fof(f21490,plain,
( spl263_1308
<=> sP4(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1308])]) ).
fof(f21494,plain,
( spl263_1309
<=> bot_bot_fun_a_bool = g ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1309])]) ).
fof(f8161,plain,
( spl263_84
<=> sP5(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_84])]) ).
fof(f8944,plain,
( spl263_249
<=> ! [X0] :
( sP4(X0)
| bot_bot_fun_a_bool = X0
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_249])]) ).
fof(f9100,plain,
( bot_bot_fun_a_bool = g
| sP4(g)
| ~ spl263_84
| ~ spl263_249 ),
inference(resolution,[],[f8945,f8163]) ).
fof(f8163,plain,
( sP5(g)
| ~ spl263_84 ),
inference(avatar_component_clause,[],[f8161]) ).
fof(f8945,plain,
( ! [X0] :
( ~ sP5(X0)
| bot_bot_fun_a_bool = X0
| sP4(X0) )
| ~ spl263_249 ),
inference(avatar_component_clause,[],[f8944]) ).
fof(f21316,plain,
spl263_1307,
inference(avatar_split_clause,[],[f7673,f21314]) ).
fof(f21314,plain,
( spl263_1307
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1307])]) ).
fof(f7673,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),
inference(forward_demodulation,[],[f6173,f6172]) ).
fof(f6172,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(cnf_transformation,[],[f2238]) ).
fof(f2238,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(rectify,[],[f942]) ).
fof(f942,axiom,
! [X22,X23,X21] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),X23)),X21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6173,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),X1),
inference(cnf_transformation,[],[f2239]) ).
fof(f2239,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),X1),
inference(rectify,[],[f238]) ).
fof(f238,axiom,
! [X22,X23,X21] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),X23)),X21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),X21)),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21312,plain,
spl263_1306,
inference(avatar_split_clause,[],[f7574,f21310]) ).
fof(f21310,plain,
( spl263_1306
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK139(X1)),hAPP_nat_nat(X1,sK139(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1306])]) ).
fof(f7574,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK139(X1)),hAPP_nat_nat(X1,sK139(X1)))) ),
inference(forward_demodulation,[],[f5843,f4876]) ).
fof(f5843,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK139(X1)),hAPP_nat_nat(X1,sK139(X1)))) ),
inference(cnf_transformation,[],[f4268]) ).
fof(f4268,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK139(X1)),hAPP_nat_nat(X1,sK139(X1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139])],[f3267,f4267]) ).
fof(f4267,plain,
! [X1] :
( ? [X2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2)))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK139(X1)),hAPP_nat_nat(X1,sK139(X1)))) ),
introduced(choice_axiom,[]) ).
fof(f3267,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
| ? [X2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2))) ),
inference(ennf_transformation,[],[f2063]) ).
fof(f2063,plain,
! [X0,X1] :
( ! [X2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))) ),
inference(rectify,[],[f802]) ).
fof(f802,axiom,
! [X81,X8] :
( ! [X28] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),hAPP_nat_nat(X8,X28)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X8)),X81)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21308,plain,
spl263_1305,
inference(avatar_split_clause,[],[f7534,f21306]) ).
fof(f21306,plain,
( spl263_1305
<=> ! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_n1699378549t_bool(fequal_nat,X0)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1305])]) ).
fof(f7534,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_n1699378549t_bool(fequal_nat,X0)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(forward_demodulation,[],[f5696,f7397]) ).
fof(f5696,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3089]) ).
fof(f3089,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1945]) ).
fof(f1945,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1 ),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X10,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21304,plain,
spl263_1304,
inference(avatar_split_clause,[],[f7533,f21302]) ).
fof(f21302,plain,
( spl263_1304
<=> ! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_i1948725293t_bool(fequal_int,X0)) = X1
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1304])]) ).
fof(f7533,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_i1948725293t_bool(fequal_int,X0)) = X1
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(forward_demodulation,[],[f5695,f7396]) ).
fof(f5695,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(cnf_transformation,[],[f3088]) ).
fof(f3088,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(ennf_transformation,[],[f1944]) ).
fof(f1944,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1 ),
inference(rectify,[],[f656]) ).
fof(f656,axiom,
! [X10,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21300,plain,
spl263_1303,
inference(avatar_split_clause,[],[f7481,f21298]) ).
fof(f21298,plain,
( spl263_1303
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),u))
| ~ hBOOL(wt(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1303])]) ).
fof(f7481,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),u))
| ~ hBOOL(wt(X1)) ),
inference(forward_demodulation,[],[f5440,f4966]) ).
fof(f5440,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),u))
| ~ hBOOL(wt(X1)) ),
inference(cnf_transformation,[],[f4172]) ).
fof(f4172,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK96(X0))),bot_bot_fun_a_bool)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),u))
& is_pname(sK96(X0)) )
| ~ hBOOL(wt(X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96])],[f2844,f4171]) ).
fof(f4171,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u))
& is_pname(X2) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK96(X0))),bot_bot_fun_a_bool)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),u))
& is_pname(sK96(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2844,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u))
& is_pname(X2) )
| ~ hBOOL(wt(X1)) ),
inference(flattening,[],[f2843]) ).
fof(f2843,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u))
& is_pname(X2) )
| ~ hBOOL(wt(X1)) ),
inference(ennf_transformation,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1] :
( hBOOL(wt(X1))
=> ( ! [X2] :
( is_pname(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u))
=> hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool))) ) )
=> hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool))) ) ),
inference(rectify,[],[f594]) ).
fof(f594,axiom,
! [X3,X31] :
( hBOOL(wt(X31))
=> ( ! [X29] :
( is_pname(X29)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),u))
=> hBOOL(hAPP_fun_a_bool_bool(p(X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X29)),bot_bot_fun_a_bool))) ) )
=> hBOOL(hAPP_fun_a_bool_bool(p(X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X31)),bot_bot_fun_a_bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21296,plain,
spl263_1302,
inference(avatar_split_clause,[],[f6746,f21294]) ).
fof(f21294,plain,
( spl263_1302
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK248(X0,X1,X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1302])]) ).
fof(f6746,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK248(X0,X1,X2))),X1)) ),
inference(cnf_transformation,[],[f4664]) ).
fof(f4664,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK248(X0,X1,X2))),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK248(X0,X1,X2)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK248])],[f3804,f4663]) ).
fof(f4663,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK248(X0,X1,X2))),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK248(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3804,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| ? [X3] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
inference(ennf_transformation,[],[f2577]) ).
fof(f2577,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1)) ),
inference(rectify,[],[f588]) ).
fof(f588,axiom,
! [X8,X9,X4] :
( ! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X8,X29)),X9)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X8,X4)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21292,plain,
spl263_1301,
inference(avatar_split_clause,[],[f6744,f21290]) ).
fof(f21290,plain,
( spl263_1301
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK247(X0,X1,X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1301])]) ).
fof(f6744,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK247(X0,X1,X2))),X1)) ),
inference(cnf_transformation,[],[f4662]) ).
fof(f4662,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK247(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK247(X0,X1,X2)),X2))
& is_pname(sK247(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK247])],[f3803,f4661]) ).
fof(f4661,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK247(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK247(X0,X1,X2)),X2))
& is_pname(sK247(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3803,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ? [X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) ) ),
inference(flattening,[],[f3802]) ).
fof(f3802,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ? [X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) ) ),
inference(ennf_transformation,[],[f2576]) ).
fof(f2576,plain,
! [X0,X1,X2] :
( ! [X3] :
( is_pname(X3)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ),
inference(rectify,[],[f589]) ).
fof(f589,axiom,
! [X8,X9,X4] :
( ! [X29] :
( is_pname(X29)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X8,X29)),X9)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X8,X4)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21288,plain,
spl263_1300,
inference(avatar_split_clause,[],[f6731,f21286]) ).
fof(f21286,plain,
( spl263_1300
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 = X2
| sP29(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1300])]) ).
fof(f6731,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 = X2
| sP29(X1,X2,X0) ),
inference(cnf_transformation,[],[f3965]) ).
fof(f3965,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& X1 = X2 )
| sP29(X1,X2,X0) ),
inference(definition_folding,[],[f3787,f3964]) ).
fof(f3964,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP29(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f3787,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& X1 = X2 )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
inference(flattening,[],[f3786]) ).
fof(f3786,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& X1 = X2 )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f2568]) ).
fof(f2568,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
=> ( ( X1 = X2
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) ) ) ),
inference(rectify,[],[f971]) ).
fof(f971,axiom,
! [X12,X24,X16] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X12,X16),X24)) )
=> ( ( X16 = X24
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X12,X16),X24)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X12,X16),X24)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X12,X16),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21284,plain,
spl263_1299,
inference(avatar_split_clause,[],[f6693,f21282]) ).
fof(f21282,plain,
( spl263_1299
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1299])]) ).
fof(f6693,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4628]) ).
fof(f4628,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ( ~ hBOOL(hAPP_a_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(flattening,[],[f4627]) ).
fof(f4627,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ( ~ hBOOL(hAPP_a_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(nnf_transformation,[],[f3769]) ).
fof(f3769,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(flattening,[],[f3768]) ).
fof(f3768,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2556]) ).
fof(f2556,plain,
! [X0,X1,X2] :
( ( is_a(X2)
& is_a(X0) )
=> ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) ) ),
inference(rectify,[],[f495]) ).
fof(f495,axiom,
! [X38,X4,X10] :
( ( is_a(X10)
& is_a(X38) )
=> ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X38),X4),X10))
<=> ( hBOOL(hAPP_a_bool(X4,X10))
| X10 = X38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21280,plain,
spl263_1298,
inference(avatar_split_clause,[],[f6670,f21278]) ).
fof(f21278,plain,
( spl263_1298
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1298])]) ).
fof(f6670,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
inference(cnf_transformation,[],[f3739]) ).
fof(f3739,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
inference(flattening,[],[f3738]) ).
fof(f3738,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
inference(ennf_transformation,[],[f2534]) ).
fof(f2534,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
=> ( X0 != X1
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
inference(rectify,[],[f404]) ).
fof(f404,axiom,
! [X7,X30,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X4)))
=> ( X7 != X30
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21276,plain,
spl263_1297,
inference(avatar_split_clause,[],[f6665,f21274]) ).
fof(f21274,plain,
( spl263_1297
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1297])]) ).
fof(f6665,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
inference(cnf_transformation,[],[f3734]) ).
fof(f3734,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
inference(flattening,[],[f3733]) ).
fof(f3733,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
inference(ennf_transformation,[],[f2530]) ).
fof(f2530,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
=> ( X0 != X1
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
inference(rectify,[],[f403]) ).
fof(f403,axiom,
! [X7,X30,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X4)))
=> ( X7 != X30
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21272,plain,
spl263_1296,
inference(avatar_split_clause,[],[f6476,f21270]) ).
fof(f21270,plain,
( spl263_1296
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK223(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1296])]) ).
fof(f6476,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK223(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4574]) ).
fof(f4574,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ( ~ hBOOL(hAPP_nat_bool(X1,sK223(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK223(X1)))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK223])],[f3512,f4573]) ).
fof(f4573,plain,
! [X1] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
=> ( ~ hBOOL(hAPP_nat_bool(X1,sK223(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK223(X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f3512,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(flattening,[],[f3511]) ).
fof(f3511,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(ennf_transformation,[],[f2380]) ).
fof(f2380,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3)))
=> hBOOL(hAPP_nat_bool(X1,X3)) )
=> hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0))) ) ),
inference(rectify,[],[f406]) ).
fof(f406,axiom,
! [X32,X12,X15] :
( hBOOL(hAPP_nat_bool(X12,X15))
=> ( ! [X28] :
( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(suc,X28)))
=> hBOOL(hAPP_nat_bool(X12,X28)) )
=> hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X32))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21267,plain,
spl263_1295,
inference(avatar_split_clause,[],[f6473,f21265]) ).
fof(f21265,plain,
( spl263_1295
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK222(X1,X2)),X2))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1295])]) ).
fof(f6473,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK222(X1,X2)),X2))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4572]) ).
fof(f21263,plain,
spl263_1294,
inference(avatar_split_clause,[],[f6464,f21261]) ).
fof(f21261,plain,
( spl263_1294
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK216(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1294])]) ).
fof(f6464,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK216(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4561]) ).
fof(f21259,plain,
spl263_1293,
inference(avatar_split_clause,[],[f6461,f21257]) ).
fof(f21257,plain,
( spl263_1293
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK215(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1293])]) ).
fof(f6461,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK215(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4559]) ).
fof(f21255,plain,
spl263_1292,
inference(avatar_split_clause,[],[f6458,f21253]) ).
fof(f21253,plain,
( spl263_1292
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK214(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1292])]) ).
fof(f6458,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK214(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f21251,plain,
spl263_1291,
inference(avatar_split_clause,[],[f6454,f21249]) ).
fof(f21249,plain,
( spl263_1291
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK213(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1291])]) ).
fof(f6454,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK213(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4555]) ).
fof(f21247,plain,
spl263_1290,
inference(avatar_split_clause,[],[f6450,f21245]) ).
fof(f21245,plain,
( spl263_1290
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK212(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1290])]) ).
fof(f6450,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK212(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4553]) ).
fof(f21243,plain,
spl263_1289,
inference(avatar_split_clause,[],[f6446,f21241]) ).
fof(f21241,plain,
( spl263_1289
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK211(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1289])]) ).
fof(f6446,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK211(X0,X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4551]) ).
fof(f21239,plain,
spl263_1288,
inference(avatar_split_clause,[],[f6428,f21237]) ).
fof(f21237,plain,
( spl263_1288
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK208(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1288])]) ).
fof(f6428,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK208(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4545]) ).
fof(f21235,plain,
spl263_1287,
inference(avatar_split_clause,[],[f6425,f21233]) ).
fof(f21233,plain,
( spl263_1287
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK207(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1287])]) ).
fof(f6425,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK207(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4543]) ).
fof(f21231,plain,
spl263_1286,
inference(avatar_split_clause,[],[f6422,f21229]) ).
fof(f21229,plain,
( spl263_1286
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK206(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1286])]) ).
fof(f6422,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK206(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4541]) ).
fof(f21227,plain,
( spl263_1284
| spl263_1285
| ~ spl263_82
| ~ spl263_248 ),
inference(avatar_split_clause,[],[f9098,f8940,f8151,f21224,f21220]) ).
fof(f21220,plain,
( spl263_1284
<=> sP0(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1284])]) ).
fof(f21224,plain,
( spl263_1285
<=> bot_bo844097828e_bool = u ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1285])]) ).
fof(f8151,plain,
( spl263_82
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_82])]) ).
fof(f8940,plain,
( spl263_248
<=> ! [X0] :
( sP0(X0)
| bot_bo844097828e_bool = X0
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_248])]) ).
fof(f9098,plain,
( bot_bo844097828e_bool = u
| sP0(u)
| ~ spl263_82
| ~ spl263_248 ),
inference(resolution,[],[f8941,f8153]) ).
fof(f8153,plain,
( sP1(u)
| ~ spl263_82 ),
inference(avatar_component_clause,[],[f8151]) ).
fof(f8941,plain,
( ! [X0] :
( ~ sP1(X0)
| bot_bo844097828e_bool = X0
| sP0(X0) )
| ~ spl263_248 ),
inference(avatar_component_clause,[],[f8940]) ).
fof(f21218,plain,
spl263_1283,
inference(avatar_split_clause,[],[f6419,f21216]) ).
fof(f21216,plain,
( spl263_1283
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK205(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1283])]) ).
fof(f6419,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK205(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4539]) ).
fof(f21214,plain,
spl263_1282,
inference(avatar_split_clause,[],[f6415,f21212]) ).
fof(f21212,plain,
( spl263_1282
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK204(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1282])]) ).
fof(f6415,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK204(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4537]) ).
fof(f21210,plain,
spl263_1281,
inference(avatar_split_clause,[],[f6411,f21208]) ).
fof(f21208,plain,
( spl263_1281
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK203(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1281])]) ).
fof(f6411,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK203(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4535]) ).
fof(f21206,plain,
spl263_1280,
inference(avatar_split_clause,[],[f6407,f21204]) ).
fof(f21204,plain,
( spl263_1280
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK202(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1280])]) ).
fof(f6407,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK202(X0,X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4533]) ).
fof(f21202,plain,
spl263_1279,
inference(avatar_split_clause,[],[f6346,f21200]) ).
fof(f21200,plain,
( spl263_1279
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK195(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1279])]) ).
fof(f6346,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK195(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4519]) ).
fof(f21198,plain,
spl263_1278,
inference(avatar_split_clause,[],[f6343,f21196]) ).
fof(f21196,plain,
( spl263_1278
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK194(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1278])]) ).
fof(f6343,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK194(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4517]) ).
fof(f21194,plain,
spl263_1277,
inference(avatar_split_clause,[],[f6340,f21192]) ).
fof(f21192,plain,
( spl263_1277
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK193(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1277])]) ).
fof(f6340,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK193(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4515]) ).
fof(f21190,plain,
spl263_1276,
inference(avatar_split_clause,[],[f6337,f21188]) ).
fof(f21188,plain,
( spl263_1276
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK192(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1276])]) ).
fof(f6337,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK192(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4513]) ).
fof(f21186,plain,
spl263_1275,
inference(avatar_split_clause,[],[f6334,f21184]) ).
fof(f21184,plain,
( spl263_1275
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1275])]) ).
fof(f6334,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4511]) ).
fof(f21182,plain,
spl263_1274,
inference(avatar_split_clause,[],[f6330,f21180]) ).
fof(f21180,plain,
( spl263_1274
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK190(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1274])]) ).
fof(f6330,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK190(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4509]) ).
fof(f21178,plain,
spl263_1273,
inference(avatar_split_clause,[],[f6326,f21176]) ).
fof(f21176,plain,
( spl263_1273
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK189(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1273])]) ).
fof(f6326,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK189(X0,X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4507]) ).
fof(f21174,plain,
spl263_1272,
inference(avatar_split_clause,[],[f6322,f21172]) ).
fof(f21172,plain,
( spl263_1272
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK188(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1272])]) ).
fof(f6322,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK188(X0,X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4505]) ).
fof(f21170,plain,
spl263_1271,
inference(avatar_split_clause,[],[f6307,f21168]) ).
fof(f21168,plain,
( spl263_1271
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK187(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1271])]) ).
fof(f6307,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK187(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4503]) ).
fof(f4503,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3] :
( image_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ is_fun_pname_bool(X3) ) )
& ( ( image_pname_a(X1,sK187(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK187(X0,X1,X2)),X2))
& is_fun_pname_bool(sK187(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) )
| ~ is_fun_a_bool(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f4501,f4502]) ).
fof(f4502,plain,
! [X0,X1,X2] :
( ? [X4] :
( image_pname_a(X1,X4) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2))
& is_fun_pname_bool(X4) )
=> ( image_pname_a(X1,sK187(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK187(X0,X1,X2)),X2))
& is_fun_pname_bool(sK187(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4501,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3] :
( image_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ is_fun_pname_bool(X3) ) )
& ( ? [X4] :
( image_pname_a(X1,X4) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2))
& is_fun_pname_bool(X4) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) )
| ~ is_fun_a_bool(X0) ),
inference(rectify,[],[f4500]) ).
fof(f4500,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3] :
( image_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ is_fun_pname_bool(X3) ) )
& ( ? [X3] :
( image_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
& is_fun_pname_bool(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) )
| ~ is_fun_a_bool(X0) ),
inference(nnf_transformation,[],[f3346]) ).
fof(f3346,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
<=> ? [X3] :
( image_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
& is_fun_pname_bool(X3) ) )
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f2296]) ).
fof(f2296,plain,
! [X0,X1,X2] :
( is_fun_a_bool(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
<=> ? [X3] :
( image_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
& is_fun_pname_bool(X3) ) ) ),
inference(rectify,[],[f579]) ).
fof(f579,axiom,
! [X9,X8,X4] :
( is_fun_a_bool(X9)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_pname_a(X8,X4)))
<=> ? [X70] :
( image_pname_a(X8,X70) = X9
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X70),X4))
& is_fun_pname_bool(X70) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21166,plain,
spl263_1270,
inference(avatar_split_clause,[],[f6298,f21164]) ).
fof(f21164,plain,
( spl263_1270
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK184(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1270])]) ).
fof(f6298,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK184(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4497]) ).
fof(f21162,plain,
spl263_1269,
inference(avatar_split_clause,[],[f6282,f21160]) ).
fof(f21160,plain,
( spl263_1269
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK179(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1269])]) ).
fof(f6282,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK179(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4487]) ).
fof(f21158,plain,
spl263_1268,
inference(avatar_split_clause,[],[f6278,f21156]) ).
fof(f21156,plain,
( spl263_1268
<=> ! [X2,X0,X1] :
( is_fun949378684l_bool(sK178(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1268])]) ).
fof(f6278,plain,
! [X2,X0,X1] :
( is_fun949378684l_bool(sK178(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4485]) ).
fof(f21154,plain,
spl263_1267,
inference(avatar_split_clause,[],[f6274,f21152]) ).
fof(f21152,plain,
( spl263_1267
<=> ! [X2,X0,X1] :
( is_fun1661590463l_bool(sK177(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1267])]) ).
fof(f6274,plain,
! [X2,X0,X1] :
( is_fun1661590463l_bool(sK177(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(cnf_transformation,[],[f4483]) ).
fof(f21150,plain,
spl263_1266,
inference(avatar_split_clause,[],[f6267,f21148]) ).
fof(f21148,plain,
( spl263_1266
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK174(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1266])]) ).
fof(f6267,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK174(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4479]) ).
fof(f21146,plain,
spl263_1265,
inference(avatar_split_clause,[],[f6251,f21144]) ).
fof(f21144,plain,
( spl263_1265
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK169(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1265])]) ).
fof(f6251,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK169(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4469]) ).
fof(f21142,plain,
spl263_1264,
inference(avatar_split_clause,[],[f6247,f21140]) ).
fof(f21140,plain,
( spl263_1264
<=> ! [X2,X0,X1] :
( is_fun949378684l_bool(sK168(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1264])]) ).
fof(f6247,plain,
! [X2,X0,X1] :
( is_fun949378684l_bool(sK168(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4467]) ).
fof(f21138,plain,
spl263_1263,
inference(avatar_split_clause,[],[f6243,f21136]) ).
fof(f21136,plain,
( spl263_1263
<=> ! [X2,X0,X1] :
( is_fun1661590463l_bool(sK167(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1263])]) ).
fof(f6243,plain,
! [X2,X0,X1] :
( is_fun1661590463l_bool(sK167(X0,X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(cnf_transformation,[],[f4465]) ).
fof(f21134,plain,
spl263_1262,
inference(avatar_split_clause,[],[f6233,f21132]) ).
fof(f21132,plain,
( spl263_1262
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK164(X0,X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1262])]) ).
fof(f6233,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK164(X0,X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4459]) ).
fof(f21130,plain,
spl263_1261,
inference(avatar_split_clause,[],[f6229,f21128]) ).
fof(f21128,plain,
( spl263_1261
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK163(X0,X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1261])]) ).
fof(f6229,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK163(X0,X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(cnf_transformation,[],[f4457]) ).
fof(f21126,plain,
spl263_1260,
inference(avatar_split_clause,[],[f6219,f21124]) ).
fof(f21124,plain,
( spl263_1260
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK160(X0,X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1260])]) ).
fof(f6219,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK160(X0,X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4451]) ).
fof(f21122,plain,
spl263_1259,
inference(avatar_split_clause,[],[f6215,f21120]) ).
fof(f21120,plain,
( spl263_1259
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK159(X0,X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1259])]) ).
fof(f6215,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK159(X0,X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(cnf_transformation,[],[f4449]) ).
fof(f21118,plain,
spl263_1258,
inference(avatar_split_clause,[],[f6212,f21116]) ).
fof(f21116,plain,
( spl263_1258
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK158(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1258])]) ).
fof(f6212,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK158(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4447]) ).
fof(f4447,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3] :
( hAPP_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ is_pname(X3) ) )
& ( ( hAPP_pname_a(X1,sK158(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK158(X0,X1,X2)),X2))
& is_pname(sK158(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) )
| ~ is_a(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f4445,f4446]) ).
fof(f4446,plain,
! [X0,X1,X2] :
( ? [X4] :
( hAPP_pname_a(X1,X4) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2))
& is_pname(X4) )
=> ( hAPP_pname_a(X1,sK158(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK158(X0,X1,X2)),X2))
& is_pname(sK158(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4445,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3] :
( hAPP_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ is_pname(X3) ) )
& ( ? [X4] :
( hAPP_pname_a(X1,X4) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2))
& is_pname(X4) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) )
| ~ is_a(X0) ),
inference(rectify,[],[f4444]) ).
fof(f4444,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3] :
( hAPP_pname_a(X1,X3) != X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ is_pname(X3) ) )
& ( ? [X3] :
( hAPP_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) )
| ~ is_a(X0) ),
inference(nnf_transformation,[],[f3291]) ).
fof(f3291,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
<=> ? [X3] :
( hAPP_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) ) )
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2268]) ).
fof(f2268,plain,
! [X0,X1,X2] :
( is_a(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
<=> ? [X3] :
( hAPP_pname_a(X1,X3) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& is_pname(X3) ) ) ),
inference(rectify,[],[f539]) ).
fof(f539,axiom,
! [X55,X8,X4] :
( is_a(X55)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X55),image_pname_a(X8,X4)))
<=> ? [X29] :
( hAPP_pname_a(X8,X29) = X55
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
& is_pname(X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21114,plain,
spl263_1257,
inference(avatar_split_clause,[],[f6210,f21112]) ).
fof(f21112,plain,
( spl263_1257
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK157(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1257])]) ).
fof(f6210,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK157(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4443]) ).
fof(f4443,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK157(X0,X1,X2)),X2))
& hAPP_pname_a(X1,sK157(X0,X1,X2)) = X0
& is_pname(sK157(X0,X1,X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f3290,f4442]) ).
fof(f4442,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& hAPP_pname_a(X1,X3) = X0
& is_pname(X3) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK157(X0,X1,X2)),X2))
& hAPP_pname_a(X1,sK157(X0,X1,X2)) = X0
& is_pname(sK157(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3290,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& hAPP_pname_a(X1,X3) = X0
& is_pname(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(flattening,[],[f3289]) ).
fof(f3289,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& hAPP_pname_a(X1,X3) = X0
& is_pname(X3) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2267]) ).
fof(f2267,plain,
! [X0,X1,X2] :
( is_a(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
=> ~ ! [X3] :
( is_pname(X3)
=> ( hAPP_pname_a(X1,X3) = X0
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ) ) ),
inference(rectify,[],[f583]) ).
fof(f583,axiom,
! [X30,X8,X4] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),image_pname_a(X8,X4)))
=> ~ ! [X29] :
( is_pname(X29)
=> ( hAPP_pname_a(X8,X29) = X30
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21110,plain,
spl263_1256,
inference(avatar_split_clause,[],[f6174,f21108]) ).
fof(f21108,plain,
( spl263_1256
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1256])]) ).
fof(f6174,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2),
inference(cnf_transformation,[],[f2240]) ).
fof(f2240,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2),
inference(rectify,[],[f907]) ).
fof(f907,axiom,
! [X14,X13,X21] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13)),X21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21106,plain,
spl263_1255,
inference(avatar_split_clause,[],[f6172,f21104]) ).
fof(f21104,plain,
( spl263_1255
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1255])]) ).
fof(f21102,plain,
spl263_1254,
inference(avatar_split_clause,[],[f6171,f21100]) ).
fof(f21100,plain,
( spl263_1254
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1254])]) ).
fof(f6171,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(cnf_transformation,[],[f2237]) ).
fof(f2237,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(rectify,[],[f1124]) ).
fof(f1124,axiom,
! [X14,X13,X21] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)),X21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21098,plain,
spl263_1253,
inference(avatar_split_clause,[],[f6170,f21096]) ).
fof(f21096,plain,
( spl263_1253
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1253])]) ).
fof(f6170,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),
inference(cnf_transformation,[],[f2236]) ).
fof(f2236,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),
inference(rectify,[],[f906]) ).
fof(f906,axiom,
! [X17,X18,X97] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X97)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X17),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21094,plain,
spl263_1252,
inference(avatar_split_clause,[],[f6168,f21092]) ).
fof(f6168,plain,
! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2),
inference(cnf_transformation,[],[f2234]) ).
fof(f2234,plain,
! [X0,X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2),
inference(rectify,[],[f893]) ).
fof(f893,axiom,
! [X85,X86,X87] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X85),X86)),X87) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X85),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X86),X87)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21090,plain,
spl263_1251,
inference(avatar_split_clause,[],[f6167,f21088]) ).
fof(f21088,plain,
( spl263_1251
<=> ! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1251])]) ).
fof(f6167,plain,
! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),
inference(cnf_transformation,[],[f2233]) ).
fof(f2233,plain,
! [X0,X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),
inference(rectify,[],[f1130]) ).
fof(f1130,axiom,
! [X135,X136,X137] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X136)),X137) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X136),X137)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21086,plain,
spl263_1250,
inference(avatar_split_clause,[],[f6166,f21084]) ).
fof(f21084,plain,
( spl263_1250
<=> ! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1250])]) ).
fof(f6166,plain,
! [X2,X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)),
inference(cnf_transformation,[],[f2232]) ).
fof(f2232,plain,
! [X0,X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X17,X18,X97] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X17),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),X97)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X17),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21082,plain,
spl263_1249,
inference(avatar_split_clause,[],[f6165,f21080]) ).
fof(f21080,plain,
( spl263_1249
<=> ! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1249])]) ).
fof(f6165,plain,
! [X2,X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)),
inference(cnf_transformation,[],[f2231]) ).
fof(f2231,plain,
! [X0,X1,X2] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)),
inference(rectify,[],[f490]) ).
fof(f490,axiom,
! [X10,X38,X4] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X38),X4)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X38),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21078,plain,
spl263_1248,
inference(avatar_split_clause,[],[f6164,f21076]) ).
fof(f21076,plain,
( spl263_1248
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1248])]) ).
fof(f6164,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),
inference(cnf_transformation,[],[f2230]) ).
fof(f2230,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),
inference(rectify,[],[f944]) ).
fof(f944,axiom,
! [X14,X21,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X21)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21074,plain,
spl263_1247,
inference(avatar_split_clause,[],[f6163,f21072]) ).
fof(f21072,plain,
( spl263_1247
<=> ! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1247])]) ).
fof(f6163,plain,
! [X2,X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),
inference(cnf_transformation,[],[f2229]) ).
fof(f2229,plain,
! [X0,X1,X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),
inference(rectify,[],[f943]) ).
fof(f943,axiom,
! [X21,X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X21),X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X21),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21070,plain,
spl263_1246,
inference(avatar_split_clause,[],[f6065,f21068]) ).
fof(f21068,plain,
( spl263_1246
<=> ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1246])]) ).
fof(f6065,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
inference(cnf_transformation,[],[f4426]) ).
fof(f4426,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ( X0 != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
& ( X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
inference(flattening,[],[f4425]) ).
fof(f4425,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ( X0 != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
& ( X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
inference(nnf_transformation,[],[f2148]) ).
fof(f2148,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
<=> ( X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(rectify,[],[f1163]) ).
fof(f1163,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X55),one_one_int)))
<=> ( X55 = X138
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X55)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21066,plain,
spl263_1245,
inference(avatar_split_clause,[],[f6052,f21064]) ).
fof(f21064,plain,
( spl263_1245
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1245])]) ).
fof(f6052,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
inference(cnf_transformation,[],[f4417]) ).
fof(f4417,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4416]) ).
fof(f4416,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2142]) ).
fof(f2142,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
inference(rectify,[],[f239]) ).
fof(f239,axiom,
! [X12,X11] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X11)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21062,plain,
spl263_1244,
inference(avatar_split_clause,[],[f6049,f21060]) ).
fof(f21060,plain,
( spl263_1244
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1244])]) ).
fof(f6049,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(cnf_transformation,[],[f4415]) ).
fof(f4415,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
& ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4414]) ).
fof(f4414,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
& ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2141]) ).
fof(f2141,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X12,X11] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X11)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21056,plain,
spl263_1243,
inference(avatar_split_clause,[],[f6046,f21054]) ).
fof(f21054,plain,
( spl263_1243
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1243])]) ).
fof(f6046,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(cnf_transformation,[],[f4413]) ).
fof(f4413,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
& ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4412]) ).
fof(f4412,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
& ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2140]) ).
fof(f2140,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X12,X11] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X11)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21052,plain,
spl263_1242,
inference(avatar_split_clause,[],[f6043,f21050]) ).
fof(f21050,plain,
( spl263_1242
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1242])]) ).
fof(f6043,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(cnf_transformation,[],[f4411]) ).
fof(f4411,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
& ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4410]) ).
fof(f4410,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
& ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2139]) ).
fof(f2139,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X12,X11] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X11)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21048,plain,
spl263_1241,
inference(avatar_split_clause,[],[f6040,f21046]) ).
fof(f21046,plain,
( spl263_1241
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1241])]) ).
fof(f6040,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(cnf_transformation,[],[f4409]) ).
fof(f4409,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
& ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4408]) ).
fof(f4408,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
& ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2138]) ).
fof(f2138,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
inference(rectify,[],[f241]) ).
fof(f241,axiom,
! [X12,X11] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X11)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21044,plain,
spl263_1240,
inference(avatar_split_clause,[],[f6037,f21042]) ).
fof(f21042,plain,
( spl263_1240
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1240])]) ).
fof(f6037,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ),
inference(cnf_transformation,[],[f4407]) ).
fof(f4407,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
& ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4406]) ).
fof(f4406,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
& ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2137]) ).
fof(f2137,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X12,X11] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X11)))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21040,plain,
spl263_1239,
inference(avatar_split_clause,[],[f6003,f21038]) ).
fof(f21038,plain,
( spl263_1239
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK156(X0,X1)),X1))
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1239])]) ).
fof(f6003,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK156(X0,X1)),X1))
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f4389]) ).
fof(f4389,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ( ! [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hAPP_nat_nat(suc,X2) != X0 )
& zero_zero_nat != X0 ) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK156(X0,X1)),X1))
& hAPP_nat_nat(suc,sK156(X0,X1)) = X0 )
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f4387,f4388]) ).
fof(f4388,plain,
! [X0,X1] :
( ? [X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
& hAPP_nat_nat(suc,X3) = X0 )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK156(X0,X1)),X1))
& hAPP_nat_nat(suc,sK156(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f4387,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ( ! [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hAPP_nat_nat(suc,X2) != X0 )
& zero_zero_nat != X0 ) )
& ( ? [X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
& hAPP_nat_nat(suc,X3) = X0 )
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
inference(rectify,[],[f4386]) ).
fof(f4386,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ( ! [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hAPP_nat_nat(suc,X2) != X0 )
& zero_zero_nat != X0 ) )
& ( ? [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hAPP_nat_nat(suc,X2) = X0 )
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
inference(flattening,[],[f4385]) ).
fof(f4385,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ( ! [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hAPP_nat_nat(suc,X2) != X0 )
& zero_zero_nat != X0 ) )
& ( ? [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hAPP_nat_nat(suc,X2) = X0 )
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
inference(nnf_transformation,[],[f2129]) ).
fof(f2129,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
<=> ( ? [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hAPP_nat_nat(suc,X2) = X0 )
| zero_zero_nat = X0 ) ),
inference(rectify,[],[f1055]) ).
fof(f1055,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),hAPP_nat_nat(suc,X16)))
<=> ( ? [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X16))
& hAPP_nat_nat(suc,X126) = X24 )
| zero_zero_nat = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21036,plain,
spl263_1238,
inference(avatar_split_clause,[],[f5936,f21034]) ).
fof(f21034,plain,
( spl263_1238
<=> ! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK152(X0,X1)))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1238])]) ).
fof(f5936,plain,
! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK152(X0,X1)))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4340]) ).
fof(f4340,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 )
& ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK152(X0,X1)))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f4338,f4339]) ).
fof(f4339,plain,
! [X0,X1] :
( ? [X3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) = X1
=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK152(X0,X1)))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f4338,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 )
& ( ? [X3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(rectify,[],[f4337]) ).
fof(f4337,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 )
& ( ? [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f2099]) ).
fof(f2099,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ? [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) = X1 ),
inference(rectify,[],[f1230]) ).
fof(f1230,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X55))
<=> ? [X28] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X138),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X28))) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21032,plain,
spl263_1237,
inference(avatar_split_clause,[],[f5814,f21030]) ).
fof(f21030,plain,
( spl263_1237
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1237])]) ).
fof(f5814,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f3247]) ).
fof(f3247,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f3246]) ).
fof(f3246,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f2048]) ).
fof(f2048,plain,
! [X0,X1] :
( ( is_fun_a_bool(X1)
& is_fun_a_bool(X0) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
=> X0 = X1 ) ) ),
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X38,X10] :
( ( is_fun_a_bool(X10)
& is_fun_a_bool(X38) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X38),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X38))
=> X10 = X38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21028,plain,
spl263_1236,
inference(avatar_split_clause,[],[f5782,f21026]) ).
fof(f21026,plain,
( spl263_1236
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,X1) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1236])]) ).
fof(f5782,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X1) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f3200]) ).
fof(f3200,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X1) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(flattening,[],[f3199]) ).
fof(f3199,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X1) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(ennf_transformation,[],[f2021]) ).
fof(f2021,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(suc,X1) = X0 ) ),
inference(rectify,[],[f272]) ).
fof(f272,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(suc,X13)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hAPP_nat_nat(suc,X13) = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21024,plain,
spl263_1235,
inference(avatar_split_clause,[],[f5752,f21022]) ).
fof(f21022,plain,
( spl263_1235
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK134(X0,X1)))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1235])]) ).
fof(f5752,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK134(X0,X1)))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4249]) ).
fof(f4249,plain,
! [X0,X1] :
( ( hAPP_nat_nat(suc,sK134(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK134(X0,X1))) )
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f3163,f4248]) ).
fof(f4248,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(suc,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
=> ( hAPP_nat_nat(suc,sK134(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK134(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f3163,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(suc,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(flattening,[],[f3162]) ).
fof(f3162,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(suc,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1995]) ).
fof(f1995,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ( hAPP_nat_nat(suc,X0) != X1
=> ~ ! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
=> hAPP_nat_nat(suc,X2) != X1 ) ) ),
inference(rectify,[],[f1026]) ).
fof(f1026,axiom,
! [X22,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X21))
=> ( hAPP_nat_nat(suc,X22) != X21
=> ~ ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X126))
=> hAPP_nat_nat(suc,X126) != X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f21020,plain,
spl263_1234,
inference(avatar_split_clause,[],[f5751,f21018]) ).
fof(f21018,plain,
( spl263_1234
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1234])]) ).
fof(f5751,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3161]) ).
fof(f3161,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(flattening,[],[f3160]) ).
fof(f3160,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1994]) ).
fof(f1994,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ( hAPP_nat_nat(suc,X0) != X1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
inference(rectify,[],[f978]) ).
fof(f978,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> ( hAPP_nat_nat(suc,X14) != X13
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X14)),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f20450,plain,
( spl263_5
| ~ spl263_706
| ~ spl263_726
| ~ spl263_1085 ),
inference(avatar_split_clause,[],[f19640,f16156,f12499,f11789,f7808]) ).
fof(f11789,plain,
( spl263_706
<=> ! [X4,X0,X2] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP30(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_706])]) ).
fof(f12499,plain,
( spl263_726
<=> ! [X0,X1] : sP30(bot_bot_fun_nat_bool,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_726])]) ).
fof(f19640,plain,
( hBOOL(fFalse)
| ~ spl263_706
| ~ spl263_726
| ~ spl263_1085 ),
inference(forward_demodulation,[],[f12574,f16157]) ).
fof(f12574,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ spl263_706
| ~ spl263_726 ),
inference(resolution,[],[f12500,f11790]) ).
fof(f11790,plain,
( ! [X2,X0,X4] :
( ~ sP30(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2)
| hBOOL(hAPP_nat_bool(X0,X4)) )
| ~ spl263_706 ),
inference(avatar_component_clause,[],[f11789]) ).
fof(f12500,plain,
( ! [X0,X1] : sP30(bot_bot_fun_nat_bool,X0,X1)
| ~ spl263_726 ),
inference(avatar_component_clause,[],[f12499]) ).
fof(f20346,plain,
( spl263_5
| ~ spl263_707
| ~ spl263_734
| ~ spl263_1085 ),
inference(avatar_split_clause,[],[f19639,f16156,f12531,f11793,f7808]) ).
fof(f11793,plain,
( spl263_707
<=> ! [X4,X0,X2] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP31(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_707])]) ).
fof(f12531,plain,
( spl263_734
<=> ! [X0,X1] : sP31(bot_bot_fun_nat_bool,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_734])]) ).
fof(f19639,plain,
( hBOOL(fFalse)
| ~ spl263_707
| ~ spl263_734
| ~ spl263_1085 ),
inference(forward_demodulation,[],[f12615,f16157]) ).
fof(f12615,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ spl263_707
| ~ spl263_734 ),
inference(resolution,[],[f12532,f11794]) ).
fof(f11794,plain,
( ! [X2,X0,X4] :
( ~ sP31(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2)
| hBOOL(hAPP_nat_bool(X0,X4)) )
| ~ spl263_707 ),
inference(avatar_component_clause,[],[f11793]) ).
fof(f12532,plain,
( ! [X0,X1] : sP31(bot_bot_fun_nat_bool,X0,X1)
| ~ spl263_734 ),
inference(avatar_component_clause,[],[f12531]) ).
fof(f20303,plain,
spl263_1233,
inference(avatar_split_clause,[],[f7452,f20301]) ).
fof(f20301,plain,
( spl263_1233
<=> ! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1233])]) ).
fof(f7452,plain,
! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5308,f4966]) ).
fof(f5308,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2757]) ).
fof(f2757,plain,
! [X0,X1] :
( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) )
& ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f1700]) ).
fof(f1700,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_a_bool(X0,X1))
=> bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
& ( hBOOL(hAPP_a_bool(X0,X1))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) ) ),
inference(rectify,[],[f737]) ).
fof(f737,axiom,
! [X12,X7] :
( ( ~ hBOOL(hAPP_a_bool(X12,X7))
=> bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X7)),X12)) )
& ( hBOOL(hAPP_a_bool(X12,X7))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X7)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f20299,plain,
spl263_1232,
inference(avatar_split_clause,[],[f7449,f20297]) ).
fof(f20297,plain,
( spl263_1232
<=> ! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1232])]) ).
fof(f7449,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0)))),
inference(forward_demodulation,[],[f5295,f4966]) ).
fof(f5295,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool))),
inference(cnf_transformation,[],[f1691]) ).
fof(f1691,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool))),
inference(rectify,[],[f659]) ).
fof(f659,axiom,
! [X7,X4] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X4) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f20295,plain,
spl263_1231,
inference(avatar_split_clause,[],[f6910,f20293]) ).
fof(f20293,plain,
( spl263_1231
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1231])]) ).
fof(f6910,plain,
! [X2,X0,X1] :
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ),
inference(cnf_transformation,[],[f4770]) ).
fof(f4770,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2)
| X1 != X2 )
& ( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ) ),
inference(nnf_transformation,[],[f2627]) ).
fof(f2627,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2)
<=> X1 = X2 ),
inference(rectify,[],[f1090]) ).
fof(f1090,axiom,
! [X15,X24,X16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X15)),X24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X15)),X16)
<=> X16 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f20291,plain,
spl263_1230,
inference(avatar_split_clause,[],[f6776,f20289]) ).
fof(f20289,plain,
( spl263_1230
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1230])]) ).
fof(f6776,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK260(X0,X1,X2)) = X1
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f19636,plain,
( spl263_5
| ~ spl263_158
| ~ spl263_1085 ),
inference(avatar_split_clause,[],[f19575,f16156,f8535,f7808]) ).
fof(f8535,plain,
( spl263_158
<=> ! [X0] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_158])]) ).
fof(f19575,plain,
( hBOOL(fFalse)
| ~ spl263_158
| ~ spl263_1085 ),
inference(superposition,[],[f8536,f16157]) ).
fof(f8536,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ spl263_158 ),
inference(avatar_component_clause,[],[f8535]) ).
fof(f19635,plain,
spl263_1229,
inference(avatar_split_clause,[],[f6768,f19633]) ).
fof(f19633,plain,
( spl263_1229
<=> ! [X2,X0,X1] :
( sP30(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1229])]) ).
fof(f6768,plain,
! [X2,X0,X1] :
( sP30(X0,X1,X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK259(X0,X1,X2)) = X1
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f19631,plain,
spl263_1228,
inference(avatar_split_clause,[],[f6637,f19629]) ).
fof(f19629,plain,
( spl263_1228
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1228])]) ).
fof(f6637,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3708]) ).
fof(f3708,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(flattening,[],[f3707]) ).
fof(f3707,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2511]) ).
fof(f2511,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
inference(rectify,[],[f234]) ).
fof(f234,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19627,plain,
spl263_1227,
inference(avatar_split_clause,[],[f6599,f19625]) ).
fof(f19625,plain,
( spl263_1227
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1227])]) ).
fof(f6599,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(cnf_transformation,[],[f3661]) ).
fof(f3661,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(flattening,[],[f3660]) ).
fof(f3660,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(ennf_transformation,[],[f2475]) ).
fof(f2475,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ) ),
inference(rectify,[],[f457]) ).
fof(f457,axiom,
! [X56,X57,X58] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X57),X58))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X56))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X57),X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19623,plain,
spl263_1226,
inference(avatar_split_clause,[],[f6575,f19621]) ).
fof(f19621,plain,
( spl263_1226
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1226])]) ).
fof(f6575,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f3633,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(flattening,[],[f3632]) ).
fof(f3632,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2459]) ).
fof(f2459,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ) ),
inference(rectify,[],[f533]) ).
fof(f533,axiom,
! [X66,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X66))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X66)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19619,plain,
spl263_1225,
inference(avatar_split_clause,[],[f6564,f19617]) ).
fof(f19617,plain,
( spl263_1225
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1225])]) ).
fof(f6564,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3616]) ).
fof(f3616,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(flattening,[],[f3615]) ).
fof(f3615,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2448]) ).
fof(f2448,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X9,X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19615,plain,
spl263_1224,
inference(avatar_split_clause,[],[f6554,f19613]) ).
fof(f19613,plain,
( spl263_1224
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1224])]) ).
fof(f6554,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3601]) ).
fof(f3601,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(flattening,[],[f3600]) ).
fof(f3600,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2438]) ).
fof(f2438,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0)) ) ),
inference(rectify,[],[f532]) ).
fof(f532,axiom,
! [X66,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X66))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X66)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19611,plain,
spl263_1223,
inference(avatar_split_clause,[],[f6544,f19609]) ).
fof(f19609,plain,
( spl263_1223
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1223])]) ).
fof(f6544,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(cnf_transformation,[],[f3585]) ).
fof(f3585,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(flattening,[],[f3584]) ).
fof(f3584,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(ennf_transformation,[],[f2428]) ).
fof(f2428,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X9,X10,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19607,plain,
spl263_1222,
inference(avatar_split_clause,[],[f6538,f19605]) ).
fof(f19605,plain,
( spl263_1222
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1222])]) ).
fof(f6538,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3575]) ).
fof(f3575,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(flattening,[],[f3574]) ).
fof(f3574,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2422]) ).
fof(f2422,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ) ),
inference(rectify,[],[f534]) ).
fof(f534,axiom,
! [X66,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X66))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X66)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19603,plain,
spl263_1221,
inference(avatar_split_clause,[],[f6528,f19601]) ).
fof(f19601,plain,
( spl263_1221
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1221])]) ).
fof(f6528,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f3559]) ).
fof(f3559,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(flattening,[],[f3558]) ).
fof(f3558,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f2412]) ).
fof(f2412,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X9,X10,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19599,plain,
spl263_1220,
inference(avatar_split_clause,[],[f6515,f19597]) ).
fof(f19597,plain,
( spl263_1220
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1220])]) ).
fof(f6515,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3540]) ).
fof(f3540,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(flattening,[],[f3539]) ).
fof(f3539,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2399]) ).
fof(f2399,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
inference(rectify,[],[f523]) ).
fof(f523,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19574,plain,
spl263_1219,
inference(avatar_split_clause,[],[f6308,f19572]) ).
fof(f19572,plain,
( spl263_1219
<=> ! [X2,X0,X1] :
( image_pname_a(X1,sK187(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1219])]) ).
fof(f6308,plain,
! [X2,X0,X1] :
( image_pname_a(X1,sK187(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4503]) ).
fof(f19570,plain,
spl263_1218,
inference(avatar_split_clause,[],[f6213,f19568]) ).
fof(f19568,plain,
( spl263_1218
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X1,sK158(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1218])]) ).
fof(f6213,plain,
! [X2,X0,X1] :
( hAPP_pname_a(X1,sK158(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4447]) ).
fof(f19566,plain,
spl263_1217,
inference(avatar_split_clause,[],[f6209,f19564]) ).
fof(f19564,plain,
( spl263_1217
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X1,sK157(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1217])]) ).
fof(f6209,plain,
! [X2,X0,X1] :
( hAPP_pname_a(X1,sK157(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4443]) ).
fof(f19562,plain,
spl263_1216,
inference(avatar_split_clause,[],[f6002,f19560]) ).
fof(f19560,plain,
( spl263_1216
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,sK156(X0,X1)) = X0
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1216])]) ).
fof(f6002,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK156(X0,X1)) = X0
| zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f4389]) ).
fof(f19556,plain,
spl263_1215,
inference(avatar_split_clause,[],[f5914,f19554]) ).
fof(f19554,plain,
( spl263_1215
<=> ! [X0,X1,X3] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
| ~ is_a(X3)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1215])]) ).
fof(f5914,plain,
! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
| ~ is_a(X3)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f4320]) ).
fof(f19552,plain,
spl263_1214,
inference(avatar_split_clause,[],[f5753,f19550]) ).
fof(f19550,plain,
( spl263_1214
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,sK134(X0,X1)) = X1
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1214])]) ).
fof(f5753,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK134(X0,X1)) = X1
| hAPP_nat_nat(suc,X0) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4249]) ).
fof(f19548,plain,
spl263_1213,
inference(avatar_split_clause,[],[f5711,f19546]) ).
fof(f19546,plain,
( spl263_1213
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1213])]) ).
fof(f5711,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f3105]) ).
fof(f3105,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(ennf_transformation,[],[f1957]) ).
fof(f1957,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1)) ),
inference(rectify,[],[f1067]) ).
fof(f1067,axiom,
! [X22,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),hAPP_nat_nat(suc,X22))),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19544,plain,
spl263_1212,
inference(avatar_split_clause,[],[f5657,f19542]) ).
fof(f19542,plain,
( spl263_1212
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1212])]) ).
fof(f5657,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3053]) ).
fof(f3053,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1922]) ).
fof(f1922,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))) ),
inference(rectify,[],[f199]) ).
fof(f199,axiom,
! [X10,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X4)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19540,plain,
spl263_1211,
inference(avatar_split_clause,[],[f5614,f19538]) ).
fof(f19538,plain,
( spl263_1211
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1211])]) ).
fof(f5614,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3013]) ).
fof(f3013,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1893]) ).
fof(f1893,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))) ),
inference(rectify,[],[f200]) ).
fof(f200,axiom,
! [X10,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X4)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19536,plain,
spl263_1210,
inference(avatar_split_clause,[],[f5576,f19534]) ).
fof(f19534,plain,
( spl263_1210
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1210])]) ).
fof(f5576,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2980]) ).
fof(f2980,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1869]) ).
fof(f1869,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))) ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X10,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X4)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19510,plain,
spl263_1209,
inference(avatar_split_clause,[],[f5536,f19508]) ).
fof(f19508,plain,
( spl263_1209
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1209])]) ).
fof(f5536,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2946]) ).
fof(f2946,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1844]) ).
fof(f1844,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X4)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19506,plain,
spl263_1208,
inference(avatar_split_clause,[],[f5502,f19504]) ).
fof(f19504,plain,
( spl263_1208
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1208])]) ).
fof(f5502,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2902]) ).
fof(f2902,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1814]) ).
fof(f1814,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))) ),
inference(rectify,[],[f197]) ).
fof(f197,axiom,
! [X10,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X4)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19502,plain,
spl263_1207,
inference(avatar_split_clause,[],[f5501,f19500]) ).
fof(f19500,plain,
( spl263_1207
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1207])]) ).
fof(f5501,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2901]) ).
fof(f2901,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1813]) ).
fof(f1813,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))) ),
inference(rectify,[],[f196]) ).
fof(f196,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X4)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19498,plain,
spl263_1206,
inference(avatar_split_clause,[],[f5500,f19496]) ).
fof(f19496,plain,
( spl263_1206
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1206])]) ).
fof(f5500,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2900]) ).
fof(f2900,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1812]) ).
fof(f1812,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X4)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19494,plain,
spl263_1205,
inference(avatar_split_clause,[],[f5499,f19492]) ).
fof(f19492,plain,
( spl263_1205
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1205])]) ).
fof(f5499,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2899]) ).
fof(f2899,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1811]) ).
fof(f1811,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))) ),
inference(rectify,[],[f194]) ).
fof(f194,axiom,
! [X10,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X4)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X10),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19490,plain,
spl263_1204,
inference(avatar_split_clause,[],[f5463,f19488]) ).
fof(f19488,plain,
( spl263_1204
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK107(X0,X1)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1204])]) ).
fof(f5463,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK107(X0,X1)),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4194]) ).
fof(f4194,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,sK107(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK107(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK107])],[f2866,f4193]) ).
fof(f4193,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,sK107(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK107(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2866,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f2865]) ).
fof(f2865,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1780]) ).
fof(f1780,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X8)),hAPP_nat_int(X8,X29))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19486,plain,
spl263_1203,
inference(avatar_split_clause,[],[f5461,f19484]) ).
fof(f19484,plain,
( spl263_1203
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK106(X0,X1)),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1203])]) ).
fof(f5461,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK106(X0,X1)),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4192]) ).
fof(f4192,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,sK106(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK106(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106])],[f2864,f4191]) ).
fof(f4191,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,sK106(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK106(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2864,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f2863]) ).
fof(f2863,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
inference(rectify,[],[f381]) ).
fof(f381,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X8)),hAPP_nat_fun_a_bool(X8,X29))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19482,plain,
spl263_1202,
inference(avatar_split_clause,[],[f5459,f19480]) ).
fof(f19480,plain,
( spl263_1202
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(X0,X1)),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1202])]) ).
fof(f5459,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(X0,X1)),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4190]) ).
fof(f4190,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,sK105(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105])],[f2862,f4189]) ).
fof(f4189,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,sK105(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2862,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f2861]) ).
fof(f2861,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1778]) ).
fof(f1778,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X8)),hAPP_n1025906991e_bool(X8,X29))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19478,plain,
spl263_1201,
inference(avatar_split_clause,[],[f5457,f19476]) ).
fof(f19476,plain,
( spl263_1201
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK104(X0,X1)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1201])]) ).
fof(f5457,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK104(X0,X1)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4188]) ).
fof(f4188,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,sK104(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK104(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f2860,f4187]) ).
fof(f4187,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,sK104(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK104(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2860,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f2859]) ).
fof(f2859,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1777]) ).
fof(f1777,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
inference(rectify,[],[f379]) ).
fof(f379,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X8)),hAPP_n1699378549t_bool(X8,X29))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19474,plain,
spl263_1200,
inference(avatar_split_clause,[],[f5455,f19472]) ).
fof(f19472,plain,
( spl263_1200
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(X0,X1)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1200])]) ).
fof(f5455,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(X0,X1)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4186]) ).
fof(f4186,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,sK103(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f2858,f4185]) ).
fof(f4185,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,sK103(X0,X1)))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2858,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f2857]) ).
fof(f2857,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1776]) ).
fof(f1776,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
inference(rectify,[],[f378]) ).
fof(f378,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X8)),hAPP_n1082236369t_bool(X8,X29))))))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19469,plain,
spl263_1199,
inference(avatar_split_clause,[],[f5453,f19467]) ).
fof(f19467,plain,
( spl263_1199
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK102(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1199])]) ).
fof(f5453,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK102(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4184]) ).
fof(f4184,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,sK102(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK102(X0,X1)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102])],[f2856,f4183]) ).
fof(f4183,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,sK102(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK102(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2856,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f2855]) ).
fof(f2855,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1775]) ).
fof(f1775,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X8)),hAPP_int_a(X8,X29))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19465,plain,
spl263_1198,
inference(avatar_split_clause,[],[f5451,f19463]) ).
fof(f19463,plain,
( spl263_1198
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK101(X0,X1)),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1198])]) ).
fof(f5451,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK101(X0,X1)),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4182]) ).
fof(f4182,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,sK101(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK101(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f2854,f4181]) ).
fof(f4181,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,sK101(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK101(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2854,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f2853]) ).
fof(f2853,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1774]) ).
fof(f1774,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X8)),hAPP_int_fun_a_bool(X8,X29))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19461,plain,
spl263_1197,
inference(avatar_split_clause,[],[f5449,f19459]) ).
fof(f19459,plain,
( spl263_1197
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK100(X0,X1)),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1197])]) ).
fof(f5449,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK100(X0,X1)),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4180]) ).
fof(f4180,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,sK100(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK100(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f2852,f4179]) ).
fof(f4179,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,sK100(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK100(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2852,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f2851]) ).
fof(f2851,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
inference(rectify,[],[f385]) ).
fof(f385,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X8)),hAPP_i7355787e_bool(X8,X29))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19457,plain,
spl263_1196,
inference(avatar_split_clause,[],[f5447,f19455]) ).
fof(f19455,plain,
( spl263_1196
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK99(X0,X1)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1196])]) ).
fof(f5447,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK99(X0,X1)),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4178]) ).
fof(f4178,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,sK99(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK99(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99])],[f2850,f4177]) ).
fof(f4177,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,sK99(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK99(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2850,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f2849]) ).
fof(f2849,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1772]) ).
fof(f1772,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X8)),hAPP_i1948725293t_bool(X8,X29))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19453,plain,
spl263_1195,
inference(avatar_split_clause,[],[f5445,f19451]) ).
fof(f19451,plain,
( spl263_1195
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK98(X0,X1)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1195])]) ).
fof(f5445,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK98(X0,X1)),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4176]) ).
fof(f4176,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,sK98(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK98(X0,X1)),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98])],[f2848,f4175]) ).
fof(f4175,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,sK98(X0,X1)))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK98(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2848,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f2847]) ).
fof(f2847,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1771]) ).
fof(f1771,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X8)),hAPP_i418383825t_bool(X8,X29))))))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19449,plain,
spl263_1194,
inference(avatar_split_clause,[],[f5443,f19447]) ).
fof(f19447,plain,
( spl263_1194
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK97(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1194])]) ).
fof(f5443,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK97(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f4174]) ).
fof(f4174,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK97(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK97(X0,X1)),X1))
& is_pname(sK97(X0,X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97])],[f2846,f4173]) ).
fof(f4173,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK97(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK97(X0,X1)),X1))
& is_pname(sK97(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2846,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f2845]) ).
fof(f2845,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1770]) ).
fof(f1770,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
=> ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) ) ) ),
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X8,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X8,X4)))
=> ? [X29] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X4)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X8)),hAPP_pname_a(X8,X29))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
& is_pname(X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19445,plain,
spl263_1193,
inference(avatar_split_clause,[],[f5410,f19443]) ).
fof(f19443,plain,
( spl263_1193
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP9(X0)
| is_a(sK95(X0))
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1193])]) ).
fof(f5410,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP9(X0)
| is_a(sK95(X0))
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f4170]) ).
fof(f4170,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP9(X0)
| ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK95(X0)),bot_bot_fun_a_bool)))
& is_a(sK95(X0)) )
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95])],[f3926,f4169]) ).
fof(f4169,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
& is_a(X2) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK95(X0)),bot_bot_fun_a_bool)))
& is_a(sK95(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3926,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP9(X0)
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
& is_a(X2) )
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(definition_folding,[],[f2813,f3925]) ).
fof(f3925,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& bot_bot_fun_a_bool != X4
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f2813,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& bot_bot_fun_a_bool != X4
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
& is_a(X2) )
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(flattening,[],[f2812]) ).
fof(f2812,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& bot_bot_fun_a_bool != X4
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
& is_a(X2) )
| bot_bot_fun_a_bool = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f1744]) ).
fof(f1744,plain,
! [X0,X1] :
( is_fun_a_bool(X1)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( bot_bot_fun_a_bool != X1
=> ( ! [X2] :
( is_a(X2)
=> hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))) )
=> ( ! [X3,X4] :
( ( is_fun_a_bool(X4)
& is_a(X3) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( bot_bot_fun_a_bool != X4
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,X4))
=> hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f886]) ).
fof(f886,axiom,
! [X12,X6] :
( is_fun_a_bool(X6)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> ( bot_bot_fun_a_bool != X6
=> ( ! [X29] :
( is_a(X29)
=> hBOOL(hAPP_fun_a_bool_bool(X12,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),bot_bot_fun_a_bool))) )
=> ( ! [X29,X78] :
( ( is_fun_a_bool(X78)
& is_a(X29) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X78))
=> ( bot_bot_fun_a_bool != X78
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X78))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,X78))
=> hBOOL(hAPP_fun_a_bool_bool(X12,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),X78))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X12,X6)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19441,plain,
spl263_1192,
inference(avatar_split_clause,[],[f5387,f19439]) ).
fof(f19439,plain,
( spl263_1192
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP8(X0)
| is_pname(sK92(X0))
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1192])]) ).
fof(f5387,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP8(X0)
| is_pname(sK92(X0))
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f4162]) ).
fof(f4162,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP8(X0)
| ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK92(X0)),bot_bo844097828e_bool)))
& is_pname(sK92(X0)) )
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92])],[f3924,f4161]) ).
fof(f4161,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
& is_pname(X2) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK92(X0)),bot_bo844097828e_bool)))
& is_pname(sK92(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3924,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP8(X0)
| ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
& is_pname(X2) )
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(definition_folding,[],[f2796,f3923]) ).
fof(f3923,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& bot_bo844097828e_bool != X4
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2796,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& bot_bo844097828e_bool != X4
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
& is_pname(X2) )
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(flattening,[],[f2795]) ).
fof(f2795,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& bot_bo844097828e_bool != X4
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
& is_pname(X2) )
| bot_bo844097828e_bool = X1
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f1738]) ).
fof(f1738,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( bot_bo844097828e_bool != X1
=> ( ! [X2] :
( is_pname(X2)
=> hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))) )
=> ( ! [X3,X4] :
( ( is_fun_pname_bool(X4)
& is_pname(X3) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( bot_bo844097828e_bool != X4
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,X4))
=> hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f889]) ).
fof(f889,axiom,
! [X12,X6] :
( is_fun_pname_bool(X6)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> ( bot_bo844097828e_bool != X6
=> ( ! [X29] :
( is_pname(X29)
=> hBOOL(hAPP_f1664156314l_bool(X12,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X29),bot_bo844097828e_bool))) )
=> ( ! [X29,X78] :
( ( is_fun_pname_bool(X78)
& is_pname(X29) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X78))
=> ( bot_bo844097828e_bool != X78
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X78))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,X78))
=> hBOOL(hAPP_f1664156314l_bool(X12,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X29),X78))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X12,X6)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19437,plain,
spl263_1191,
inference(avatar_split_clause,[],[f5292,f19435]) ).
fof(f19435,plain,
( spl263_1191
<=> ! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1191])]) ).
fof(f5292,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)),
inference(cnf_transformation,[],[f1688]) ).
fof(f1688,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)),
inference(rectify,[],[f480]) ).
fof(f480,axiom,
! [X7,X12] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),collect_a(X12)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19433,plain,
spl263_1190,
inference(avatar_split_clause,[],[f5288,f19431]) ).
fof(f19431,plain,
( spl263_1190
<=> ! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1190])]) ).
fof(f5288,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),
inference(cnf_transformation,[],[f1684]) ).
fof(f1684,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),
inference(rectify,[],[f544]) ).
fof(f544,axiom,
! [X29,X67] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),X67) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X29)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X67))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f19429,plain,
spl263_1189,
inference(avatar_split_clause,[],[f5282,f19427]) ).
fof(f19427,plain,
( spl263_1189
<=> ! [X0,X1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1189])]) ).
fof(f5282,plain,
! [X0,X1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),
inference(cnf_transformation,[],[f1678]) ).
fof(f1678,plain,
! [X0,X1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),
inference(rectify,[],[f547]) ).
fof(f547,axiom,
! [X29,X67] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X29),X67) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X29)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X67))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f18194,plain,
( spl263_1188
| ~ spl263_146
| ~ spl263_923 ),
inference(avatar_split_clause,[],[f15318,f14712,f8487,f18192]) ).
fof(f18192,plain,
( spl263_1188
<=> ! [X0] : ~ sP23(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1188])]) ).
fof(f8487,plain,
( spl263_146
<=> ! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_146])]) ).
fof(f14712,plain,
( spl263_923
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK209(X0,X1)),sK210(X0,X1))))
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_923])]) ).
fof(f15318,plain,
( ! [X0] : ~ sP23(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)
| ~ spl263_146
| ~ spl263_923 ),
inference(resolution,[],[f14713,f8488]) ).
fof(f8488,plain,
( ! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0))
| ~ spl263_146 ),
inference(avatar_component_clause,[],[f8487]) ).
fof(f14713,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK209(X0,X1)),sK210(X0,X1))))
| ~ sP23(X0,X1) )
| ~ spl263_923 ),
inference(avatar_component_clause,[],[f14712]) ).
fof(f17947,plain,
spl263_1187,
inference(avatar_split_clause,[],[f7707,f17945]) ).
fof(f17945,plain,
( spl263_1187
<=> ! [X2,X0,X1] :
( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = image_nat_int(X0,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1187])]) ).
fof(f7707,plain,
! [X2,X0,X1] :
( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = image_nat_int(X0,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(forward_demodulation,[],[f6561,f6162]) ).
fof(f6162,plain,
! [X2,X0,X1] : image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)),
inference(cnf_transformation,[],[f2228]) ).
fof(f2228,plain,
! [X0,X1,X2] : image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)),
inference(rectify,[],[f574]) ).
fof(f574,axiom,
! [X8,X7,X9] : image_nat_int(X8,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X8,X7)),image_nat_int(X8,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6561,plain,
! [X2,X0,X1] :
( image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3611]) ).
fof(f3611,plain,
! [X0,X1,X2] :
( image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2445]) ).
fof(f2445,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ),
inference(rectify,[],[f576]) ).
fof(f576,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> image_nat_int(X8,X4) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X8,X10)),image_nat_int(X8,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17943,plain,
( spl263_1186
| ~ spl263_145
| ~ spl263_921 ),
inference(avatar_split_clause,[],[f15313,f14704,f8483,f17941]) ).
fof(f17941,plain,
( spl263_1186
<=> ! [X0] : ~ sP22(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1186])]) ).
fof(f8483,plain,
( spl263_145
<=> ! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_145])]) ).
fof(f14704,plain,
( spl263_921
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK200(X0,X1)),sK201(X0,X1))))
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_921])]) ).
fof(f15313,plain,
( ! [X0] : ~ sP22(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)
| ~ spl263_145
| ~ spl263_921 ),
inference(resolution,[],[f14705,f8484]) ).
fof(f8484,plain,
( ! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0))
| ~ spl263_145 ),
inference(avatar_component_clause,[],[f8483]) ).
fof(f14705,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK200(X0,X1)),sK201(X0,X1))))
| ~ sP22(X0,X1) )
| ~ spl263_921 ),
inference(avatar_component_clause,[],[f14704]) ).
fof(f17939,plain,
spl263_1185,
inference(avatar_split_clause,[],[f7701,f17937]) ).
fof(f17937,plain,
( spl263_1185
<=> ! [X2,X0,X1] :
( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = image_pname_a(X0,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1185])]) ).
fof(f7701,plain,
! [X2,X0,X1] :
( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = image_pname_a(X0,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(forward_demodulation,[],[f6521,f6161]) ).
fof(f6161,plain,
! [X2,X0,X1] : image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)),
inference(cnf_transformation,[],[f2227]) ).
fof(f2227,plain,
! [X0,X1,X2] : image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)),
inference(rectify,[],[f575]) ).
fof(f575,axiom,
! [X8,X7,X9] : image_pname_a(X8,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X9)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X8,X7)),image_pname_a(X8,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6521,plain,
! [X2,X0,X1] :
( image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3548]) ).
fof(f3548,plain,
! [X0,X1,X2] :
( image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2405]) ).
fof(f2405,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ),
inference(rectify,[],[f577]) ).
fof(f577,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> image_pname_a(X8,X4) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X8,X10)),image_pname_a(X8,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17935,plain,
spl263_1184,
inference(avatar_split_clause,[],[f7451,f17933]) ).
fof(f17933,plain,
( spl263_1184
<=> ! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1184])]) ).
fof(f7451,plain,
! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5306,f4966]) ).
fof(f5306,plain,
! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2756]) ).
fof(f2756,plain,
! [X0,X1] :
( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) )
& ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f1699]) ).
fof(f1699,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_a_bool(X0,X1))
=> bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) )
& ( hBOOL(hAPP_a_bool(X0,X1))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) ) ),
inference(rectify,[],[f740]) ).
fof(f740,axiom,
! [X12,X7] :
( ( ~ hBOOL(hAPP_a_bool(X12,X7))
=> bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X7)),X12)) )
& ( hBOOL(hAPP_a_bool(X12,X7))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X7)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17931,plain,
spl263_1183,
inference(avatar_split_clause,[],[f7448,f17929]) ).
fof(f17929,plain,
( spl263_1183
<=> ! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1183])]) ).
fof(f7448,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0))),
inference(forward_demodulation,[],[f5294,f7397]) ).
fof(f5294,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool))),
inference(cnf_transformation,[],[f1690]) ).
fof(f1690,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool))),
inference(rectify,[],[f660]) ).
fof(f660,axiom,
! [X7,X4] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X4) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17927,plain,
spl263_1182,
inference(avatar_split_clause,[],[f7447,f17925]) ).
fof(f17925,plain,
( spl263_1182
<=> ! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1182])]) ).
fof(f7447,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0))),
inference(forward_demodulation,[],[f5293,f7396]) ).
fof(f5293,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool))),
inference(cnf_transformation,[],[f1689]) ).
fof(f1689,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool))),
inference(rectify,[],[f661]) ).
fof(f661,axiom,
! [X7,X4] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X4) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17923,plain,
spl263_1181,
inference(avatar_split_clause,[],[f7441,f17921]) ).
fof(f17921,plain,
( spl263_1181
<=> ! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(fequal_nat,X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1181])]) ).
fof(f7441,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(fequal_nat,X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),
inference(forward_demodulation,[],[f5286,f7401]) ).
fof(f7401,plain,
! [X0] : hAPP_n1699378549t_bool(fequal_nat,X0) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0),
inference(forward_demodulation,[],[f7400,f7397]) ).
fof(f7400,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0),
inference(forward_demodulation,[],[f4970,f4876]) ).
fof(f4970,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),
inference(cnf_transformation,[],[f1516]) ).
fof(f1516,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),
inference(rectify,[],[f745]) ).
fof(f745,axiom,
! [X7] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5286,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),
inference(cnf_transformation,[],[f1682]) ).
fof(f1682,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),
inference(rectify,[],[f546]) ).
fof(f546,axiom,
! [X29,X67] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),X67) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X29)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X67))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17919,plain,
spl263_1180,
inference(avatar_split_clause,[],[f7439,f17917]) ).
fof(f17917,plain,
( spl263_1180
<=> ! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(fequal_int,X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1180])]) ).
fof(f7439,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(fequal_int,X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))),
inference(forward_demodulation,[],[f5284,f7399]) ).
fof(f7399,plain,
! [X0] : hAPP_i1948725293t_bool(fequal_int,X0) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0),
inference(forward_demodulation,[],[f7398,f7396]) ).
fof(f7398,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0),
inference(forward_demodulation,[],[f4969,f4874]) ).
fof(f4969,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),
inference(cnf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),
inference(rectify,[],[f744]) ).
fof(f744,axiom,
! [X7] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5284,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))),
inference(cnf_transformation,[],[f1680]) ).
fof(f1680,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))),
inference(rectify,[],[f477]) ).
fof(f477,axiom,
! [X7,X9] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X7)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17915,plain,
spl263_1179,
inference(avatar_split_clause,[],[f7414,f17913]) ).
fof(f17913,plain,
( spl263_1179
<=> ! [X0] :
( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1179])]) ).
fof(f7414,plain,
! [X0] :
( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(forward_demodulation,[],[f7043,f4958]) ).
fof(f4958,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0),
inference(cnf_transformation,[],[f1504]) ).
fof(f1504,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0),
inference(rectify,[],[f956]) ).
fof(f956,axiom,
! [X13] : hAPP_nat_nat(suc,X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7043,plain,
! [X0] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f4988,f4948]) ).
fof(f4948,plain,
! [X0] : succ(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int),
inference(cnf_transformation,[],[f1494]) ).
fof(f1494,plain,
! [X0] : succ(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int),
inference(rectify,[],[f1269]) ).
fof(f1269,axiom,
! [X21] : succ(X21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4988,plain,
! [X0] :
( number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f2696]) ).
fof(f2696,plain,
! [X0] :
( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
inference(ennf_transformation,[],[f1530]) ).
fof(f1530,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) ) ),
inference(rectify,[],[f1272]) ).
fof(f1272,axiom,
! [X132] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X132),pls))
=> number_number_of_nat(succ(X132)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X132)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X132),pls))
=> one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X132)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17911,plain,
spl263_1178,
inference(avatar_split_clause,[],[f7406,f17909]) ).
fof(f17909,plain,
( spl263_1178
<=> ! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1178])]) ).
fof(f7406,plain,
! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat))),X0),
inference(forward_demodulation,[],[f7405,f7392]) ).
fof(f7392,plain,
number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat)),
inference(forward_demodulation,[],[f7391,f4848]) ).
fof(f7391,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),
inference(forward_demodulation,[],[f7027,f7020]) ).
fof(f7020,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int),
inference(definition_unfolding,[],[f4855,f4948,f4973]) ).
fof(f4855,plain,
succ(pls) = bit1(pls),
inference(cnf_transformation,[],[f1273]) ).
fof(f1273,axiom,
succ(pls) = bit1(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7027,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),
inference(definition_unfolding,[],[f4869,f4973,f4973]) ).
fof(f4869,plain,
number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,axiom,
number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7405,plain,
! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int)))),X0),
inference(forward_demodulation,[],[f7038,f7020]) ).
fof(f7038,plain,
! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)))),X0),
inference(definition_unfolding,[],[f4980,f4973,f4973]) ).
fof(f4980,plain,
! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X0),
inference(cnf_transformation,[],[f1526]) ).
fof(f1526,plain,
! [X0] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X0),
inference(rectify,[],[f1279]) ).
fof(f1279,axiom,
! [X13] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X13))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17907,plain,
spl263_1177,
inference(avatar_split_clause,[],[f7082,f17905]) ).
fof(f17905,plain,
( spl263_1177
<=> ! [X4,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK87(X0))))
| ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1177])]) ).
fof(f7082,plain,
! [X0,X4] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK87(X0))))
| ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
inference(definition_unfolding,[],[f5186,f4830]) ).
fof(f5186,plain,
! [X0,X4] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK87(X0))))
| ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ),
inference(cnf_transformation,[],[f4154]) ).
fof(f4154,plain,
! [X0] :
( ( ( hBOOL(hAPP_int_bool(X0,sK86(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK86(X0))) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK87(X0))))
| ! [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86,sK87])],[f4151,f4153,f4152]) ).
fof(f4152,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( hBOOL(hAPP_int_bool(X0,sK86(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK86(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f4153,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
=> hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK87(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f4151,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ! [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(rectify,[],[f4150]) ).
fof(f4150,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ! [X1] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
inference(nnf_transformation,[],[f1622]) ).
fof(f1622,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
<=> ? [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f1226]) ).
fof(f1226,axiom,
! [X12] :
( ? [X29] :
( hBOOL(hAPP_int_bool(X12,X29))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X29)) )
<=> ? [X29] : hBOOL(hAPP_int_bool(X12,hAPP_nat_int(semiri1621563631at_int,X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17903,plain,
spl263_1176,
inference(avatar_split_clause,[],[f7079,f17901]) ).
fof(f17901,plain,
( spl263_1176
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK82(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1176])]) ).
fof(f7079,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK82(X0)))) ),
inference(definition_unfolding,[],[f5181,f4830]) ).
fof(f5181,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK82(X0)))) ),
inference(cnf_transformation,[],[f4141]) ).
fof(f4141,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK82(X0)))) )
& ( ! [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ( ~ hBOOL(hAPP_int_bool(X0,sK83(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK83(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82,sK83])],[f4138,f4140,f4139]) ).
fof(f4139,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
=> ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK82(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f4140,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) )
=> ( ~ hBOOL(hAPP_int_bool(X0,sK83(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK83(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f4138,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ? [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
inference(rectify,[],[f4137]) ).
fof(f4137,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ? [X1] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
inference(nnf_transformation,[],[f2751]) ).
fof(f2751,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
<=> ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> hBOOL(hAPP_int_bool(X0,X1)) )
<=> ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f1227]) ).
fof(f1227,axiom,
! [X12] :
( ! [X29] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X29))
=> hBOOL(hAPP_int_bool(X12,X29)) )
<=> ! [X29] : hBOOL(hAPP_int_bool(X12,hAPP_nat_int(semiri1621563631at_int,X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17899,plain,
( spl263_1175
| ~ spl263_144
| ~ spl263_920 ),
inference(avatar_split_clause,[],[f15305,f14700,f8479,f17897]) ).
fof(f17897,plain,
( spl263_1175
<=> ! [X0] : ~ sP21(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1175])]) ).
fof(f8479,plain,
( spl263_144
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_144])]) ).
fof(f14700,plain,
( spl263_920
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK198(X0,X1)),sK199(X0,X1))))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_920])]) ).
fof(f15305,plain,
( ! [X0] : ~ sP21(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)
| ~ spl263_144
| ~ spl263_920 ),
inference(resolution,[],[f14701,f8480]) ).
fof(f8480,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0))
| ~ spl263_144 ),
inference(avatar_component_clause,[],[f8479]) ).
fof(f14701,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK198(X0,X1)),sK199(X0,X1))))
| ~ sP21(X0,X1) )
| ~ spl263_920 ),
inference(avatar_component_clause,[],[f14700]) ).
fof(f17895,plain,
spl263_1174,
inference(avatar_split_clause,[],[f6864,f17893]) ).
fof(f17893,plain,
( spl263_1174
<=> ! [X2,X0,X1] :
( zero_zero_nat = X0
| X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1174])]) ).
fof(f6864,plain,
! [X2,X0,X1] :
( zero_zero_nat = X0
| X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ),
inference(cnf_transformation,[],[f4745]) ).
fof(f4745,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)
| ( zero_zero_nat != X0
& X1 != X2 ) )
& ( zero_zero_nat = X0
| X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ),
inference(flattening,[],[f4744]) ).
fof(f4744,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)
| ( zero_zero_nat != X0
& X1 != X2 ) )
& ( zero_zero_nat = X0
| X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ),
inference(nnf_transformation,[],[f2607]) ).
fof(f2607,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)
<=> ( zero_zero_nat = X0
| X1 = X2 ) ),
inference(rectify,[],[f1088]) ).
fof(f1088,axiom,
! [X15,X24,X16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X16)
<=> ( zero_zero_nat = X15
| X16 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17891,plain,
spl263_1173,
inference(avatar_split_clause,[],[f6861,f17889]) ).
fof(f17889,plain,
( spl263_1173
<=> ! [X2,X0,X1] :
( zero_zero_nat = X1
| X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1173])]) ).
fof(f6861,plain,
! [X2,X0,X1] :
( zero_zero_nat = X1
| X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ),
inference(cnf_transformation,[],[f4743]) ).
fof(f4743,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
| ( zero_zero_nat != X1
& X0 != X2 ) )
& ( zero_zero_nat = X1
| X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ),
inference(flattening,[],[f4742]) ).
fof(f4742,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
| ( zero_zero_nat != X1
& X0 != X2 ) )
& ( zero_zero_nat = X1
| X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ),
inference(nnf_transformation,[],[f2606]) ).
fof(f2606,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)
<=> ( zero_zero_nat = X1
| X0 = X2 ) ),
inference(rectify,[],[f1089]) ).
fof(f1089,axiom,
! [X24,X15,X16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X15)
<=> ( zero_zero_nat = X15
| X16 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17887,plain,
spl263_1172,
inference(avatar_split_clause,[],[f6777,f17885]) ).
fof(f17885,plain,
( spl263_1172
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1172])]) ).
fof(f6777,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f17883,plain,
spl263_1171,
inference(avatar_split_clause,[],[f6769,f17881]) ).
fof(f17881,plain,
( spl263_1171
<=> ! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1171])]) ).
fof(f6769,plain,
! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f17879,plain,
spl263_1170,
inference(avatar_split_clause,[],[f6762,f17877]) ).
fof(f17877,plain,
( spl263_1170
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK258(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1170])]) ).
fof(f6762,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK258(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4684]) ).
fof(f4684,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ! [X3] :
( image_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
& ( ( image_nat_int(X1,sK258(X0,X1,X2)) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK258(X0,X1,X2)),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK258])],[f4682,f4683]) ).
fof(f4683,plain,
! [X0,X1,X2] :
( ? [X4] :
( image_nat_int(X1,X4) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2)) )
=> ( image_nat_int(X1,sK258(X0,X1,X2)) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK258(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4682,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ! [X3] :
( image_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
& ( ? [X4] :
( image_nat_int(X1,X4) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
inference(rectify,[],[f4681]) ).
fof(f4681,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ! [X3] :
( image_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
& ( ? [X3] :
( image_nat_int(X1,X3) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
inference(nnf_transformation,[],[f2583]) ).
fof(f2583,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
<=> ? [X3] :
( image_nat_int(X1,X3) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) ),
inference(rectify,[],[f578]) ).
fof(f578,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_nat_int(X8,X4)))
<=> ? [X70] :
( image_nat_int(X8,X70) = X9
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X70),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17875,plain,
spl263_1169,
inference(avatar_split_clause,[],[f6759,f17873]) ).
fof(f17873,plain,
( spl263_1169
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK257(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1169])]) ).
fof(f6759,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK257(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4680]) ).
fof(f4680,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
| ! [X3] :
( hAPP_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
& ( ( hAPP_nat_int(X1,sK257(X0,X1,X2)) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK257(X0,X1,X2)),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK257])],[f4678,f4679]) ).
fof(f4679,plain,
! [X0,X1,X2] :
( ? [X4] :
( hAPP_nat_int(X1,X4) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) )
=> ( hAPP_nat_int(X1,sK257(X0,X1,X2)) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK257(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4678,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
| ! [X3] :
( hAPP_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
& ( ? [X4] :
( hAPP_nat_int(X1,X4) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
inference(rectify,[],[f4677]) ).
fof(f4677,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
| ! [X3] :
( hAPP_nat_int(X1,X3) != X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
& ( ? [X3] :
( hAPP_nat_int(X1,X3) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
inference(nnf_transformation,[],[f2582]) ).
fof(f2582,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
<=> ? [X3] :
( hAPP_nat_int(X1,X3) = X0
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X55,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X55),image_nat_int(X8,X4)))
<=> ? [X29] :
( hAPP_nat_int(X8,X29) = X55
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17871,plain,
spl263_1168,
inference(avatar_split_clause,[],[f6745,f17869]) ).
fof(f17869,plain,
( spl263_1168
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK248(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1168])]) ).
fof(f6745,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK248(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f4664]) ).
fof(f17867,plain,
spl263_1167,
inference(avatar_split_clause,[],[f6743,f17865]) ).
fof(f17865,plain,
( spl263_1167
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK247(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1167])]) ).
fof(f6743,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK247(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f4662]) ).
fof(f17863,plain,
spl263_1166,
inference(avatar_split_clause,[],[f6652,f17861]) ).
fof(f17861,plain,
( spl263_1166
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK239(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1166])]) ).
fof(f6652,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK239(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4626]) ).
fof(f4626,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK239(X0,X1,X2)),X2))
& hAPP_nat_int(X1,sK239(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK239])],[f3723,f4625]) ).
fof(f4625,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
& hAPP_nat_int(X1,X3) = X0 )
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK239(X0,X1,X2)),X2))
& hAPP_nat_int(X1,sK239(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f3723,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
& hAPP_nat_int(X1,X3) = X0 )
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(ennf_transformation,[],[f2520]) ).
fof(f2520,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
=> ~ ! [X3] :
( hAPP_nat_int(X1,X3) = X0
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
inference(rectify,[],[f582]) ).
fof(f582,axiom,
! [X30,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),image_nat_int(X8,X4)))
=> ~ ! [X29] :
( hAPP_nat_int(X8,X29) = X30
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17859,plain,
spl263_1165,
inference(avatar_split_clause,[],[f6505,f17857]) ).
fof(f17857,plain,
( spl263_1165
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2)))
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1165])]) ).
fof(f6505,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2)))
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f4601]) ).
fof(f4601,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2))) )
& ( hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2))) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK230(X0,X1,X2)),X2)) )
| ~ sP26(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK230])],[f4599,f4600]) ).
fof(f4600,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ hBOOL(hAPP_int_bool(X0,X3))
| ~ hBOOL(hAPP_int_bool(X1,X3)) )
& ( hBOOL(hAPP_int_bool(X0,X3))
| hBOOL(hAPP_int_bool(X1,X3)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2)) )
=> ( ( ~ hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2))) )
& ( hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2))) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK230(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f4599,plain,
! [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ hBOOL(hAPP_int_bool(X0,X3))
| ~ hBOOL(hAPP_int_bool(X1,X3)) )
& ( hBOOL(hAPP_int_bool(X0,X3))
| hBOOL(hAPP_int_bool(X1,X3)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2)) )
| ~ sP26(X0,X1) ),
inference(rectify,[],[f4598]) ).
fof(f4598,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( ~ hBOOL(hAPP_int_bool(X1,X6))
| ~ hBOOL(hAPP_int_bool(X0,X6)) )
& ( hBOOL(hAPP_int_bool(X1,X6))
| hBOOL(hAPP_int_bool(X0,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
| ~ sP26(X1,X0) ),
inference(flattening,[],[f4597]) ).
fof(f4597,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( ~ hBOOL(hAPP_int_bool(X1,X6))
| ~ hBOOL(hAPP_int_bool(X0,X6)) )
& ( hBOOL(hAPP_int_bool(X1,X6))
| hBOOL(hAPP_int_bool(X0,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
| ~ sP26(X1,X0) ),
inference(nnf_transformation,[],[f3958]) ).
fof(f3958,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( hBOOL(hAPP_int_bool(X0,X6))
<~> hBOOL(hAPP_int_bool(X1,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
| ~ sP26(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f17855,plain,
spl263_1164,
inference(avatar_split_clause,[],[f6504,f17853]) ).
fof(f17853,plain,
( spl263_1164
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2)))
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1164])]) ).
fof(f6504,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK230(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK230(X0,X1,X2)))
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f4601]) ).
fof(f17851,plain,
spl263_1163,
inference(avatar_split_clause,[],[f6500,f17849]) ).
fof(f17849,plain,
( spl263_1163
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1163])]) ).
fof(f6500,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f4591]) ).
fof(f4591,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2))) )
& ( hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2))) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK226(X0,X1,X2))) )
| ~ sP25(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK226])],[f4589,f4590]) ).
fof(f4590,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ hBOOL(hAPP_int_bool(X0,X3))
| ~ hBOOL(hAPP_int_bool(X1,X3)) )
& ( hBOOL(hAPP_int_bool(X0,X3))
| hBOOL(hAPP_int_bool(X1,X3)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) )
=> ( ( ~ hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2))) )
& ( hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2))) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK226(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f4589,plain,
! [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ hBOOL(hAPP_int_bool(X0,X3))
| ~ hBOOL(hAPP_int_bool(X1,X3)) )
& ( hBOOL(hAPP_int_bool(X0,X3))
| hBOOL(hAPP_int_bool(X1,X3)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) )
| ~ sP25(X0,X1) ),
inference(rectify,[],[f4588]) ).
fof(f4588,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( ~ hBOOL(hAPP_int_bool(X1,X6))
| ~ hBOOL(hAPP_int_bool(X0,X6)) )
& ( hBOOL(hAPP_int_bool(X1,X6))
| hBOOL(hAPP_int_bool(X0,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
| ~ sP25(X1,X0) ),
inference(flattening,[],[f4587]) ).
fof(f4587,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( ~ hBOOL(hAPP_int_bool(X1,X6))
| ~ hBOOL(hAPP_int_bool(X0,X6)) )
& ( hBOOL(hAPP_int_bool(X1,X6))
| hBOOL(hAPP_int_bool(X0,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
| ~ sP25(X1,X0) ),
inference(nnf_transformation,[],[f3956]) ).
fof(f3956,plain,
! [X1,X0] :
( ! [X5] :
? [X6] :
( ( hBOOL(hAPP_int_bool(X0,X6))
<~> hBOOL(hAPP_int_bool(X1,X6)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
| ~ sP25(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f17847,plain,
spl263_1162,
inference(avatar_split_clause,[],[f6499,f17845]) ).
fof(f17845,plain,
( spl263_1162
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1162])]) ).
fof(f6499,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK226(X0,X1,X2)))
| hBOOL(hAPP_int_bool(X1,sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f4591]) ).
fof(f17843,plain,
spl263_1161,
inference(avatar_split_clause,[],[f6477,f17841]) ).
fof(f17841,plain,
( spl263_1161
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK223(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1161])]) ).
fof(f6477,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK223(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4574]) ).
fof(f17839,plain,
spl263_1160,
inference(avatar_split_clause,[],[f6474,f17837]) ).
fof(f17837,plain,
( spl263_1160
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| hBOOL(hAPP_int_bool(X1,sK222(X1,X2)))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1160])]) ).
fof(f6474,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| hBOOL(hAPP_int_bool(X1,sK222(X1,X2)))
| sP24(X1,X2)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4572]) ).
fof(f17835,plain,
spl263_1159,
inference(avatar_split_clause,[],[f6456,f17833]) ).
fof(f17833,plain,
( spl263_1159
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK214(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1159])]) ).
fof(f6456,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK214(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f17831,plain,
spl263_1158,
inference(avatar_split_clause,[],[f6452,f17829]) ).
fof(f17829,plain,
( spl263_1158
<=> ! [X2,X0,X1] :
( is_fun949378684l_bool(sK213(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1158])]) ).
fof(f6452,plain,
! [X2,X0,X1] :
( is_fun949378684l_bool(sK213(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4555]) ).
fof(f17827,plain,
spl263_1157,
inference(avatar_split_clause,[],[f6448,f17825]) ).
fof(f17825,plain,
( spl263_1157
<=> ! [X2,X0,X1] :
( is_fun1661590463l_bool(sK212(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1157])]) ).
fof(f6448,plain,
! [X2,X0,X1] :
( is_fun1661590463l_bool(sK212(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4553]) ).
fof(f17823,plain,
spl263_1156,
inference(avatar_split_clause,[],[f6444,f17821]) ).
fof(f17821,plain,
( spl263_1156
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK211(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1156])]) ).
fof(f6444,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK211(X0,X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f4551]) ).
fof(f17819,plain,
spl263_1155,
inference(avatar_split_clause,[],[f6417,f17817]) ).
fof(f17817,plain,
( spl263_1155
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK205(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1155])]) ).
fof(f6417,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK205(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4539]) ).
fof(f17814,plain,
spl263_1154,
inference(avatar_split_clause,[],[f6413,f17812]) ).
fof(f17812,plain,
( spl263_1154
<=> ! [X2,X0,X1] :
( is_fun949378684l_bool(sK204(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1154])]) ).
fof(f6413,plain,
! [X2,X0,X1] :
( is_fun949378684l_bool(sK204(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4537]) ).
fof(f17810,plain,
spl263_1153,
inference(avatar_split_clause,[],[f6409,f17808]) ).
fof(f17808,plain,
( spl263_1153
<=> ! [X2,X0,X1] :
( is_fun1661590463l_bool(sK203(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1153])]) ).
fof(f6409,plain,
! [X2,X0,X1] :
( is_fun1661590463l_bool(sK203(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4535]) ).
fof(f17806,plain,
spl263_1152,
inference(avatar_split_clause,[],[f6405,f17804]) ).
fof(f17804,plain,
( spl263_1152
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK202(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1152])]) ).
fof(f6405,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK202(X0,X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f4533]) ).
fof(f17802,plain,
spl263_1151,
inference(avatar_split_clause,[],[f6332,f17800]) ).
fof(f17800,plain,
( spl263_1151
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK191(X0,X1,X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1151])]) ).
fof(f6332,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK191(X0,X1,X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4511]) ).
fof(f17798,plain,
spl263_1150,
inference(avatar_split_clause,[],[f6328,f17796]) ).
fof(f17796,plain,
( spl263_1150
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK190(X0,X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1150])]) ).
fof(f6328,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK190(X0,X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4509]) ).
fof(f17794,plain,
spl263_1149,
inference(avatar_split_clause,[],[f6324,f17792]) ).
fof(f17792,plain,
( spl263_1149
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK189(X0,X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1149])]) ).
fof(f6324,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK189(X0,X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f4507]) ).
fof(f17790,plain,
spl263_1148,
inference(avatar_split_clause,[],[f6320,f17788]) ).
fof(f17788,plain,
( spl263_1148
<=> ! [X2,X0,X1] :
( is_fun_a_bool(sK188(X0,X1,X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1148])]) ).
fof(f6320,plain,
! [X2,X0,X1] :
( is_fun_a_bool(sK188(X0,X1,X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f4505]) ).
fof(f17786,plain,
spl263_1147,
inference(avatar_split_clause,[],[f6162,f17784]) ).
fof(f17784,plain,
( spl263_1147
<=> ! [X2,X0,X1] : image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1147])]) ).
fof(f17782,plain,
spl263_1146,
inference(avatar_split_clause,[],[f6161,f17780]) ).
fof(f17780,plain,
( spl263_1146
<=> ! [X2,X0,X1] : image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1146])]) ).
fof(f17778,plain,
spl263_1145,
inference(avatar_split_clause,[],[f5945,f17776]) ).
fof(f17776,plain,
( spl263_1145
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK154(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1145])]) ).
fof(f5945,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK154(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4351]) ).
fof(f4351,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 )
& ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK154(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154])],[f4349,f4350]) ).
fof(f4350,plain,
! [X0,X1] :
( ? [X3] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3)) = X1
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK154(X0,X1))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f4349,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 )
& ( ? [X3] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
inference(rectify,[],[f4348]) ).
fof(f4348,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 )
& ( ? [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2103]) ).
fof(f2103,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
<=> ? [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 ),
inference(rectify,[],[f1007]) ).
fof(f1007,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16))
<=> ? [X118] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X118)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17774,plain,
spl263_1144,
inference(avatar_split_clause,[],[f5938,f17772]) ).
fof(f17772,plain,
( spl263_1144
<=> ! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK153(X0,X1))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1144])]) ).
fof(f5938,plain,
! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK153(X0,X1))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f4344]) ).
fof(f4344,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 )
& ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK153(X0,X1))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f4342,f4343]) ).
fof(f4343,plain,
! [X0,X1] :
( ? [X3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X3)) = X1
=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK153(X0,X1))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f4342,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 )
& ( ? [X3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X3)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(rectify,[],[f4341]) ).
fof(f4341,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ! [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 )
& ( ? [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f2100]) ).
fof(f2100,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
<=> ? [X2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) = X1 ),
inference(rectify,[],[f1212]) ).
fof(f1212,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X138),X55))
<=> ? [X28] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X138),hAPP_nat_int(semiri1621563631at_int,X28)) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17770,plain,
spl263_1143,
inference(avatar_split_clause,[],[f5803,f17768]) ).
fof(f17768,plain,
( spl263_1143
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1143])]) ).
fof(f5803,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f3227]) ).
fof(f3227,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(flattening,[],[f3226]) ).
fof(f3226,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(ennf_transformation,[],[f2040]) ).
fof(f2040,plain,
! [X0,X1] :
( ( is_pname(X1)
& is_pname(X0) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
=> X0 = X1 ) ),
inference(rectify,[],[f702]) ).
fof(f702,axiom,
! [X30,X7] :
( ( is_pname(X7)
& is_pname(X30) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),bot_bo844097828e_bool)))
=> X7 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17766,plain,
spl263_1142,
inference(avatar_split_clause,[],[f5775,f17764]) ).
fof(f17764,plain,
( spl263_1142
<=> ! [X0,X1] :
( X0 = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1142])]) ).
fof(f5775,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ),
inference(cnf_transformation,[],[f3188]) ).
fof(f3188,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ),
inference(flattening,[],[f3187]) ).
fof(f3187,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ),
inference(ennf_transformation,[],[f2014]) ).
fof(f2014,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
=> ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)
=> X0 = X1 ) ),
inference(rectify,[],[f1033]) ).
fof(f1033,axiom,
! [X14,X13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13) = zero_zero_nat
=> ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),X14)
=> X13 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17762,plain,
spl263_1141,
inference(avatar_split_clause,[],[f5771,f17760]) ).
fof(f17760,plain,
( spl263_1141
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1141])]) ).
fof(f5771,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4255]) ).
fof(f4255,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(nnf_transformation,[],[f3183]) ).
fof(f3183,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
<=> X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2011]) ).
fof(f2011,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
<=> X0 = X1 ) ),
inference(rectify,[],[f1013]) ).
fof(f1013,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),hAPP_nat_nat(suc,X24)))
<=> X16 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17758,plain,
spl263_1140,
inference(avatar_split_clause,[],[f5761,f17756]) ).
fof(f17756,plain,
( spl263_1140
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1140])]) ).
fof(f5761,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3170]) ).
fof(f3170,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2002]) ).
fof(f2002,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1 ),
inference(rectify,[],[f948]) ).
fof(f948,axiom,
! [X13,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17754,plain,
spl263_1139,
inference(avatar_split_clause,[],[f5760,f17752]) ).
fof(f17752,plain,
( spl263_1139
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1139])]) ).
fof(f5760,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3169]) ).
fof(f3169,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2001]) ).
fof(f2001,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0 ),
inference(rectify,[],[f283]) ).
fof(f283,axiom,
! [X22,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X13))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),X22)) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17750,plain,
spl263_1138,
inference(avatar_split_clause,[],[f5754,f17748]) ).
fof(f17748,plain,
( spl263_1138
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK135(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1138])]) ).
fof(f5754,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK135(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4251]) ).
fof(f4251,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK135(X0,X1))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f3164,f4250]) ).
fof(f4250,plain,
! [X0,X1] :
( ? [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK135(X0,X1))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3164,plain,
! [X0,X1] :
( ? [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1996]) ).
fof(f1996,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ? [X2] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 ),
inference(rectify,[],[f1023]) ).
fof(f1023,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> ? [X118] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X118)) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17746,plain,
spl263_1137,
inference(avatar_split_clause,[],[f5699,f17744]) ).
fof(f17744,plain,
( spl263_1137
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1137])]) ).
fof(f5699,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3093]) ).
fof(f3093,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(flattening,[],[f3092]) ).
fof(f3092,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1948]) ).
fof(f1948,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
=> X0 = X1 ) ),
inference(rectify,[],[f976]) ).
fof(f976,axiom,
! [X13,X14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),hAPP_nat_nat(suc,X14)))
=> X13 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17742,plain,
spl263_1136,
inference(avatar_split_clause,[],[f5698,f17740]) ).
fof(f17740,plain,
( spl263_1136
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1136])]) ).
fof(f5698,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3091]) ).
fof(f3091,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1947]) ).
fof(f1947,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0 ),
inference(rectify,[],[f1017]) ).
fof(f1017,axiom,
! [X14,X13] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17738,plain,
spl263_1135,
inference(avatar_split_clause,[],[f5678,f17736]) ).
fof(f17736,plain,
( spl263_1135
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(X0,sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1135])]) ).
fof(f5678,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(X0,sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4236]) ).
fof(f17733,plain,
spl263_1134,
inference(avatar_split_clause,[],[f5676,f17731]) ).
fof(f17731,plain,
( spl263_1134
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1134])]) ).
fof(f5676,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK131(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4236]) ).
fof(f17729,plain,
spl263_1133,
inference(avatar_split_clause,[],[f5674,f17727]) ).
fof(f17727,plain,
( spl263_1133
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(hAPP_f54304608l_bool(X0,sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1133])]) ).
fof(f5674,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(hAPP_f54304608l_bool(X0,sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4234]) ).
fof(f17725,plain,
spl263_1132,
inference(avatar_split_clause,[],[f5672,f17723]) ).
fof(f17723,plain,
( spl263_1132
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1132])]) ).
fof(f5672,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4234]) ).
fof(f17721,plain,
spl263_1131,
inference(avatar_split_clause,[],[f5635,f17719]) ).
fof(f17719,plain,
( spl263_1131
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(X0,sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1131])]) ).
fof(f5635,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(X0,sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4225]) ).
fof(f17717,plain,
spl263_1130,
inference(avatar_split_clause,[],[f5633,f17715]) ).
fof(f17715,plain,
( spl263_1130
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1130])]) ).
fof(f5633,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK124(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4225]) ).
fof(f17713,plain,
spl263_1129,
inference(avatar_split_clause,[],[f5631,f17711]) ).
fof(f17711,plain,
( spl263_1129
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| hBOOL(hAPP_f448129468l_bool(X0,sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1129])]) ).
fof(f5631,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| hBOOL(hAPP_f448129468l_bool(X0,sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4223]) ).
fof(f17709,plain,
spl263_1128,
inference(avatar_split_clause,[],[f5629,f17707]) ).
fof(f17707,plain,
( spl263_1128
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1128])]) ).
fof(f5629,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK122(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4223]) ).
fof(f17705,plain,
spl263_1127,
inference(avatar_split_clause,[],[f5320,f17703]) ).
fof(f17703,plain,
( spl263_1127
<=> ! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1127])]) ).
fof(f5320,plain,
! [X0,X1] :
( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f2763]) ).
fof(f2763,plain,
! [X0,X1] :
( ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(ennf_transformation,[],[f1706]) ).
fof(f1706,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
=> zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0) ) ),
inference(rectify,[],[f1202]) ).
fof(f1202,axiom,
! [X18,X17] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X18),X17))
=> zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X17),X18) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X18),X17))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X17),X18) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X17),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17701,plain,
spl263_1126,
inference(avatar_split_clause,[],[f5280,f17699]) ).
fof(f17699,plain,
( spl263_1126
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1126])]) ).
fof(f5280,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),
inference(cnf_transformation,[],[f1676]) ).
fof(f1676,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),
inference(rectify,[],[f1210]) ).
fof(f1210,axiom,
! [X14,X13] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X14)),hAPP_nat_int(semiri1621563631at_int,X13)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17697,plain,
spl263_1125,
inference(avatar_split_clause,[],[f5277,f17695]) ).
fof(f17695,plain,
( spl263_1125
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1125])]) ).
fof(f5277,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(cnf_transformation,[],[f1673]) ).
fof(f1673,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(rectify,[],[f1213]) ).
fof(f1213,axiom,
! [X14,X13] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X14)),hAPP_nat_int(semiri1621563631at_int,X13)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17693,plain,
spl263_1124,
inference(avatar_split_clause,[],[f5276,f17691]) ).
fof(f17691,plain,
( spl263_1124
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1124])]) ).
fof(f5276,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),
inference(cnf_transformation,[],[f1672]) ).
fof(f1672,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),
inference(rectify,[],[f1218]) ).
fof(f1218,axiom,
! [X17,X18] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X17)),hAPP_nat_int(semiri1621563631at_int,X18)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X17),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17689,plain,
spl263_1123,
inference(avatar_split_clause,[],[f5275,f17687]) ).
fof(f17687,plain,
( spl263_1123
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1123])]) ).
fof(f5275,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(cnf_transformation,[],[f1671]) ).
fof(f1671,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(rectify,[],[f1112]) ).
fof(f1112,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X14)),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17685,plain,
spl263_1122,
inference(avatar_split_clause,[],[f5274,f17683]) ).
fof(f17683,plain,
( spl263_1122
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1122])]) ).
fof(f5274,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1),
inference(cnf_transformation,[],[f1670]) ).
fof(f1670,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1),
inference(rectify,[],[f854]) ).
fof(f854,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),hAPP_nat_nat(suc,X13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),one_one_nat)),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17681,plain,
spl263_1121,
inference(avatar_split_clause,[],[f5273,f17679]) ).
fof(f5273,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),
inference(cnf_transformation,[],[f1669]) ).
fof(f1669,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),
inference(rectify,[],[f1065]) ).
fof(f1065,axiom,
! [X24,X16] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),hAPP_nat_nat(suc,X16)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17677,plain,
spl263_1120,
inference(avatar_split_clause,[],[f5272,f17675]) ).
fof(f17675,plain,
( spl263_1120
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1120])]) ).
fof(f5272,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(cnf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),
inference(rectify,[],[f1111]) ).
fof(f1111,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),hAPP_nat_nat(suc,X13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17673,plain,
spl263_1119,
inference(avatar_split_clause,[],[f5124,f17671]) ).
fof(f17671,plain,
( spl263_1119
<=> ! [X4,X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK78(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1119])]) ).
fof(f5124,plain,
! [X0,X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK78(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f4101]) ).
fof(f4101,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK78(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f4098,f4100,f4099]) ).
fof(f4099,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4100,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK78(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4098,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f4097]) ).
fof(f4097,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(nnf_transformation,[],[f2750]) ).
fof(f2750,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(ennf_transformation,[],[f1592]) ).
fof(f1592,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ),
inference(rectify,[],[f593]) ).
fof(f593,axiom,
! [X71] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X71))
<=> ? [X34] :
! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X71))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17669,plain,
spl263_1118,
inference(avatar_split_clause,[],[f5121,f17667]) ).
fof(f17667,plain,
( spl263_1118
<=> ! [X4,X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK76(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1118])]) ).
fof(f5121,plain,
! [X0,X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK76(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f4096]) ).
fof(f4096,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK75(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK75(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK76(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76])],[f4093,f4095,f4094]) ).
fof(f4094,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK75(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK75(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4095,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK76(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4093,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f4092]) ).
fof(f4092,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(nnf_transformation,[],[f2749]) ).
fof(f2749,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(ennf_transformation,[],[f1591]) ).
fof(f1591,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ) ),
inference(rectify,[],[f1002]) ).
fof(f1002,axiom,
! [X71] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X71))
<=> ? [X34] :
! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X71))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f17499,plain,
( spl263_1117
| ~ spl263_1097 ),
inference(avatar_split_clause,[],[f16209,f16206,f17497]) ).
fof(f17497,plain,
( spl263_1117
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1117])]) ).
fof(f16206,plain,
( spl263_1097
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1097])]) ).
fof(f16209,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| hBOOL(hAPP_int_bool(nat_neg,X0)) )
| ~ spl263_1097 ),
inference(forward_demodulation,[],[f16207,f6168]) ).
fof(f16207,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| hBOOL(hAPP_int_bool(nat_neg,X0)) )
| ~ spl263_1097 ),
inference(avatar_component_clause,[],[f16206]) ).
fof(f17495,plain,
( spl263_1116
| ~ spl263_1095 ),
inference(avatar_split_clause,[],[f16200,f16197,f17493]) ).
fof(f17493,plain,
( spl263_1116
<=> ! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1116])]) ).
fof(f16197,plain,
( spl263_1095
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1095])]) ).
fof(f16200,plain,
( ! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) )
| ~ spl263_1095 ),
inference(forward_demodulation,[],[f16198,f6168]) ).
fof(f16198,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
| ~ spl263_1095 ),
inference(avatar_component_clause,[],[f16197]) ).
fof(f17491,plain,
( spl263_1115
| ~ spl263_1094 ),
inference(avatar_split_clause,[],[f16195,f16192,f17489]) ).
fof(f17489,plain,
( spl263_1115
<=> ! [X0] :
( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1115])]) ).
fof(f16192,plain,
( spl263_1094
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1094])]) ).
fof(f16195,plain,
( ! [X0] :
( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) )
| ~ spl263_1094 ),
inference(forward_demodulation,[],[f16193,f6168]) ).
fof(f16193,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) )
| ~ spl263_1094 ),
inference(avatar_component_clause,[],[f16192]) ).
fof(f16684,plain,
( spl263_1114
| ~ spl263_550
| ~ spl263_986 ),
inference(avatar_split_clause,[],[f15762,f15759,f10706,f16682]) ).
fof(f16682,plain,
( spl263_1114
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1114])]) ).
fof(f10706,plain,
( spl263_550
<=> ! [X2,X0,X1] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_550])]) ).
fof(f15759,plain,
( spl263_986
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_986])]) ).
fof(f15762,plain,
( ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl263_550
| ~ spl263_986 ),
inference(forward_demodulation,[],[f15760,f10707]) ).
fof(f10707,plain,
( ! [X2,X0,X1] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2))
| ~ spl263_550 ),
inference(avatar_component_clause,[],[f10706]) ).
fof(f15760,plain,
( ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl263_986 ),
inference(avatar_component_clause,[],[f15759]) ).
fof(f16680,plain,
( spl263_1113
| ~ spl263_550
| ~ spl263_985 ),
inference(avatar_split_clause,[],[f15757,f15754,f10706,f16678]) ).
fof(f16678,plain,
( spl263_1113
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1113])]) ).
fof(f15754,plain,
( spl263_985
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_985])]) ).
fof(f15757,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl263_550
| ~ spl263_985 ),
inference(forward_demodulation,[],[f15755,f10707]) ).
fof(f15755,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) )
| ~ spl263_985 ),
inference(avatar_component_clause,[],[f15754]) ).
fof(f16676,plain,
( spl263_1112
| ~ spl263_550
| ~ spl263_984 ),
inference(avatar_split_clause,[],[f15752,f15749,f10706,f16674]) ).
fof(f16674,plain,
( spl263_1112
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1112])]) ).
fof(f15749,plain,
( spl263_984
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_984])]) ).
fof(f15752,plain,
( ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ spl263_550
| ~ spl263_984 ),
inference(forward_demodulation,[],[f15750,f10707]) ).
fof(f15750,plain,
( ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ spl263_984 ),
inference(avatar_component_clause,[],[f15749]) ).
fof(f16672,plain,
( spl263_1111
| ~ spl263_550
| ~ spl263_983 ),
inference(avatar_split_clause,[],[f15747,f15744,f10706,f16670]) ).
fof(f16670,plain,
( spl263_1111
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1111])]) ).
fof(f15744,plain,
( spl263_983
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_983])]) ).
fof(f15747,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ spl263_550
| ~ spl263_983 ),
inference(forward_demodulation,[],[f15745,f10707]) ).
fof(f15745,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) )
| ~ spl263_983 ),
inference(avatar_component_clause,[],[f15744]) ).
fof(f16429,plain,
( spl263_1110
| ~ spl263_147
| ~ spl263_532 ),
inference(avatar_split_clause,[],[f11027,f10633,f8491,f16427]) ).
fof(f16427,plain,
( spl263_1110
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1110])]) ).
fof(f8491,plain,
( spl263_147
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_147])]) ).
fof(f10633,plain,
( spl263_532
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_532])]) ).
fof(f11027,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0))
| ~ spl263_147
| ~ spl263_532 ),
inference(resolution,[],[f10634,f8492]) ).
fof(f8492,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0))
| ~ spl263_147 ),
inference(avatar_component_clause,[],[f8491]) ).
fof(f10634,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) )
| ~ spl263_532 ),
inference(avatar_component_clause,[],[f10633]) ).
fof(f16354,plain,
( spl263_1109
| ~ spl263_144
| ~ spl263_532 ),
inference(avatar_split_clause,[],[f11026,f10633,f8479,f16352]) ).
fof(f16352,plain,
( spl263_1109
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1109])]) ).
fof(f11026,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool))
| ~ spl263_144
| ~ spl263_532 ),
inference(resolution,[],[f10634,f8480]) ).
fof(f16253,plain,
spl263_1108,
inference(avatar_split_clause,[],[f7657,f16251]) ).
fof(f16251,plain,
( spl263_1108
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1108])]) ).
fof(f7657,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f7656,f4876]) ).
fof(f7656,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f7655,f4876]) ).
fof(f7655,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f6058,f4876]) ).
fof(f6058,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(cnf_transformation,[],[f4421]) ).
fof(f4421,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
& ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4420]) ).
fof(f4420,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
& ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2144]) ).
fof(f2144,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ) ),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X12,X11] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X11)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16249,plain,
( spl263_1107
| ~ spl263_255
| ~ spl263_386 ),
inference(avatar_split_clause,[],[f9802,f9691,f8968,f16247]) ).
fof(f16247,plain,
( spl263_1107
<=> ! [X0] : bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1107])]) ).
fof(f8968,plain,
( spl263_255
<=> ! [X0,X1] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_255])]) ).
fof(f9691,plain,
( spl263_386
<=> ! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_386])]) ).
fof(f9802,plain,
( ! [X0] : bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X0)
| ~ spl263_255
| ~ spl263_386 ),
inference(superposition,[],[f8969,f9692]) ).
fof(f9692,plain,
( ! [X0] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0)
| ~ spl263_386 ),
inference(avatar_component_clause,[],[f9691]) ).
fof(f8969,plain,
( ! [X0,X1] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)
| ~ spl263_255 ),
inference(avatar_component_clause,[],[f8968]) ).
fof(f16245,plain,
spl263_1106,
inference(avatar_split_clause,[],[f7650,f16243]) ).
fof(f16243,plain,
( spl263_1106
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1106])]) ).
fof(f7650,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f7649,f4874]) ).
fof(f7649,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
inference(forward_demodulation,[],[f7648,f4874]) ).
fof(f7648,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
inference(forward_demodulation,[],[f6055,f4874]) ).
fof(f6055,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
inference(cnf_transformation,[],[f4419]) ).
fof(f4419,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
& ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f4418]) ).
fof(f4418,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
& ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f2143]) ).
fof(f2143,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X12,X11] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X12),X11))))
<=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X11)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16241,plain,
spl263_1105,
inference(avatar_split_clause,[],[f7564,f16239]) ).
fof(f16239,plain,
( spl263_1105
<=> ! [X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) != collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1105])]) ).
fof(f7564,plain,
! [X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) != collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(forward_demodulation,[],[f7563,f4966]) ).
fof(f7563,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(forward_demodulation,[],[f5799,f4966]) ).
fof(f5799,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f3221]) ).
fof(f3221,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f3220]) ).
fof(f3220,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2037]) ).
fof(f2037,plain,
! [X0,X1] :
( ( is_a(X1)
& is_a(X0) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)
=> X0 = X1 ) ),
inference(rectify,[],[f696]) ).
fof(f696,axiom,
! [X7,X30] :
( ( is_a(X30)
& is_a(X7) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),bot_bot_fun_a_bool)
=> X7 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16237,plain,
spl263_1104,
inference(avatar_split_clause,[],[f7562,f16235]) ).
fof(f16235,plain,
( spl263_1104
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1104])]) ).
fof(f7562,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(forward_demodulation,[],[f5798,f4966]) ).
fof(f5798,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f3219]) ).
fof(f3219,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f3218]) ).
fof(f3218,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2036]) ).
fof(f2036,plain,
! [X0,X1] :
( ( is_a(X1)
& is_a(X0) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
=> X0 = X1 ) ),
inference(rectify,[],[f699]) ).
fof(f699,axiom,
! [X30,X7] :
( ( is_a(X7)
& is_a(X30) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool)))
=> X7 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16233,plain,
spl263_1103,
inference(avatar_split_clause,[],[f7559,f16231]) ).
fof(f16231,plain,
( spl263_1103
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
| hAPP_n1699378549t_bool(fequal_nat,X1) = X0
| bot_bot_fun_nat_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1103])]) ).
fof(f7559,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
| hAPP_n1699378549t_bool(fequal_nat,X1) = X0
| bot_bot_fun_nat_bool = X0 ),
inference(forward_demodulation,[],[f7558,f7397]) ).
fof(f7558,plain,
! [X0,X1] :
( hAPP_n1699378549t_bool(fequal_nat,X1) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(forward_demodulation,[],[f5792,f7397]) ).
fof(f5792,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(cnf_transformation,[],[f3211]) ).
fof(f3211,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(flattening,[],[f3210]) ).
fof(f3210,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(ennf_transformation,[],[f2030]) ).
fof(f2030,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0
| bot_bot_fun_nat_bool = X0 ) ),
inference(rectify,[],[f768]) ).
fof(f768,axiom,
! [X4,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool)))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool) = X4
| bot_bot_fun_nat_bool = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16229,plain,
spl263_1102,
inference(avatar_split_clause,[],[f7556,f16227]) ).
fof(f16227,plain,
( spl263_1102
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
| hAPP_i1948725293t_bool(fequal_int,X1) = X0
| bot_bot_fun_int_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1102])]) ).
fof(f7556,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
| hAPP_i1948725293t_bool(fequal_int,X1) = X0
| bot_bot_fun_int_bool = X0 ),
inference(forward_demodulation,[],[f7555,f7396]) ).
fof(f7555,plain,
! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X1) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(forward_demodulation,[],[f5790,f7396]) ).
fof(f5790,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(cnf_transformation,[],[f3208]) ).
fof(f3208,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(flattening,[],[f3207]) ).
fof(f3207,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(ennf_transformation,[],[f2028]) ).
fof(f2028,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)))
=> ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0
| bot_bot_fun_int_bool = X0 ) ),
inference(rectify,[],[f769]) ).
fof(f769,axiom,
! [X4,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool)))
=> ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool) = X4
| bot_bot_fun_int_bool = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16225,plain,
spl263_1101,
inference(avatar_split_clause,[],[f7493,f16223]) ).
fof(f16223,plain,
( spl263_1101
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK108(X0,X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1101])]) ).
fof(f7493,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK108(X0,X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(forward_demodulation,[],[f5467,f4959]) ).
fof(f4959,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat),
inference(cnf_transformation,[],[f1505]) ).
fof(f1505,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat),
inference(rectify,[],[f957]) ).
fof(f957,axiom,
! [X13] : hAPP_nat_nat(suc,X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),one_one_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5467,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK108(X0,X1)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4196]) ).
fof(f16221,plain,
spl263_1100,
inference(avatar_split_clause,[],[f7471,f16219]) ).
fof(f16219,plain,
( spl263_1100
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1100])]) ).
fof(f7471,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ),
inference(forward_demodulation,[],[f7470,f4875]) ).
fof(f7470,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(forward_demodulation,[],[f5318,f4958]) ).
fof(f5318,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(cnf_transformation,[],[f2762]) ).
fof(f2762,plain,
! [X0,X1] :
( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X1))),X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) ),
inference(ennf_transformation,[],[f1705]) ).
fof(f1705,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X1))),X0) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ) ),
inference(rectify,[],[f1268]) ).
fof(f1268,axiom,
! [X13,X132] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),X13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X132))),X13) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X13) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16217,plain,
spl263_1099,
inference(avatar_split_clause,[],[f7446,f16215]) ).
fof(f16215,plain,
( spl263_1099
<=> ! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1099])]) ).
fof(f7446,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)),
inference(forward_demodulation,[],[f7445,f4876]) ).
fof(f7445,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)),
inference(forward_demodulation,[],[f5291,f7401]) ).
fof(f5291,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),
inference(cnf_transformation,[],[f1687]) ).
fof(f1687,plain,
! [X0,X1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X7,X12] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),collect_nat(X12)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16213,plain,
spl263_1098,
inference(avatar_split_clause,[],[f7444,f16211]) ).
fof(f16211,plain,
( spl263_1098
<=> ! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1098])]) ).
fof(f7444,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)),
inference(forward_demodulation,[],[f7443,f4874]) ).
fof(f7443,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)),
inference(forward_demodulation,[],[f5290,f7399]) ).
fof(f5290,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0))),X1)),
inference(cnf_transformation,[],[f1686]) ).
fof(f1686,plain,
! [X0,X1] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0))),X1)),
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X7,X12] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),collect_int(X12)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16208,plain,
spl263_1097,
inference(avatar_split_clause,[],[f7430,f16206]) ).
fof(f7430,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ),
inference(forward_demodulation,[],[f7429,f4875]) ).
fof(f7429,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))) ),
inference(forward_demodulation,[],[f7058,f4875]) ).
fof(f7058,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))) ),
inference(definition_unfolding,[],[f5147,f4973]) ).
fof(f5147,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0)))) ),
inference(cnf_transformation,[],[f4112]) ).
fof(f4112,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0)))) ) ),
inference(nnf_transformation,[],[f1603]) ).
fof(f1603,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
<=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(rectify,[],[f1274]) ).
fof(f1274,axiom,
! [X138] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X138))))
<=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X138))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16204,plain,
( spl263_1096
| ~ spl263_254
| ~ spl263_385 ),
inference(avatar_split_clause,[],[f9801,f9686,f8964,f16202]) ).
fof(f16202,plain,
( spl263_1096
<=> ! [X0] : bot_bot_fun_int_bool != hAPP_i1948725293t_bool(fequal_int,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1096])]) ).
fof(f8964,plain,
( spl263_254
<=> ! [X0,X1] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_254])]) ).
fof(f9686,plain,
( spl263_385
<=> ! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_385])]) ).
fof(f9801,plain,
( ! [X0] : bot_bot_fun_int_bool != hAPP_i1948725293t_bool(fequal_int,X0)
| ~ spl263_254
| ~ spl263_385 ),
inference(superposition,[],[f8965,f9687]) ).
fof(f9687,plain,
( ! [X0] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0)
| ~ spl263_385 ),
inference(avatar_component_clause,[],[f9686]) ).
fof(f8965,plain,
( ! [X0,X1] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)
| ~ spl263_254 ),
inference(avatar_component_clause,[],[f8964]) ).
fof(f16199,plain,
spl263_1095,
inference(avatar_split_clause,[],[f7428,f16197]) ).
fof(f7428,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
inference(forward_demodulation,[],[f7427,f4875]) ).
fof(f7427,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(forward_demodulation,[],[f7057,f4875]) ).
fof(f7057,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f5148,f4973]) ).
fof(f5148,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f4112]) ).
fof(f16194,plain,
spl263_1094,
inference(avatar_split_clause,[],[f7408,f16192]) ).
fof(f7408,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) ),
inference(forward_demodulation,[],[f7040,f4875]) ).
fof(f7040,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f4981,f4973]) ).
fof(f4981,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(bit1(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2693]) ).
fof(f2693,plain,
! [X0] :
( ( number_number_of_nat(bit1(X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),number_number_of_nat(X0)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( zero_zero_nat = number_number_of_nat(bit1(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
inference(ennf_transformation,[],[f1527]) ).
fof(f1527,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> number_number_of_nat(bit1(X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),number_number_of_nat(X0))) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> zero_zero_nat = number_number_of_nat(bit1(X0)) ) ),
inference(rectify,[],[f1271]) ).
fof(f1271,axiom,
! [X134] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X134)))
=> number_number_of_nat(bit1(X134)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X134)),number_number_of_nat(X134))) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X134)))
=> zero_zero_nat = number_number_of_nat(bit1(X134)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16190,plain,
spl263_1093,
inference(avatar_split_clause,[],[f7151,f16188]) ).
fof(f16188,plain,
( spl263_1093
<=> ! [X2,X1] :
( sP4(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1093])]) ).
fof(f7151,plain,
! [X2,X1] :
( sP4(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ),
inference(equality_resolution,[],[f5031]) ).
fof(f5031,plain,
! [X2,X0,X1] :
( sP4(X0)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f4012]) ).
fof(f4012,plain,
! [X0] :
( ( sP4(X0)
| ! [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ) )
& ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK48(X0)),sK49(X0)))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK48(X0)),sK49(X0)) = X0
& is_fun_a_bool(sK49(X0))
& is_a(sK48(X0)) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f4010,f4011]) ).
fof(f4011,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4) = X0
& is_fun_a_bool(X4)
& is_a(X3) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK48(X0)),sK49(X0)))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK48(X0)),sK49(X0)) = X0
& is_fun_a_bool(sK49(X0))
& is_a(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4010,plain,
! [X0] :
( ( sP4(X0)
| ! [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ) )
& ( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4) = X0
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f4009]) ).
fof(f4009,plain,
! [X0] :
( ( sP4(X0)
| ! [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ) )
& ( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0
& is_fun_a_bool(X2)
& is_a(X1) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f3917]) ).
fof(f3917,plain,
! [X0] :
( sP4(X0)
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0
& is_fun_a_bool(X2)
& is_a(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f16186,plain,
spl263_1092,
inference(avatar_split_clause,[],[f7145,f16184]) ).
fof(f16184,plain,
( spl263_1092
<=> ! [X2,X1] :
( sP0(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1092])]) ).
fof(f7145,plain,
! [X2,X1] :
( sP0(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
inference(equality_resolution,[],[f5004]) ).
fof(f5004,plain,
! [X2,X0,X1] :
( sP0(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f3993,plain,
! [X0] :
( ( sP0(X0)
| ! [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ) )
& ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK42(X0)),sK43(X0)))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK42(X0)),sK43(X0)) = X0
& is_fun_pname_bool(sK43(X0))
& is_pname(sK42(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f3991,f3992]) ).
fof(f3992,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4) = X0
& is_fun_pname_bool(X4)
& is_pname(X3) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK42(X0)),sK43(X0)))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK42(X0)),sK43(X0)) = X0
& is_fun_pname_bool(sK43(X0))
& is_pname(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3991,plain,
! [X0] :
( ( sP0(X0)
| ! [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ) )
& ( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4) = X0
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f3990]) ).
fof(f3990,plain,
! [X0] :
( ( sP0(X0)
| ! [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ) )
& ( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0
& is_fun_pname_bool(X2)
& is_pname(X1) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f3911]) ).
fof(f3911,plain,
! [X0] :
( sP0(X0)
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0
& is_fun_pname_bool(X2)
& is_pname(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f16182,plain,
spl263_1091,
inference(avatar_split_clause,[],[f7103,f16180]) ).
fof(f16180,plain,
( spl263_1091
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1091])]) ).
fof(f7103,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(definition_unfolding,[],[f5931,f4830]) ).
fof(f5931,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4334]) ).
fof(f4334,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f2097]) ).
fof(f2097,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) ),
inference(rectify,[],[f1144]) ).
fof(f1144,axiom,
! [X15,X133] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X133))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X15),X133)),zero_zero_int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16178,plain,
spl263_1090,
inference(avatar_split_clause,[],[f7102,f16176]) ).
fof(f16176,plain,
( spl263_1090
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1090])]) ).
fof(f7102,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls)) ),
inference(definition_unfolding,[],[f5932,f4830]) ).
fof(f5932,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) ),
inference(cnf_transformation,[],[f4334]) ).
fof(f16174,plain,
spl263_1089,
inference(avatar_split_clause,[],[f7087,f16172]) ).
fof(f16172,plain,
( spl263_1089
<=> ! [X0,X1] :
( one_one_int = X1
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1089])]) ).
fof(f7087,plain,
! [X0,X1] :
( one_one_int = X1
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(definition_unfolding,[],[f5705,f4830]) ).
fof(f5705,plain,
! [X0,X1] :
( one_one_int = X1
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f4244]) ).
fof(f4244,plain,
! [X0,X1] :
( ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| one_one_int != X0
| one_one_int != X1 )
& ( ( one_one_int = X0
& one_one_int = X1 )
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(flattening,[],[f4243]) ).
fof(f4243,plain,
! [X0,X1] :
( ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| one_one_int != X0
| one_one_int != X1 )
& ( ( one_one_int = X0
& one_one_int = X1 )
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(nnf_transformation,[],[f3098]) ).
fof(f3098,plain,
! [X0,X1] :
( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
<=> ( one_one_int = X0
& one_one_int = X1 ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f1953]) ).
fof(f1953,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
=> ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
<=> ( one_one_int = X0
& one_one_int = X1 ) ) ),
inference(rectify,[],[f1138]) ).
fof(f1138,axiom,
! [X16,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X24))
=> ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X24),X16)
<=> ( one_one_int = X16
& one_one_int = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16170,plain,
spl263_1088,
inference(avatar_split_clause,[],[f7086,f16168]) ).
fof(f16168,plain,
( spl263_1088
<=> ! [X0,X1] :
( one_one_int = X0
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1088])]) ).
fof(f7086,plain,
! [X0,X1] :
( one_one_int = X0
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(definition_unfolding,[],[f5706,f4830]) ).
fof(f5706,plain,
! [X0,X1] :
( one_one_int = X0
| one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f4244]) ).
fof(f16166,plain,
spl263_1087,
inference(avatar_split_clause,[],[f7046,f16164]) ).
fof(f16164,plain,
( spl263_1087
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1087])]) ).
fof(f7046,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5069,f4830,f4830]) ).
fof(f5069,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f2737]) ).
fof(f2737,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1564]) ).
fof(f1564,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0))) ),
inference(rectify,[],[f1145]) ).
fof(f1145,axiom,
! [X97] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X97))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16162,plain,
spl263_1086,
inference(avatar_split_clause,[],[f6843,f16160]) ).
fof(f16160,plain,
( spl263_1086
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1086])]) ).
fof(f6843,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4733]) ).
fof(f16158,plain,
( spl263_1085
| ~ spl263_9
| ~ spl263_325
| ~ spl263_342 ),
inference(avatar_split_clause,[],[f9523,f9337,f9268,f7828,f16156]) ).
fof(f7828,plain,
( spl263_9
<=> is_bool(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_9])]) ).
fof(f9268,plain,
( spl263_325
<=> ! [X0,X1] :
( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_325])]) ).
fof(f9337,plain,
( spl263_342
<=> bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_342])]) ).
fof(f9523,plain,
( ! [X0] : fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0)
| ~ spl263_9
| ~ spl263_325
| ~ spl263_342 ),
inference(forward_demodulation,[],[f9505,f9339]) ).
fof(f9339,plain,
( bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse)
| ~ spl263_342 ),
inference(avatar_component_clause,[],[f9337]) ).
fof(f9505,plain,
( ! [X0] : fFalse = hAPP_nat_bool(cOMBK_bool_nat(fFalse),X0)
| ~ spl263_9
| ~ spl263_325 ),
inference(resolution,[],[f9269,f7830]) ).
fof(f7830,plain,
( is_bool(fFalse)
| ~ spl263_9 ),
inference(avatar_component_clause,[],[f7828]) ).
fof(f9269,plain,
( ! [X0,X1] :
( ~ is_bool(X0)
| hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 )
| ~ spl263_325 ),
inference(avatar_component_clause,[],[f9268]) ).
fof(f16154,plain,
spl263_1084,
inference(avatar_split_clause,[],[f6842,f16152]) ).
fof(f16152,plain,
( spl263_1084
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1084])]) ).
fof(f6842,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4733]) ).
fof(f16150,plain,
spl263_1083,
inference(avatar_split_clause,[],[f6838,f16148]) ).
fof(f16148,plain,
( spl263_1083
<=> ! [X2,X0,X1] :
( sP35(X0,X1,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1083])]) ).
fof(f6838,plain,
! [X2,X0,X1] :
( sP35(X0,X1,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(cnf_transformation,[],[f4730]) ).
fof(f16146,plain,
spl263_1082,
inference(avatar_split_clause,[],[f6835,f16144]) ).
fof(f16144,plain,
( spl263_1082
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ sP35(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1082])]) ).
fof(f6835,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f4730]) ).
fof(f16142,plain,
spl263_1081,
inference(avatar_split_clause,[],[f6826,f16140]) ).
fof(f16140,plain,
( spl263_1081
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1081])]) ).
fof(f6826,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4723]) ).
fof(f16138,plain,
spl263_1080,
inference(avatar_split_clause,[],[f6825,f16136]) ).
fof(f16136,plain,
( spl263_1080
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1080])]) ).
fof(f6825,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4723]) ).
fof(f16134,plain,
spl263_1079,
inference(avatar_split_clause,[],[f6821,f16132]) ).
fof(f16132,plain,
( spl263_1079
<=> ! [X2,X0,X1] :
( sP34(X0,X1,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1079])]) ).
fof(f6821,plain,
! [X2,X0,X1] :
( sP34(X0,X1,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(cnf_transformation,[],[f4720]) ).
fof(f16130,plain,
spl263_1078,
inference(avatar_split_clause,[],[f6818,f16128]) ).
fof(f16128,plain,
( spl263_1078
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ sP34(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1078])]) ).
fof(f6818,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f4720]) ).
fof(f16126,plain,
spl263_1077,
inference(avatar_split_clause,[],[f6809,f16124]) ).
fof(f16124,plain,
( spl263_1077
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1077])]) ).
fof(f6809,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4713]) ).
fof(f16122,plain,
spl263_1076,
inference(avatar_split_clause,[],[f6808,f16120]) ).
fof(f16120,plain,
( spl263_1076
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1076])]) ).
fof(f6808,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4713]) ).
fof(f16118,plain,
spl263_1075,
inference(avatar_split_clause,[],[f6804,f16116]) ).
fof(f16116,plain,
( spl263_1075
<=> ! [X2,X0,X1] :
( sP33(X0,X1,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1075])]) ).
fof(f6804,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(cnf_transformation,[],[f4710]) ).
fof(f4710,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) )
| ~ sP33(X0,X1,X2) ) ),
inference(rectify,[],[f4709]) ).
fof(f4709,plain,
! [X2,X0,X1] :
( ( sP33(X2,X0,X1)
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
| ~ sP33(X2,X0,X1) ) ),
inference(flattening,[],[f4708]) ).
fof(f4708,plain,
! [X2,X0,X1] :
( ( sP33(X2,X0,X1)
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
| ~ sP33(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3972]) ).
fof(f3972,plain,
! [X2,X0,X1] :
( sP33(X2,X0,X1)
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
fof(f16114,plain,
( spl263_1074
| ~ spl263_9
| ~ spl263_324
| ~ spl263_349 ),
inference(avatar_split_clause,[],[f9495,f9437,f9264,f7828,f16112]) ).
fof(f9264,plain,
( spl263_324
<=> ! [X0,X1] :
( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_324])]) ).
fof(f9437,plain,
( spl263_349
<=> bot_bot_fun_int_bool = cOMBK_bool_int(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_349])]) ).
fof(f9495,plain,
( ! [X0] : fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0)
| ~ spl263_9
| ~ spl263_324
| ~ spl263_349 ),
inference(forward_demodulation,[],[f9477,f9439]) ).
fof(f9439,plain,
( bot_bot_fun_int_bool = cOMBK_bool_int(fFalse)
| ~ spl263_349 ),
inference(avatar_component_clause,[],[f9437]) ).
fof(f9477,plain,
( ! [X0] : fFalse = hAPP_int_bool(cOMBK_bool_int(fFalse),X0)
| ~ spl263_9
| ~ spl263_324 ),
inference(resolution,[],[f9265,f7830]) ).
fof(f9265,plain,
( ! [X0,X1] :
( ~ is_bool(X0)
| hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 )
| ~ spl263_324 ),
inference(avatar_component_clause,[],[f9264]) ).
fof(f16110,plain,
spl263_1073,
inference(avatar_split_clause,[],[f6801,f16108]) ).
fof(f16108,plain,
( spl263_1073
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1073])]) ).
fof(f6801,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f4710]) ).
fof(f16106,plain,
spl263_1072,
inference(avatar_split_clause,[],[f6795,f16104]) ).
fof(f16104,plain,
( spl263_1072
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1072])]) ).
fof(f6795,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4705]) ).
fof(f16102,plain,
spl263_1071,
inference(avatar_split_clause,[],[f6794,f16100]) ).
fof(f16100,plain,
( spl263_1071
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1071])]) ).
fof(f6794,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4705]) ).
fof(f16098,plain,
spl263_1070,
inference(avatar_split_clause,[],[f6787,f16096]) ).
fof(f16096,plain,
( spl263_1070
<=> ! [X2,X0,X1] :
( sP32(X0,X1,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1070])]) ).
fof(f6787,plain,
! [X2,X0,X1] :
( sP32(X0,X1,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(cnf_transformation,[],[f4700]) ).
fof(f4700,plain,
! [X0,X1,X2] :
( ( sP32(X0,X1,X2)
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) )
& ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) )
| ~ sP32(X0,X1,X2) ) ),
inference(rectify,[],[f4699]) ).
fof(f4699,plain,
! [X2,X0,X1] :
( ( sP32(X2,X0,X1)
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
| ~ sP32(X2,X0,X1) ) ),
inference(flattening,[],[f4698]) ).
fof(f4698,plain,
! [X2,X0,X1] :
( ( sP32(X2,X0,X1)
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
& ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
| ~ sP32(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3970]) ).
fof(f3970,plain,
! [X2,X0,X1] :
( sP32(X2,X0,X1)
<=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f16094,plain,
spl263_1069,
inference(avatar_split_clause,[],[f6784,f16092]) ).
fof(f16092,plain,
( spl263_1069
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ sP32(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1069])]) ).
fof(f6784,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ sP32(X0,X1,X2) ),
inference(cnf_transformation,[],[f4700]) ).
fof(f16090,plain,
spl263_1068,
inference(avatar_split_clause,[],[f6763,f16088]) ).
fof(f16088,plain,
( spl263_1068
<=> ! [X2,X0,X1] :
( image_nat_int(X1,sK258(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1068])]) ).
fof(f6763,plain,
! [X2,X0,X1] :
( image_nat_int(X1,sK258(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4684]) ).
fof(f16086,plain,
spl263_1067,
inference(avatar_split_clause,[],[f6760,f16084]) ).
fof(f16084,plain,
( spl263_1067
<=> ! [X2,X0,X1] :
( hAPP_nat_int(X1,sK257(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1067])]) ).
fof(f6760,plain,
! [X2,X0,X1] :
( hAPP_nat_int(X1,sK257(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4680]) ).
fof(f16082,plain,
spl263_1066,
inference(avatar_split_clause,[],[f6695,f16080]) ).
fof(f16080,plain,
( spl263_1066
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1066])]) ).
fof(f6695,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4628]) ).
fof(f16078,plain,
spl263_1065,
inference(avatar_split_clause,[],[f6673,f16076]) ).
fof(f16076,plain,
( spl263_1065
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1065])]) ).
fof(f6673,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f3742]) ).
fof(f3742,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(ennf_transformation,[],[f2537]) ).
fof(f2537,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
inference(rectify,[],[f938]) ).
fof(f938,axiom,
! [X14,X21,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X21)),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16074,plain,
spl263_1064,
inference(avatar_split_clause,[],[f6672,f16072]) ).
fof(f16072,plain,
( spl263_1064
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1064])]) ).
fof(f6672,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f3741]) ).
fof(f3741,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(ennf_transformation,[],[f2536]) ).
fof(f2536,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rectify,[],[f937]) ).
fof(f937,axiom,
! [X14,X21,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X21)),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16070,plain,
( spl263_1063
| ~ spl263_37
| ~ spl263_119 ),
inference(avatar_split_clause,[],[f8410,f8334,f7960,f16068]) ).
fof(f16068,plain,
( spl263_1063
<=> ! [X0] :
( ~ sP13(X0)
| sP5(sK117(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1063])]) ).
fof(f8334,plain,
( spl263_119
<=> ! [X0] :
( is_fun_a_bool(sK117(X0))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_119])]) ).
fof(f8410,plain,
( ! [X0] :
( ~ sP13(X0)
| sP5(sK117(X0)) )
| ~ spl263_37
| ~ spl263_119 ),
inference(resolution,[],[f8335,f7961]) ).
fof(f8335,plain,
( ! [X0] :
( is_fun_a_bool(sK117(X0))
| ~ sP13(X0) )
| ~ spl263_119 ),
inference(avatar_component_clause,[],[f8334]) ).
fof(f16066,plain,
spl263_1062,
inference(avatar_split_clause,[],[f6671,f16064]) ).
fof(f16064,plain,
( spl263_1062
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1062])]) ).
fof(f6671,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(cnf_transformation,[],[f3740]) ).
fof(f3740,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
inference(ennf_transformation,[],[f2535]) ).
fof(f2535,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
inference(rectify,[],[f991]) ).
fof(f991,axiom,
! [X22,X23,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X23)),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16062,plain,
spl263_1061,
inference(avatar_split_clause,[],[f6667,f16060]) ).
fof(f16060,plain,
( spl263_1061
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1061])]) ).
fof(f6667,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3736]) ).
fof(f3736,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2532]) ).
fof(f2532,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(rectify,[],[f824]) ).
fof(f824,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16058,plain,
spl263_1060,
inference(avatar_split_clause,[],[f6666,f16056]) ).
fof(f16056,plain,
( spl263_1060
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1060])]) ).
fof(f6666,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f3735,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2531]) ).
fof(f2531,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
inference(rectify,[],[f820]) ).
fof(f820,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16054,plain,
spl263_1059,
inference(avatar_split_clause,[],[f6662,f16052]) ).
fof(f16052,plain,
( spl263_1059
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1059])]) ).
fof(f6662,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3731]) ).
fof(f3731,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2528]) ).
fof(f2528,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(rectify,[],[f823]) ).
fof(f823,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16050,plain,
spl263_1058,
inference(avatar_split_clause,[],[f6661,f16048]) ).
fof(f16048,plain,
( spl263_1058
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1058])]) ).
fof(f6661,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3730]) ).
fof(f3730,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2527]) ).
fof(f2527,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ),
inference(rectify,[],[f819]) ).
fof(f819,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16046,plain,
spl263_1057,
inference(avatar_split_clause,[],[f6658,f16044]) ).
fof(f16044,plain,
( spl263_1057
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1057])]) ).
fof(f6658,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3728]) ).
fof(f3728,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2525]) ).
fof(f2525,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2)))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(rectify,[],[f825]) ).
fof(f825,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9)))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16042,plain,
spl263_1056,
inference(avatar_split_clause,[],[f6657,f16040]) ).
fof(f16040,plain,
( spl263_1056
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1056])]) ).
fof(f6657,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3727]) ).
fof(f3727,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2524]) ).
fof(f2524,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2)))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
inference(rectify,[],[f821]) ).
fof(f821,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9)))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16038,plain,
spl263_1055,
inference(avatar_split_clause,[],[f6654,f16036]) ).
fof(f16036,plain,
( spl263_1055
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1055])]) ).
fof(f6654,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3725]) ).
fof(f3725,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2522]) ).
fof(f2522,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(rectify,[],[f826]) ).
fof(f826,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16034,plain,
spl263_1054,
inference(avatar_split_clause,[],[f6653,f16032]) ).
fof(f16032,plain,
( spl263_1054
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1054])]) ).
fof(f6653,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
inference(cnf_transformation,[],[f3724]) ).
fof(f3724,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
inference(ennf_transformation,[],[f2521]) ).
fof(f2521,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ),
inference(rectify,[],[f822]) ).
fof(f822,axiom,
! [X31,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16030,plain,
spl263_1053,
inference(avatar_split_clause,[],[f6651,f16028]) ).
fof(f16028,plain,
( spl263_1053
<=> ! [X2,X0,X1] :
( hAPP_nat_int(X1,sK239(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1053])]) ).
fof(f6651,plain,
! [X2,X0,X1] :
( hAPP_nat_int(X1,sK239(X0,X1,X2)) = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
inference(cnf_transformation,[],[f4626]) ).
fof(f16026,plain,
( spl263_1052
| ~ spl263_38
| ~ spl263_119 ),
inference(avatar_split_clause,[],[f8409,f8334,f7964,f16024]) ).
fof(f16024,plain,
( spl263_1052
<=> ! [X0] :
( ~ sP13(X0)
| sP7(sK117(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1052])]) ).
fof(f8409,plain,
( ! [X0] :
( ~ sP13(X0)
| sP7(sK117(X0)) )
| ~ spl263_38
| ~ spl263_119 ),
inference(resolution,[],[f8335,f7965]) ).
fof(f16022,plain,
spl263_1051,
inference(avatar_split_clause,[],[f6615,f16020]) ).
fof(f16020,plain,
( spl263_1051
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1051])]) ).
fof(f6615,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3684]) ).
fof(f3684,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2491]) ).
fof(f2491,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
inference(rectify,[],[f961]) ).
fof(f961,axiom,
! [X97,X17,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16018,plain,
spl263_1050,
inference(avatar_split_clause,[],[f6613,f16016]) ).
fof(f16016,plain,
( spl263_1050
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1050])]) ).
fof(f6613,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3682]) ).
fof(f3682,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2489]) ).
fof(f2489,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(rectify,[],[f960]) ).
fof(f960,axiom,
! [X18,X17,X97] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X97))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16014,plain,
spl263_1049,
inference(avatar_split_clause,[],[f6606,f16012]) ).
fof(f16012,plain,
( spl263_1049
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1049])]) ).
fof(f6606,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3670]) ).
fof(f3670,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2482]) ).
fof(f2482,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2)) ),
inference(rectify,[],[f1000]) ).
fof(f1000,axiom,
! [X13,X23,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X13)),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16010,plain,
spl263_1048,
inference(avatar_split_clause,[],[f6603,f16008]) ).
fof(f16008,plain,
( spl263_1048
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1048])]) ).
fof(f6603,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f3667,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2479]) ).
fof(f2479,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
inference(rectify,[],[f992]) ).
fof(f992,axiom,
! [X97,X17,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16006,plain,
spl263_1047,
inference(avatar_split_clause,[],[f6602,f16004]) ).
fof(f16004,plain,
( spl263_1047
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1047])]) ).
fof(f6602,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f3666,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2478]) ).
fof(f2478,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
inference(rectify,[],[f987]) ).
fof(f987,axiom,
! [X14,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f16002,plain,
spl263_1046,
inference(avatar_split_clause,[],[f6568,f16000]) ).
fof(f16000,plain,
( spl263_1046
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1046])]) ).
fof(f6568,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f3620,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2452]) ).
fof(f2452,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))) ),
inference(rectify,[],[f580]) ).
fof(f580,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X8,X4)),image_nat_int(X8,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15998,plain,
spl263_1045,
inference(avatar_split_clause,[],[f6565,f15996]) ).
fof(f15996,plain,
( spl263_1045
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1045])]) ).
fof(f6565,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3617]) ).
fof(f3617,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2449]) ).
fof(f2449,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
inference(rectify,[],[f570]) ).
fof(f570,axiom,
! [X30,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15994,plain,
spl263_1044,
inference(avatar_split_clause,[],[f6560,f15992]) ).
fof(f15992,plain,
( spl263_1044
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1044])]) ).
fof(f6560,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3610]) ).
fof(f3610,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2444]) ).
fof(f2444,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2))) ),
inference(rectify,[],[f540]) ).
fof(f540,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X8,X10)),image_nat_int(X8,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15990,plain,
spl263_1043,
inference(avatar_split_clause,[],[f6559,f15988]) ).
fof(f15988,plain,
( spl263_1043
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1043])]) ).
fof(f6559,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3609]) ).
fof(f3609,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2443]) ).
fof(f2443,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X30,X7,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),X9))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15986,plain,
spl263_1042,
inference(avatar_split_clause,[],[f6545,f15984]) ).
fof(f15984,plain,
( spl263_1042
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1042])]) ).
fof(f6545,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3586]) ).
fof(f3586,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2429]) ).
fof(f2429,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
inference(rectify,[],[f569]) ).
fof(f569,axiom,
! [X30,X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15982,plain,
( spl263_1041
| ~ spl263_37
| ~ spl263_117 ),
inference(avatar_split_clause,[],[f8408,f8326,f7960,f15980]) ).
fof(f15980,plain,
( spl263_1041
<=> ! [X0] :
( ~ sP12(X0)
| sP5(sK115(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1041])]) ).
fof(f8326,plain,
( spl263_117
<=> ! [X0] :
( is_fun_a_bool(sK115(X0))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_117])]) ).
fof(f8408,plain,
( ! [X0] :
( ~ sP12(X0)
| sP5(sK115(X0)) )
| ~ spl263_37
| ~ spl263_117 ),
inference(resolution,[],[f8327,f7961]) ).
fof(f8327,plain,
( ! [X0] :
( is_fun_a_bool(sK115(X0))
| ~ sP12(X0) )
| ~ spl263_117 ),
inference(avatar_component_clause,[],[f8326]) ).
fof(f15978,plain,
spl263_1040,
inference(avatar_split_clause,[],[f6541,f15976]) ).
fof(f15976,plain,
( spl263_1040
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1040])]) ).
fof(f6541,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(cnf_transformation,[],[f3580]) ).
fof(f3580,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(ennf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X30,X7,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),X9))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15974,plain,
spl263_1039,
inference(avatar_split_clause,[],[f6529,f15972]) ).
fof(f15972,plain,
( spl263_1039
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1039])]) ).
fof(f6529,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3560]) ).
fof(f3560,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2413]) ).
fof(f2413,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
inference(rectify,[],[f568]) ).
fof(f568,axiom,
! [X30,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15970,plain,
spl263_1038,
inference(avatar_split_clause,[],[f6525,f15968]) ).
fof(f15968,plain,
( spl263_1038
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1038])]) ).
fof(f6525,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f3554]) ).
fof(f3554,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f2409]) ).
fof(f2409,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X30,X7,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),X9))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15966,plain,
spl263_1037,
inference(avatar_split_clause,[],[f6520,f15964]) ).
fof(f6520,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3547]) ).
fof(f3547,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2404]) ).
fof(f2404,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
inference(rectify,[],[f541]) ).
fof(f541,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X8,X10)),image_pname_a(X8,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15962,plain,
spl263_1036,
inference(avatar_split_clause,[],[f6519,f15960]) ).
fof(f15960,plain,
( spl263_1036
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1036])]) ).
fof(f6519,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3546]) ).
fof(f3546,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2))) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X30,X7,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),X9))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15958,plain,
spl263_1035,
inference(avatar_split_clause,[],[f6514,f15956]) ).
fof(f15956,plain,
( spl263_1035
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1035])]) ).
fof(f6514,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3538]) ).
fof(f3538,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
inference(rectify,[],[f581]) ).
fof(f581,axiom,
! [X8,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X8,X4)),image_pname_a(X8,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15954,plain,
spl263_1034,
inference(avatar_split_clause,[],[f6443,f15952]) ).
fof(f15952,plain,
( spl263_1034
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1034])]) ).
fof(f6443,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3490]) ).
fof(f3490,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3489]) ).
fof(f3489,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2368]) ).
fof(f2368,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f325]) ).
fof(f325,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_nat_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15950,plain,
spl263_1033,
inference(avatar_split_clause,[],[f6442,f15948]) ).
fof(f15948,plain,
( spl263_1033
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1033])]) ).
fof(f6442,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3488]) ).
fof(f3488,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3487]) ).
fof(f3487,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2367]) ).
fof(f2367,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_nat_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15946,plain,
spl263_1032,
inference(avatar_split_clause,[],[f6441,f15944]) ).
fof(f15944,plain,
( spl263_1032
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1032])]) ).
fof(f6441,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3486]) ).
fof(f3486,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3485]) ).
fof(f3485,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2366]) ).
fof(f2366,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f302]) ).
fof(f302,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_nat_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15942,plain,
spl263_1031,
inference(avatar_split_clause,[],[f6440,f15940]) ).
fof(f15940,plain,
( spl263_1031
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1031])]) ).
fof(f6440,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3484]) ).
fof(f3484,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3483]) ).
fof(f3483,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2365]) ).
fof(f2365,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
inference(rectify,[],[f301]) ).
fof(f301,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_nat_fun_a_bool(X8,X4)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15938,plain,
( spl263_1030
| ~ spl263_38
| ~ spl263_117 ),
inference(avatar_split_clause,[],[f8407,f8326,f7964,f15936]) ).
fof(f15936,plain,
( spl263_1030
<=> ! [X0] :
( ~ sP12(X0)
| sP7(sK115(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1030])]) ).
fof(f8407,plain,
( ! [X0] :
( ~ sP12(X0)
| sP7(sK115(X0)) )
| ~ spl263_38
| ~ spl263_117 ),
inference(resolution,[],[f8327,f7965]) ).
fof(f15934,plain,
spl263_1029,
inference(avatar_split_clause,[],[f6439,f15932]) ).
fof(f15932,plain,
( spl263_1029
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1029])]) ).
fof(f6439,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3482]) ).
fof(f3482,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3481]) ).
fof(f3481,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2364]) ).
fof(f2364,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_1655916159e_bool(X8,X4)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15930,plain,
spl263_1028,
inference(avatar_split_clause,[],[f6438,f15928]) ).
fof(f15928,plain,
( spl263_1028
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1028])]) ).
fof(f6438,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3480]) ).
fof(f3480,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3479]) ).
fof(f3479,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2363]) ).
fof(f2363,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_26036933t_bool(X8,X4)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15926,plain,
spl263_1027,
inference(avatar_split_clause,[],[f6437,f15924]) ).
fof(f15924,plain,
( spl263_1027
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1027])]) ).
fof(f6437,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(cnf_transformation,[],[f3478]) ).
fof(f3478,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(flattening,[],[f3477]) ).
fof(f3477,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(ennf_transformation,[],[f2362]) ).
fof(f2362,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_1556378401t_bool(X8,X4)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15922,plain,
spl263_1026,
inference(avatar_split_clause,[],[f6404,f15920]) ).
fof(f15920,plain,
( spl263_1026
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1026])]) ).
fof(f6404,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3458]) ).
fof(f3458,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3457]) ).
fof(f3457,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_int_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15918,plain,
spl263_1025,
inference(avatar_split_clause,[],[f6403,f15916]) ).
fof(f15916,plain,
( spl263_1025
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1025])]) ).
fof(f6403,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3456]) ).
fof(f3456,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3455]) ).
fof(f3455,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_int_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15914,plain,
spl263_1024,
inference(avatar_split_clause,[],[f6402,f15912]) ).
fof(f15912,plain,
( spl263_1024
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1024])]) ).
fof(f6402,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3454]) ).
fof(f3454,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3453]) ).
fof(f3453,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2350]) ).
fof(f2350,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
inference(rectify,[],[f307]) ).
fof(f307,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_int_fun_a_bool(X8,X4)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15910,plain,
spl263_1023,
inference(avatar_split_clause,[],[f6401,f15908]) ).
fof(f15908,plain,
( spl263_1023
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1023])]) ).
fof(f6401,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3452]) ).
fof(f3452,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3451]) ).
fof(f3451,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2349]) ).
fof(f2349,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_637364955e_bool(X8,X4)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15906,plain,
spl263_1022,
inference(avatar_split_clause,[],[f6400,f15904]) ).
fof(f15904,plain,
( spl263_1022
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1022])]) ).
fof(f6400,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3450]) ).
fof(f3450,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3449]) ).
fof(f3449,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2348]) ).
fof(f2348,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_892525857t_bool(X8,X4)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15902,plain,
spl263_1021,
inference(avatar_split_clause,[],[f6399,f15900]) ).
fof(f15900,plain,
( spl263_1021
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1021])]) ).
fof(f6399,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(cnf_transformation,[],[f3448]) ).
fof(f3448,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(flattening,[],[f3447]) ).
fof(f3447,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(ennf_transformation,[],[f2347]) ).
fof(f2347,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_275383677t_bool(X8,X4)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15898,plain,
spl263_1020,
inference(avatar_split_clause,[],[f6391,f15896]) ).
fof(f15896,plain,
( spl263_1020
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1020])]) ).
fof(f6391,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f3442]) ).
fof(f3442,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f3441]) ).
fof(f3441,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f314]) ).
fof(f314,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_a_nat(X8,X4)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15894,plain,
( spl263_1019
| ~ spl263_35
| ~ spl263_115 ),
inference(avatar_split_clause,[],[f8406,f8318,f7952,f15892]) ).
fof(f15892,plain,
( spl263_1019
<=> ! [X0] :
( ~ sP11(X0)
| sP1(sK113(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1019])]) ).
fof(f8318,plain,
( spl263_115
<=> ! [X0] :
( is_fun_pname_bool(sK113(X0))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_115])]) ).
fof(f8406,plain,
( ! [X0] :
( ~ sP11(X0)
| sP1(sK113(X0)) )
| ~ spl263_35
| ~ spl263_115 ),
inference(resolution,[],[f8319,f7953]) ).
fof(f8319,plain,
( ! [X0] :
( is_fun_pname_bool(sK113(X0))
| ~ sP11(X0) )
| ~ spl263_115 ),
inference(avatar_component_clause,[],[f8318]) ).
fof(f15890,plain,
spl263_1018,
inference(avatar_split_clause,[],[f6390,f15888]) ).
fof(f15888,plain,
( spl263_1018
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1018])]) ).
fof(f6390,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f3440]) ).
fof(f3440,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f3439]) ).
fof(f3439,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f2343]) ).
fof(f2343,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f319]) ).
fof(f319,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_a_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15886,plain,
spl263_1017,
inference(avatar_split_clause,[],[f6389,f15884]) ).
fof(f15884,plain,
( spl263_1017
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1017])]) ).
fof(f6389,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f3438]) ).
fof(f3438,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f3437]) ).
fof(f3437,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f2342]) ).
fof(f2342,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_a_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15882,plain,
spl263_1016,
inference(avatar_split_clause,[],[f6388,f15880]) ).
fof(f15880,plain,
( spl263_1016
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1016])]) ).
fof(f6388,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f3436]) ).
fof(f3436,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f3435]) ).
fof(f3435,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f2341]) ).
fof(f2341,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f309]) ).
fof(f309,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_a_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15878,plain,
spl263_1015,
inference(avatar_split_clause,[],[f6378,f15876]) ).
fof(f15876,plain,
( spl263_1015
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1015])]) ).
fof(f6378,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3430]) ).
fof(f3430,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3429]) ).
fof(f3429,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f324]) ).
fof(f324,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_pname_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15874,plain,
spl263_1014,
inference(avatar_split_clause,[],[f6377,f15872]) ).
fof(f15872,plain,
( spl263_1014
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1014])]) ).
fof(f6377,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3428]) ).
fof(f3428,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3427]) ).
fof(f3427,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2337]) ).
fof(f2337,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_pname_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15870,plain,
spl263_1013,
inference(avatar_split_clause,[],[f6376,f15868]) ).
fof(f15868,plain,
( spl263_1013
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1013])]) ).
fof(f6376,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3426]) ).
fof(f3426,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3425]) ).
fof(f3425,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2336]) ).
fof(f2336,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
inference(rectify,[],[f294]) ).
fof(f294,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X9),image_47868345e_bool(X8,X4)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15866,plain,
spl263_1012,
inference(avatar_split_clause,[],[f6375,f15864]) ).
fof(f15864,plain,
( spl263_1012
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1012])]) ).
fof(f6375,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3424]) ).
fof(f3424,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3423]) ).
fof(f3423,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2335]) ).
fof(f2335,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X9),image_112932426a_bool(X8,X4)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15862,plain,
spl263_1011,
inference(avatar_split_clause,[],[f6374,f15860]) ).
fof(f15860,plain,
( spl263_1011
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1011])]) ).
fof(f6374,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3422]) ).
fof(f3422,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3421]) ).
fof(f3421,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2334]) ).
fof(f2334,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
inference(rectify,[],[f292]) ).
fof(f292,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X9),image_1512837979t_bool(X8,X4)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15858,plain,
spl263_1010,
inference(avatar_split_clause,[],[f6373,f15856]) ).
fof(f15856,plain,
( spl263_1010
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1010])]) ).
fof(f6373,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f3420]) ).
fof(f3420,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f3419]) ).
fof(f3419,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
inference(rectify,[],[f293]) ).
fof(f293,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X9),image_2129980159t_bool(X8,X4)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15854,plain,
spl263_1009,
inference(avatar_split_clause,[],[f6363,f15852]) ).
fof(f15852,plain,
( spl263_1009
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1009])]) ).
fof(f6363,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f3414]) ).
fof(f3414,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3413]) ).
fof(f3413,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2330]) ).
fof(f2330,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f315]) ).
fof(f315,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_1431733819ol_nat(X8,X4)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15850,plain,
( spl263_1008
| ~ spl263_36
| ~ spl263_115 ),
inference(avatar_split_clause,[],[f8405,f8318,f7956,f15848]) ).
fof(f15848,plain,
( spl263_1008
<=> ! [X0] :
( ~ sP11(X0)
| sP3(sK113(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1008])]) ).
fof(f8405,plain,
( ! [X0] :
( ~ sP11(X0)
| sP3(sK113(X0)) )
| ~ spl263_36
| ~ spl263_115 ),
inference(resolution,[],[f8319,f7957]) ).
fof(f15846,plain,
spl263_1007,
inference(avatar_split_clause,[],[f6362,f15844]) ).
fof(f15844,plain,
( spl263_1007
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1007])]) ).
fof(f6362,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f3412]) ).
fof(f3412,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3411]) ).
fof(f3411,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f316]) ).
fof(f316,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_496248727ol_nat(X8,X4)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15842,plain,
spl263_1006,
inference(avatar_split_clause,[],[f6361,f15840]) ).
fof(f15840,plain,
( spl263_1006
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1006])]) ).
fof(f6361,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(cnf_transformation,[],[f3410]) ).
fof(f3410,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(flattening,[],[f3409]) ).
fof(f3409,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(ennf_transformation,[],[f2328]) ).
fof(f2328,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f318]) ).
fof(f318,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_fun_a_bool_nat(X8,X4)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15838,plain,
spl263_1005,
inference(avatar_split_clause,[],[f6360,f15836]) ).
fof(f15836,plain,
( spl263_1005
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1005])]) ).
fof(f6360,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(cnf_transformation,[],[f3408]) ).
fof(f3408,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(flattening,[],[f3407]) ).
fof(f3407,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(ennf_transformation,[],[f2327]) ).
fof(f2327,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),image_1551609309ol_nat(X8,X4)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15834,plain,
spl263_1004,
inference(avatar_split_clause,[],[f6359,f15832]) ).
fof(f15832,plain,
( spl263_1004
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1004])]) ).
fof(f6359,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(cnf_transformation,[],[f3406]) ).
fof(f3406,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(flattening,[],[f3405]) ).
fof(f3405,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(ennf_transformation,[],[f2326]) ).
fof(f2326,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f323]) ).
fof(f323,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_fun_a_bool_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15830,plain,
spl263_1003,
inference(avatar_split_clause,[],[f6358,f15828]) ).
fof(f15828,plain,
( spl263_1003
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1003])]) ).
fof(f6358,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(cnf_transformation,[],[f3404]) ).
fof(f3404,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(flattening,[],[f3403]) ).
fof(f3403,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(ennf_transformation,[],[f2325]) ).
fof(f2325,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f322]) ).
fof(f322,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_41399353ol_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15826,plain,
spl263_1002,
inference(avatar_split_clause,[],[f6357,f15824]) ).
fof(f15824,plain,
( spl263_1002
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1002])]) ).
fof(f6357,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f3402]) ).
fof(f3402,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3401]) ).
fof(f3401,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2324]) ).
fof(f2324,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f321]) ).
fof(f321,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_1133522419ol_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15822,plain,
spl263_1001,
inference(avatar_split_clause,[],[f6356,f15820]) ).
fof(f15820,plain,
( spl263_1001
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1001])]) ).
fof(f6356,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f3400]) ).
fof(f3400,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3399]) ).
fof(f3399,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2323]) ).
fof(f2323,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f320]) ).
fof(f320,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),image_2069007511ol_int(X8,X4)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15818,plain,
spl263_1000,
inference(avatar_split_clause,[],[f6355,f15816]) ).
fof(f15816,plain,
( spl263_1000
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1000])]) ).
fof(f6355,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(cnf_transformation,[],[f3398]) ).
fof(f3398,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(flattening,[],[f3397]) ).
fof(f3397,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(ennf_transformation,[],[f2322]) ).
fof(f2322,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_876012084bool_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15814,plain,
spl263_999,
inference(avatar_split_clause,[],[f6354,f15812]) ).
fof(f15812,plain,
( spl263_999
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_999])]) ).
fof(f6354,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f3396]) ).
fof(f3396,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3395]) ).
fof(f3395,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2321]) ).
fof(f2321,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_nat_bool_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15810,plain,
spl263_998,
inference(avatar_split_clause,[],[f6353,f15808]) ).
fof(f15808,plain,
( spl263_998
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_998])]) ).
fof(f6353,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f3394]) ).
fof(f3394,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3393]) ).
fof(f3393,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2320]) ).
fof(f2320,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f288]) ).
fof(f288,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_int_bool_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15806,plain,
( spl263_997
| ~ spl263_35
| ~ spl263_113 ),
inference(avatar_split_clause,[],[f8399,f8310,f7952,f15804]) ).
fof(f15804,plain,
( spl263_997
<=> ! [X0] :
( ~ sP10(X0)
| sP1(sK111(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_997])]) ).
fof(f8310,plain,
( spl263_113
<=> ! [X0] :
( is_fun_pname_bool(sK111(X0))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_113])]) ).
fof(f8399,plain,
( ! [X0] :
( ~ sP10(X0)
| sP1(sK111(X0)) )
| ~ spl263_35
| ~ spl263_113 ),
inference(resolution,[],[f8311,f7953]) ).
fof(f8311,plain,
( ! [X0] :
( is_fun_pname_bool(sK111(X0))
| ~ sP10(X0) )
| ~ spl263_113 ),
inference(avatar_component_clause,[],[f8310]) ).
fof(f15802,plain,
spl263_996,
inference(avatar_split_clause,[],[f6352,f15800]) ).
fof(f15800,plain,
( spl263_996
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_996])]) ).
fof(f6352,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(cnf_transformation,[],[f3392]) ).
fof(f3392,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(flattening,[],[f3391]) ).
fof(f3391,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(ennf_transformation,[],[f2319]) ).
fof(f2319,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),image_fun_a_bool_a(X8,X4)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15798,plain,
spl263_995,
inference(avatar_split_clause,[],[f6351,f15796]) ).
fof(f15796,plain,
( spl263_995
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_995])]) ).
fof(f6351,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(cnf_transformation,[],[f3390]) ).
fof(f3390,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(flattening,[],[f3389]) ).
fof(f3389,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(ennf_transformation,[],[f2318]) ).
fof(f2318,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1921560913_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15794,plain,
spl263_994,
inference(avatar_split_clause,[],[f6350,f15792]) ).
fof(f15792,plain,
( spl263_994
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_994])]) ).
fof(f6350,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(cnf_transformation,[],[f3388]) ).
fof(f3388,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(flattening,[],[f3387]) ).
fof(f3387,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(ennf_transformation,[],[f2317]) ).
fof(f2317,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_62782965_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15790,plain,
spl263_993,
inference(avatar_split_clause,[],[f6349,f15788]) ).
fof(f15788,plain,
( spl263_993
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_993])]) ).
fof(f6349,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(cnf_transformation,[],[f3386]) ).
fof(f3386,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(flattening,[],[f3385]) ).
fof(f3385,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(ennf_transformation,[],[f2316]) ).
fof(f2316,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f312]) ).
fof(f312,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1283814551_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15786,plain,
spl263_992,
inference(avatar_split_clause,[],[f6348,f15784]) ).
fof(f15784,plain,
( spl263_992
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_992])]) ).
fof(f6348,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(cnf_transformation,[],[f3384]) ).
fof(f3384,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(flattening,[],[f3383]) ).
fof(f3383,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(ennf_transformation,[],[f2315]) ).
fof(f2315,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f313]) ).
fof(f313,axiom,
! [X9,X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),image_1854862208_pname(X8,X4)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15782,plain,
spl263_991,
inference(avatar_split_clause,[],[f6084,f15780]) ).
fof(f15780,plain,
( spl263_991
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_991])]) ).
fof(f6084,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
inference(cnf_transformation,[],[f4435]) ).
fof(f4435,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ) ),
inference(nnf_transformation,[],[f2156]) ).
fof(f2156,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
inference(rectify,[],[f1059]) ).
fof(f1059,axiom,
! [X16,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X16),X24)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15778,plain,
spl263_990,
inference(avatar_split_clause,[],[f6083,f15776]) ).
fof(f15776,plain,
( spl263_990
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_990])]) ).
fof(f6083,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ),
inference(cnf_transformation,[],[f4435]) ).
fof(f15774,plain,
spl263_989,
inference(avatar_split_clause,[],[f6081,f15772]) ).
fof(f15772,plain,
( spl263_989
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_989])]) ).
fof(f6081,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
inference(cnf_transformation,[],[f4434]) ).
fof(f15770,plain,
spl263_988,
inference(avatar_split_clause,[],[f6080,f15768]) ).
fof(f15768,plain,
( spl263_988
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_988])]) ).
fof(f6080,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
inference(cnf_transformation,[],[f4434]) ).
fof(f15766,plain,
spl263_987,
inference(avatar_split_clause,[],[f6078,f15764]) ).
fof(f15764,plain,
( spl263_987
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_987])]) ).
fof(f6078,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ),
inference(cnf_transformation,[],[f4432]) ).
fof(f4432,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ) ),
inference(nnf_transformation,[],[f2154]) ).
fof(f2154,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(rectify,[],[f1161]) ).
fof(f1161,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X138),one_one_int)),X55))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15761,plain,
spl263_986,
inference(avatar_split_clause,[],[f6075,f15759]) ).
fof(f6075,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4430]) ).
fof(f4430,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
inference(nnf_transformation,[],[f2152]) ).
fof(f2152,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f1217]) ).
fof(f1217,axiom,
! [X10,X38] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X10)),hAPP_nat_int(semiri1621563631at_int,X38)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X10),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15756,plain,
spl263_985,
inference(avatar_split_clause,[],[f6074,f15754]) ).
fof(f6074,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(cnf_transformation,[],[f4430]) ).
fof(f15751,plain,
spl263_984,
inference(avatar_split_clause,[],[f6071,f15749]) ).
fof(f6071,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4428]) ).
fof(f4428,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
inference(nnf_transformation,[],[f2150]) ).
fof(f2150,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(rectify,[],[f1208]) ).
fof(f1208,axiom,
! [X24,X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X24)),hAPP_nat_int(semiri1621563631at_int,X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15746,plain,
spl263_983,
inference(avatar_split_clause,[],[f6070,f15744]) ).
fof(f6070,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(cnf_transformation,[],[f4428]) ).
fof(f15742,plain,
spl263_982,
inference(avatar_split_clause,[],[f6069,f15740]) ).
fof(f15740,plain,
( spl263_982
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_982])]) ).
fof(f6069,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4427]) ).
fof(f4427,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ) ),
inference(nnf_transformation,[],[f2149]) ).
fof(f2149,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(rectify,[],[f1155]) ).
fof(f1155,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X138),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X55),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15738,plain,
spl263_981,
inference(avatar_split_clause,[],[f6068,f15736]) ).
fof(f15736,plain,
( spl263_981
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_981])]) ).
fof(f6068,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ),
inference(cnf_transformation,[],[f4427]) ).
fof(f15734,plain,
spl263_980,
inference(avatar_split_clause,[],[f6066,f15732]) ).
fof(f15732,plain,
( spl263_980
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_980])]) ).
fof(f6066,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4426]) ).
fof(f15730,plain,
spl263_979,
inference(avatar_split_clause,[],[f6064,f15728]) ).
fof(f15728,plain,
( spl263_979
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_979])]) ).
fof(f6064,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f4424]) ).
fof(f4424,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
inference(nnf_transformation,[],[f2147]) ).
fof(f2147,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(rectify,[],[f1160]) ).
fof(f1160,axiom,
! [X138,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X55),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X138),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15726,plain,
spl263_978,
inference(avatar_split_clause,[],[f6063,f15724]) ).
fof(f15724,plain,
( spl263_978
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_978])]) ).
fof(f6063,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
inference(cnf_transformation,[],[f4424]) ).
fof(f15713,plain,
( ~ spl263_977
| ~ spl263_144
| ~ spl263_931 ),
inference(avatar_split_clause,[],[f15508,f14746,f8479,f15710]) ).
fof(f15710,plain,
( spl263_977
<=> sP13(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_977])]) ).
fof(f14746,plain,
( spl263_931
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),collect_a(hAPP_a_fun_a_bool(fequal_a,sK116(X0))))))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_931])]) ).
fof(f15508,plain,
( ~ sP13(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool))
| ~ spl263_144
| ~ spl263_931 ),
inference(resolution,[],[f14747,f8480]) ).
fof(f14747,plain,
( ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),collect_a(hAPP_a_fun_a_bool(fequal_a,sK116(X0))))))
| ~ sP13(X0) )
| ~ spl263_931 ),
inference(avatar_component_clause,[],[f14746]) ).
fof(f15708,plain,
( spl263_976
| ~ spl263_543
| ~ spl263_749
| ~ spl263_975 ),
inference(avatar_split_clause,[],[f15704,f15700,f12592,f10678,f15706]) ).
fof(f15706,plain,
( spl263_976
<=> ! [X0,X1,X3] :
( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_976])]) ).
fof(f15700,plain,
( spl263_975
<=> ! [X0,X1,X3] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_975])]) ).
fof(f15704,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_749
| ~ spl263_975 ),
inference(forward_demodulation,[],[f15703,f12593]) ).
fof(f15703,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X3),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_543
| ~ spl263_975 ),
inference(forward_demodulation,[],[f15701,f10679]) ).
fof(f15701,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl263_975 ),
inference(avatar_component_clause,[],[f15700]) ).
fof(f15702,plain,
spl263_975,
inference(avatar_split_clause,[],[f5929,f15700]) ).
fof(f5929,plain,
! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f4333]) ).
fof(f15698,plain,
spl263_974,
inference(avatar_split_clause,[],[f5928,f15696]) ).
fof(f15696,plain,
( spl263_974
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_974])]) ).
fof(f5928,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(cnf_transformation,[],[f4329]) ).
fof(f4329,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
inference(nnf_transformation,[],[f2095]) ).
fof(f2095,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(rectify,[],[f1241]) ).
fof(f1241,axiom,
! [X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X4)),image_nat_int(semiri1621563631at_int,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15694,plain,
spl263_973,
inference(avatar_split_clause,[],[f5926,f15692]) ).
fof(f15692,plain,
( spl263_973
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_973])]) ).
fof(f5926,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(cnf_transformation,[],[f4328]) ).
fof(f4328,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ) ),
inference(nnf_transformation,[],[f2094]) ).
fof(f2094,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(rectify,[],[f1240]) ).
fof(f1240,axiom,
! [X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X4),X9))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X4)),image_nat_int(semiri1621563631at_int,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15690,plain,
spl263_972,
inference(avatar_split_clause,[],[f5925,f15688]) ).
fof(f15688,plain,
( spl263_972
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_972])]) ).
fof(f5925,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f4328]) ).
fof(f15686,plain,
spl263_971,
inference(avatar_split_clause,[],[f5924,f15684]) ).
fof(f15684,plain,
( spl263_971
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_971])]) ).
fof(f5924,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(cnf_transformation,[],[f4327]) ).
fof(f4327,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2093]) ).
fof(f2093,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
inference(rectify,[],[f1244]) ).
fof(f1244,axiom,
! [X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X10)),image_nat_int(semiri1621563631at_int,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15675,plain,
( spl263_970
| ~ spl263_542
| ~ spl263_748
| ~ spl263_969 ),
inference(avatar_split_clause,[],[f15671,f15667,f12588,f10674,f15673]) ).
fof(f15673,plain,
( spl263_970
<=> ! [X0,X1,X3] :
( hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_970])]) ).
fof(f15667,plain,
( spl263_969
<=> ! [X0,X1,X3] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_969])]) ).
fof(f15671,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_748
| ~ spl263_969 ),
inference(forward_demodulation,[],[f15670,f12589]) ).
fof(f15670,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X3),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_542
| ~ spl263_969 ),
inference(forward_demodulation,[],[f15668,f10675]) ).
fof(f15668,plain,
( ! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
| ~ spl263_969 ),
inference(avatar_component_clause,[],[f15667]) ).
fof(f15669,plain,
spl263_969,
inference(avatar_split_clause,[],[f5919,f15667]) ).
fof(f5919,plain,
! [X3,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f4325]) ).
fof(f15665,plain,
spl263_968,
inference(avatar_split_clause,[],[f5793,f15663]) ).
fof(f15663,plain,
( spl263_968
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_968])]) ).
fof(f5793,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f3212]) ).
fof(f3212,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
inference(ennf_transformation,[],[f2031]) ).
fof(f2031,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(rectify,[],[f982]) ).
fof(f982,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X14)),hAPP_nat_nat(suc,X13)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15661,plain,
spl263_967,
inference(avatar_split_clause,[],[f5784,f15659]) ).
fof(f15659,plain,
( spl263_967
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK137(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_967])]) ).
fof(f5784,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK137(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f4257]) ).
fof(f4257,plain,
! [X0,X1] :
( ( hAPP_nat_nat(suc,sK137(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK137(X0,X1))) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f3202,f4256]) ).
fof(f4256,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(suc,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
=> ( hAPP_nat_nat(suc,sK137(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK137(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f3202,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(suc,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(ennf_transformation,[],[f2023]) ).
fof(f2023,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
=> ~ ! [X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
=> hAPP_nat_nat(suc,X2) != X1 ) ),
inference(rectify,[],[f1027]) ).
fof(f1027,axiom,
! [X22,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X22)),X21))
=> ~ ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X126))
=> hAPP_nat_nat(suc,X126) != X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15657,plain,
spl263_966,
inference(avatar_split_clause,[],[f5750,f15655]) ).
fof(f15655,plain,
( spl263_966
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_966])]) ).
fof(f5750,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3159]) ).
fof(f3159,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1993]) ).
fof(f1993,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
inference(rectify,[],[f963]) ).
fof(f963,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X14)),hAPP_nat_nat(suc,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15653,plain,
spl263_965,
inference(avatar_split_clause,[],[f5736,f15651]) ).
fof(f15651,plain,
( spl263_965
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_965])]) ).
fof(f5736,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f3143]) ).
fof(f3143,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(ennf_transformation,[],[f1980]) ).
fof(f1980,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ),
inference(rectify,[],[f1162]) ).
fof(f1162,axiom,
! [X134,X97] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X134),X97))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X134),one_one_int)),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15649,plain,
spl263_964,
inference(avatar_split_clause,[],[f5688,f15647]) ).
fof(f15647,plain,
( spl263_964
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_964])]) ).
fof(f5688,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f4237]) ).
fof(f4237,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1))) ) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(nnf_transformation,[],[f3082]) ).
fof(f3082,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1940]) ).
fof(f1940,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f677]) ).
fof(f677,axiom,
! [X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15645,plain,
spl263_963,
inference(avatar_split_clause,[],[f5656,f15643]) ).
fof(f15643,plain,
( spl263_963
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_963])]) ).
fof(f5656,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3052]) ).
fof(f3052,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15641,plain,
spl263_962,
inference(avatar_split_clause,[],[f5655,f15639]) ).
fof(f15639,plain,
( spl263_962
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_962])]) ).
fof(f5655,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3051]) ).
fof(f3051,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1920]) ).
fof(f1920,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f174]) ).
fof(f174,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15637,plain,
spl263_961,
inference(avatar_split_clause,[],[f5645,f15635]) ).
fof(f15635,plain,
( spl263_961
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_961])]) ).
fof(f5645,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f4226]) ).
fof(f4226,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1))) ) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(nnf_transformation,[],[f3042]) ).
fof(f3042,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) )
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1911]) ).
fof(f1911,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f676]) ).
fof(f676,axiom,
! [X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15633,plain,
spl263_960,
inference(avatar_split_clause,[],[f5613,f15631]) ).
fof(f15631,plain,
( spl263_960
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_960])]) ).
fof(f5613,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3012]) ).
fof(f3012,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1892]) ).
fof(f1892,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1))) ),
inference(rectify,[],[f175]) ).
fof(f175,axiom,
! [X8,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X8,X4))),hAPP_f957591787ol_nat(finite_card_int,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15629,plain,
spl263_959,
inference(avatar_split_clause,[],[f5575,f15627]) ).
fof(f15627,plain,
( spl263_959
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_959])]) ).
fof(f5575,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2979]) ).
fof(f2979,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1868]) ).
fof(f1868,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X8,X4))),hAPP_fun_a_bool_nat(finite_card_a,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15625,plain,
spl263_958,
inference(avatar_split_clause,[],[f5574,f15623]) ).
fof(f15623,plain,
( spl263_958
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_958])]) ).
fof(f5574,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2978]) ).
fof(f2978,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1867]) ).
fof(f1867,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f156]) ).
fof(f156,axiom,
! [X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X8,X4))),hAPP_fun_a_bool_nat(finite_card_a,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15621,plain,
spl263_957,
inference(avatar_split_clause,[],[f5573,f15619]) ).
fof(f15619,plain,
( spl263_957
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_957])]) ).
fof(f5573,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2977]) ).
fof(f2977,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1866]) ).
fof(f1866,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X8,X4))),hAPP_fun_a_bool_nat(finite_card_a,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15617,plain,
spl263_956,
inference(avatar_split_clause,[],[f5572,f15615]) ).
fof(f15615,plain,
( spl263_956
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_956])]) ).
fof(f5572,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2976]) ).
fof(f2976,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f173]) ).
fof(f173,axiom,
! [X8,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X8,X4))),hAPP_fun_a_bool_nat(finite_card_a,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15613,plain,
spl263_955,
inference(avatar_split_clause,[],[f5566,f15611]) ).
fof(f15611,plain,
( spl263_955
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_955])]) ).
fof(f5566,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f4207]) ).
fof(f4207,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1))) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(nnf_transformation,[],[f2971]) ).
fof(f2971,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1860]) ).
fof(f1860,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f678]) ).
fof(f678,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15609,plain,
spl263_954,
inference(avatar_split_clause,[],[f5557,f15607]) ).
fof(f15607,plain,
( spl263_954
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK113(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK112(X0)),bot_bo844097828e_bool))))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_954])]) ).
fof(f5557,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK113(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK112(X0)),bot_bo844097828e_bool))))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f4206,plain,
! [X0] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK113(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK112(X0)),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK113(X0)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK112(X0)),sK113(X0)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK113(X0)))
& is_fun_pname_bool(sK113(X0))
& is_pname(sK112(X0)) )
| ~ sP11(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f4204,f4205]) ).
fof(f4205,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK113(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK112(X0)),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK113(X0)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK112(X0)),sK113(X0)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK113(X0)))
& is_fun_pname_bool(sK113(X0))
& is_pname(sK112(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4204,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
| ~ sP11(X0) ),
inference(rectify,[],[f4203]) ).
fof(f4203,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f3929]) ).
fof(f3929,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f15605,plain,
spl263_953,
inference(avatar_split_clause,[],[f5535,f15603]) ).
fof(f15603,plain,
( spl263_953
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_953])]) ).
fof(f5535,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2945]) ).
fof(f2945,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1843]) ).
fof(f1843,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15601,plain,
spl263_952,
inference(avatar_split_clause,[],[f5534,f15599]) ).
fof(f15599,plain,
( spl263_952
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_952])]) ).
fof(f5534,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2944]) ).
fof(f2944,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1842]) ).
fof(f1842,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15597,plain,
spl263_951,
inference(avatar_split_clause,[],[f5533,f15595]) ).
fof(f15595,plain,
( spl263_951
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_951])]) ).
fof(f5533,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2943]) ).
fof(f2943,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1841]) ).
fof(f1841,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f167]) ).
fof(f167,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15593,plain,
spl263_950,
inference(avatar_split_clause,[],[f5532,f15591]) ).
fof(f15591,plain,
( spl263_950
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_950])]) ).
fof(f5532,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2942]) ).
fof(f2942,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1840]) ).
fof(f1840,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f155]) ).
fof(f155,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15589,plain,
spl263_949,
inference(avatar_split_clause,[],[f5498,f15587]) ).
fof(f15587,plain,
( spl263_949
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_949])]) ).
fof(f5498,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2898]) ).
fof(f2898,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1810]) ).
fof(f1810,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X8,X4))),hAPP_f55526627ol_nat(finite1340463720e_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15585,plain,
spl263_948,
inference(avatar_split_clause,[],[f5497,f15583]) ).
fof(f15583,plain,
( spl263_948
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_948])]) ).
fof(f5497,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2897]) ).
fof(f2897,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1809]) ).
fof(f1809,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X8,X4))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15581,plain,
spl263_947,
inference(avatar_split_clause,[],[f5496,f15579]) ).
fof(f15579,plain,
( spl263_947
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_947])]) ).
fof(f5496,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2896]) ).
fof(f2896,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1808]) ).
fof(f1808,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X8,X4))),hAPP_f521865025ol_nat(finite1876863882t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15577,plain,
spl263_946,
inference(avatar_split_clause,[],[f5495,f15575]) ).
fof(f15575,plain,
( spl263_946
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_946])]) ).
fof(f5495,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2895]) ).
fof(f2895,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X8,X4))),hAPP_f696928925ol_nat(finite346522414t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15573,plain,
spl263_945,
inference(avatar_split_clause,[],[f5494,f15571]) ).
fof(f15571,plain,
( spl263_945
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_945])]) ).
fof(f5494,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2894]) ).
fof(f2894,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1806]) ).
fof(f1806,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X8,X4))),hAPP_f55526627ol_nat(finite1340463720e_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15569,plain,
spl263_944,
inference(avatar_split_clause,[],[f5493,f15567]) ).
fof(f15567,plain,
( spl263_944
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_944])]) ).
fof(f5493,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2893]) ).
fof(f2893,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1805]) ).
fof(f1805,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X8,X4))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15565,plain,
spl263_943,
inference(avatar_split_clause,[],[f5492,f15563]) ).
fof(f15563,plain,
( spl263_943
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_943])]) ).
fof(f5492,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2892]) ).
fof(f2892,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1804]) ).
fof(f1804,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X8,X4))),hAPP_f696928925ol_nat(finite346522414t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15561,plain,
spl263_942,
inference(avatar_split_clause,[],[f5491,f15559]) ).
fof(f15559,plain,
( spl263_942
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_942])]) ).
fof(f5491,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2891]) ).
fof(f2891,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1803]) ).
fof(f1803,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X8,X4))),hAPP_f521865025ol_nat(finite1876863882t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15557,plain,
spl263_941,
inference(avatar_split_clause,[],[f5490,f15555]) ).
fof(f15555,plain,
( spl263_941
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_941])]) ).
fof(f5490,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2890]) ).
fof(f2890,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X8,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X8,X4))),hAPP_f521865025ol_nat(finite1876863882t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15553,plain,
spl263_940,
inference(avatar_split_clause,[],[f5489,f15551]) ).
fof(f15551,plain,
( spl263_940
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_940])]) ).
fof(f5489,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2889]) ).
fof(f2889,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1801]) ).
fof(f1801,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X8,X4))),hAPP_f696928925ol_nat(finite346522414t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15549,plain,
spl263_939,
inference(avatar_split_clause,[],[f5488,f15547]) ).
fof(f15547,plain,
( spl263_939
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_939])]) ).
fof(f5488,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2888]) ).
fof(f2888,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1800]) ).
fof(f1800,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X8,X4))),hAPP_f55526627ol_nat(finite1340463720e_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15545,plain,
spl263_938,
inference(avatar_split_clause,[],[f5487,f15543]) ).
fof(f15543,plain,
( spl263_938
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_938])]) ).
fof(f5487,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2887]) ).
fof(f2887,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1799]) ).
fof(f1799,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X8,X4))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15541,plain,
spl263_937,
inference(avatar_split_clause,[],[f5468,f15539]) ).
fof(f15539,plain,
( spl263_937
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(X0,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_937])]) ).
fof(f5468,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(X0,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4198]) ).
fof(f15537,plain,
spl263_936,
inference(avatar_split_clause,[],[f5465,f15535]) ).
fof(f15535,plain,
( spl263_936
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK108(X0,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_936])]) ).
fof(f5465,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK108(X0,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4196]) ).
fof(f15533,plain,
spl263_935,
inference(avatar_split_clause,[],[f5117,f15531]) ).
fof(f15531,plain,
( spl263_935
<=> ! [X0] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK74(X0)),sK73(X0)) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_935])]) ).
fof(f5117,plain,
! [X0] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK74(X0)),sK73(X0)) = X0
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f4091]) ).
fof(f4091,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 )
& bot_bot_fun_nat_bool != X0 ) )
& ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK73(X0)))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK74(X0)),sK73(X0)) = X0 )
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f4089,f4090]) ).
fof(f4090,plain,
! [X0] :
( ? [X3,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3) = X0 )
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK73(X0)))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK74(X0)),sK73(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f4089,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 )
& bot_bot_fun_nat_bool != X0 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3) = X0 )
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f4088]) ).
fof(f4088,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 )
& bot_bot_fun_nat_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 )
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(flattening,[],[f4087]) ).
fof(f4087,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 )
& bot_bot_fun_nat_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 )
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(nnf_transformation,[],[f1590]) ).
fof(f1590,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 )
| bot_bot_fun_nat_bool = X0 ) ),
inference(rectify,[],[f800]) ).
fof(f800,axiom,
! [X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
<=> ( ? [X80,X77] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X80))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X77),X80) = X7 )
| bot_bot_fun_nat_bool = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15529,plain,
spl263_934,
inference(avatar_split_clause,[],[f5111,f15527]) ).
fof(f15527,plain,
( spl263_934
<=> ! [X0] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK72(X0)),sK71(X0)) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_934])]) ).
fof(f5111,plain,
! [X0] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK72(X0)),sK71(X0)) = X0
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
inference(cnf_transformation,[],[f4085]) ).
fof(f4085,plain,
! [X0] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 )
& bot_bot_fun_int_bool != X0 ) )
& ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK71(X0)))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK72(X0)),sK71(X0)) = X0 )
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f4083,f4084]) ).
fof(f4084,plain,
! [X0] :
( ? [X3,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3) = X0 )
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK71(X0)))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK72(X0)),sK71(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f4083,plain,
! [X0] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 )
& bot_bot_fun_int_bool != X0 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3) = X0 )
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f4082]) ).
fof(f4082,plain,
! [X0] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 )
& bot_bot_fun_int_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 )
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(flattening,[],[f4081]) ).
fof(f4081,plain,
! [X0] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 )
& bot_bot_fun_int_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 )
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(nnf_transformation,[],[f1588]) ).
fof(f1588,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 )
| bot_bot_fun_int_bool = X0 ) ),
inference(rectify,[],[f799]) ).
fof(f799,axiom,
! [X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
<=> ( ? [X80,X77] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X80))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X77),X80) = X7 )
| bot_bot_fun_int_bool = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14997,plain,
( spl263_933
| ~ spl263_141
| ~ spl263_859 ),
inference(avatar_split_clause,[],[f14338,f13432,f8467,f14995]) ).
fof(f14995,plain,
( spl263_933
<=> ! [X0,X1] : ~ sP36(nat_neg,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_933])]) ).
fof(f8467,plain,
( spl263_141
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_141])]) ).
fof(f13432,plain,
( spl263_859
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
| ~ sP36(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_859])]) ).
fof(f14338,plain,
( ! [X0,X1] : ~ sP36(nat_neg,X0,X1)
| ~ spl263_141
| ~ spl263_859 ),
inference(resolution,[],[f13433,f8468]) ).
fof(f8468,plain,
( ! [X0] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ spl263_141 ),
inference(avatar_component_clause,[],[f8467]) ).
fof(f13433,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
| ~ sP36(X0,X2,X1) )
| ~ spl263_859 ),
inference(avatar_component_clause,[],[f13432]) ).
fof(f14752,plain,
spl263_932,
inference(avatar_split_clause,[],[f7700,f14750]) ).
fof(f14750,plain,
( spl263_932
<=> ! [X2,X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_932])]) ).
fof(f7700,plain,
! [X2,X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(forward_demodulation,[],[f6518,f4966]) ).
fof(f6518,plain,
! [X2,X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f3545]) ).
fof(f3545,plain,
! [X0,X1,X2] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f2402]) ).
fof(f2402,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2) ),
inference(rectify,[],[f773]) ).
fof(f773,axiom,
! [X31,X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> image_pname_a(cOMBK_a_pname(X31),X4) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),bot_bot_fun_a_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14748,plain,
spl263_931,
inference(avatar_split_clause,[],[f7502,f14746]) ).
fof(f7502,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),collect_a(hAPP_a_fun_a_bool(fequal_a,sK116(X0))))))
| ~ sP13(X0) ),
inference(forward_demodulation,[],[f5597,f4966]) ).
fof(f5597,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK116(X0)),bot_bot_fun_a_bool))))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f4215,plain,
! [X0] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK116(X0)),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK117(X0)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK116(X0)),sK117(X0)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK117(X0)))
& is_fun_a_bool(sK117(X0))
& is_a(sK116(X0)) )
| ~ sP13(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117])],[f4213,f4214]) ).
fof(f4214,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK117(X0)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK116(X0)),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK117(X0)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK116(X0)),sK117(X0)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK117(X0)))
& is_fun_a_bool(sK117(X0))
& is_a(sK116(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4213,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
| ~ sP13(X0) ),
inference(rectify,[],[f4212]) ).
fof(f4212,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f3933]) ).
fof(f3933,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f14744,plain,
spl263_930,
inference(avatar_split_clause,[],[f7482,f14742]) ).
fof(f14742,plain,
( spl263_930
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
| is_pname(sK96(X0))
| ~ hBOOL(wt(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_930])]) ).
fof(f7482,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
| is_pname(sK96(X0))
| ~ hBOOL(wt(X1)) ),
inference(forward_demodulation,[],[f5439,f4966]) ).
fof(f5439,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
| is_pname(sK96(X0))
| ~ hBOOL(wt(X1)) ),
inference(cnf_transformation,[],[f4172]) ).
fof(f14740,plain,
spl263_929,
inference(avatar_split_clause,[],[f7463,f14738]) ).
fof(f14738,plain,
( spl263_929
<=> ! [X0,X1] :
( hAPP_n1699378549t_bool(fequal_nat,X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_929])]) ).
fof(f7463,plain,
! [X0,X1] :
( hAPP_n1699378549t_bool(fequal_nat,X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(forward_demodulation,[],[f7462,f4876]) ).
fof(f7462,plain,
! [X0,X1] :
( hAPP_n1699378549t_bool(fequal_nat,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5314,f7397]) ).
fof(f5314,plain,
! [X0,X1] :
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2760]) ).
fof(f2760,plain,
! [X0,X1] :
( ( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0))
| hBOOL(hAPP_nat_bool(X0,X1)) )
& ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f1703]) ).
fof(f1703,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_nat_bool(X0,X1))
=> bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) )
& ( hBOOL(hAPP_nat_bool(X0,X1))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ),
inference(rectify,[],[f742]) ).
fof(f742,axiom,
! [X12,X7] :
( ( ~ hBOOL(hAPP_nat_bool(X12,X7))
=> bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X7)),X12)) )
& ( hBOOL(hAPP_nat_bool(X12,X7))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X7)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14736,plain,
spl263_928,
inference(avatar_split_clause,[],[f7455,f14734]) ).
fof(f14734,plain,
( spl263_928
<=> ! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)
| ~ hBOOL(hAPP_int_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_928])]) ).
fof(f7455,plain,
! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)
| ~ hBOOL(hAPP_int_bool(X0,X1)) ),
inference(forward_demodulation,[],[f7454,f4874]) ).
fof(f7454,plain,
! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0))
| ~ hBOOL(hAPP_int_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5310,f7396]) ).
fof(f5310,plain,
! [X0,X1] :
( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2758]) ).
fof(f2758,plain,
! [X0,X1] :
( ( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0))
| hBOOL(hAPP_int_bool(X0,X1)) )
& ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X0,X1)) ) ),
inference(ennf_transformation,[],[f1701]) ).
fof(f1701,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_int_bool(X0,X1))
=> bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) )
& ( hBOOL(hAPP_int_bool(X0,X1))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ),
inference(rectify,[],[f741]) ).
fof(f741,axiom,
! [X12,X7] :
( ( ~ hBOOL(hAPP_int_bool(X12,X7))
=> bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X7)),X12)) )
& ( hBOOL(hAPP_int_bool(X12,X7))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X7)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14732,plain,
spl263_927,
inference(avatar_split_clause,[],[f7409,f14730]) ).
fof(f14730,plain,
( spl263_927
<=> ! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_927])]) ).
fof(f7409,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) ),
inference(forward_demodulation,[],[f7041,f4875]) ).
fof(f7041,plain,
! [X0] :
( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f4984,f4948]) ).
fof(f4984,plain,
! [X0] :
( number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2694]) ).
fof(f2694,plain,
! [X0] :
( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
inference(ennf_transformation,[],[f1528]) ).
fof(f1528,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) ),
inference(rectify,[],[f1270]) ).
fof(f1270,axiom,
! [X132] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> number_number_of_nat(succ(X132)) = hAPP_nat_nat(suc,number_number_of_nat(X132)) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X132)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14727,plain,
spl263_926,
inference(avatar_split_clause,[],[f7020,f14724]) ).
fof(f14724,plain,
( spl263_926
<=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_926])]) ).
fof(f14722,plain,
spl263_925,
inference(avatar_split_clause,[],[f6778,f14720]) ).
fof(f14720,plain,
( spl263_925
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_925])]) ).
fof(f6778,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK260(X0,X1,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f14718,plain,
spl263_924,
inference(avatar_split_clause,[],[f6770,f14716]) ).
fof(f14716,plain,
( spl263_924
<=> ! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_924])]) ).
fof(f6770,plain,
! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,sK259(X0,X1,X2)))
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f14714,plain,
spl263_923,
inference(avatar_split_clause,[],[f6435,f14712]) ).
fof(f6435,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK209(X0,X1)),sK210(X0,X1))))
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f4549]) ).
fof(f4549,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK209(X0,X1)),sK210(X0,X1))))
& hBOOL(hAPP_f54304608l_bool(X0,sK210(X0,X1)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),sK210(X0,X1)))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK210(X0,X1))) )
| ~ sP23(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK209,sK210])],[f4547,f4548]) ).
fof(f4548,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK209(X0,X1)),sK210(X0,X1))))
& hBOOL(hAPP_f54304608l_bool(X0,sK210(X0,X1)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),sK210(X0,X1)))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK210(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f4547,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
& hBOOL(hAPP_f54304608l_bool(X0,X3))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
| ~ sP23(X0,X1) ),
inference(rectify,[],[f4546]) ).
fof(f4546,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ sP23(X0,X1) ),
inference(nnf_transformation,[],[f3952]) ).
fof(f14710,plain,
( spl263_922
| ~ spl263_146
| ~ spl263_855 ),
inference(avatar_split_clause,[],[f14268,f13416,f8487,f14708]) ).
fof(f14708,plain,
( spl263_922
<=> ! [X0,X1] : sP35(X0,bot_bot_fun_nat_bool,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_922])]) ).
fof(f13416,plain,
( spl263_855
<=> ! [X2,X0,X1] :
( sP35(X2,X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_855])]) ).
fof(f14268,plain,
( ! [X0,X1] : sP35(X0,bot_bot_fun_nat_bool,X1)
| ~ spl263_146
| ~ spl263_855 ),
inference(resolution,[],[f13417,f8488]) ).
fof(f13417,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
| sP35(X2,X0,X1) )
| ~ spl263_855 ),
inference(avatar_component_clause,[],[f13416]) ).
fof(f14706,plain,
spl263_921,
inference(avatar_split_clause,[],[f6397,f14704]) ).
fof(f6397,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK200(X0,X1)),sK201(X0,X1))))
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f4531]) ).
fof(f4531,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK200(X0,X1)),sK201(X0,X1))))
& hBOOL(hAPP_f448129468l_bool(X0,sK201(X0,X1)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),sK201(X0,X1)))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK201(X0,X1))) )
| ~ sP22(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201])],[f4529,f4530]) ).
fof(f4530,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK200(X0,X1)),sK201(X0,X1))))
& hBOOL(hAPP_f448129468l_bool(X0,sK201(X0,X1)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),sK201(X0,X1)))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK201(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f4529,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
& hBOOL(hAPP_f448129468l_bool(X0,X3))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
| ~ sP22(X0,X1) ),
inference(rectify,[],[f4528]) ).
fof(f4528,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ sP22(X0,X1) ),
inference(nnf_transformation,[],[f3950]) ).
fof(f14702,plain,
spl263_920,
inference(avatar_split_clause,[],[f6386,f14700]) ).
fof(f6386,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK198(X0,X1)),sK199(X0,X1))))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f4527,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK198(X0,X1)),sK199(X0,X1))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK199(X0,X1)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),sK199(X0,X1)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK199(X0,X1)))
& is_fun_a_bool(sK199(X0,X1))
& is_a(sK198(X0,X1)) )
| ~ sP21(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199])],[f4525,f4526]) ).
fof(f4526,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK198(X0,X1)),sK199(X0,X1))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK199(X0,X1)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),sK199(X0,X1)))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK199(X0,X1)))
& is_fun_a_bool(sK199(X0,X1))
& is_a(sK198(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f4525,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ sP21(X0,X1) ),
inference(rectify,[],[f4524]) ).
fof(f4524,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ sP21(X0,X1) ),
inference(nnf_transformation,[],[f3948]) ).
fof(f14698,plain,
spl263_919,
inference(avatar_split_clause,[],[f6370,f14696]) ).
fof(f14696,plain,
( spl263_919
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK196(X0,X1)),sK197(X0,X1))))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_919])]) ).
fof(f6370,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK196(X0,X1)),sK197(X0,X1))))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f4523,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK196(X0,X1)),sK197(X0,X1))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK197(X0,X1)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),sK197(X0,X1)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK197(X0,X1)))
& is_fun_pname_bool(sK197(X0,X1))
& is_pname(sK196(X0,X1)) )
| ~ sP20(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196,sK197])],[f4521,f4522]) ).
fof(f4522,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK196(X0,X1)),sK197(X0,X1))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK197(X0,X1)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),sK197(X0,X1)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK197(X0,X1)))
& is_fun_pname_bool(sK197(X0,X1))
& is_pname(sK196(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f4521,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ sP20(X0,X1) ),
inference(rectify,[],[f4520]) ).
fof(f4520,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ sP20(X0,X1) ),
inference(nnf_transformation,[],[f3946]) ).
fof(f14694,plain,
spl263_918,
inference(avatar_split_clause,[],[f6306,f14692]) ).
fof(f14692,plain,
( spl263_918
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK187(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_918])]) ).
fof(f6306,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK187(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4503]) ).
fof(f14690,plain,
spl263_917,
inference(avatar_split_clause,[],[f6211,f14688]) ).
fof(f14688,plain,
( spl263_917
<=> ! [X2,X0,X1] :
( is_pname(sK158(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_917])]) ).
fof(f6211,plain,
! [X2,X0,X1] :
( is_pname(sK158(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4447]) ).
fof(f14686,plain,
spl263_916,
inference(avatar_split_clause,[],[f6208,f14684]) ).
fof(f14684,plain,
( spl263_916
<=> ! [X2,X0,X1] :
( is_pname(sK157(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_916])]) ).
fof(f6208,plain,
! [X2,X0,X1] :
( is_pname(sK157(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4443]) ).
fof(f14682,plain,
spl263_915,
inference(avatar_split_clause,[],[f5950,f14680]) ).
fof(f14680,plain,
( spl263_915
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK155(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_915])]) ).
fof(f5950,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK155(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4357]) ).
fof(f4357,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK155(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f4355,f4356]) ).
fof(f4356,plain,
! [X0,X1] :
( ? [X3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3) = X1
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK155(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f4355,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 )
& ( ? [X3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(rectify,[],[f4354]) ).
fof(f4354,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 )
& ( ? [X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2105]) ).
fof(f2105,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
<=> ? [X2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 ),
inference(rectify,[],[f931]) ).
fof(f931,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16))
<=> ? [X118] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X118) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14678,plain,
spl263_914,
inference(avatar_split_clause,[],[f5935,f14676]) ).
fof(f14676,plain,
( spl263_914
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_914])]) ).
fof(f5935,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f4336]) ).
fof(f4336,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(flattening,[],[f4335]) ).
fof(f4335,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f2098]) ).
fof(f2098,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(rectify,[],[f1157]) ).
fof(f1157,axiom,
! [X55,X138] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X55),X138))
<=> ( X55 != X138
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X55),X138)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14674,plain,
spl263_913,
inference(avatar_split_clause,[],[f5785,f14672]) ).
fof(f14672,plain,
( spl263_913
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,sK137(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_913])]) ).
fof(f5785,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK137(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f4257]) ).
fof(f14670,plain,
spl263_912,
inference(avatar_split_clause,[],[f5766,f14668]) ).
fof(f14668,plain,
( spl263_912
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_912])]) ).
fof(f5766,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3177]) ).
fof(f3177,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(flattening,[],[f3176]) ).
fof(f3176,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2007]) ).
fof(f2007,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
=> X0 = X1 ) ),
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X59,X60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X59),X60))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X60),X59))
=> X59 = X60 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14666,plain,
( spl263_911
| ~ spl263_416
| ~ spl263_855 ),
inference(avatar_split_clause,[],[f14267,f13416,f9907,f14664]) ).
fof(f14664,plain,
( spl263_911
<=> ! [X0,X1] : sP35(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_911])]) ).
fof(f9907,plain,
( spl263_416
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_416])]) ).
fof(f14267,plain,
( ! [X0,X1] : sP35(X0,X0,X1)
| ~ spl263_416
| ~ spl263_855 ),
inference(resolution,[],[f13417,f9908]) ).
fof(f9908,plain,
( ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
| ~ spl263_416 ),
inference(avatar_component_clause,[],[f9907]) ).
fof(f14662,plain,
spl263_910,
inference(avatar_split_clause,[],[f5765,f14660]) ).
fof(f14660,plain,
( spl263_910
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_910])]) ).
fof(f5765,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3175]) ).
fof(f3175,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(flattening,[],[f3174]) ).
fof(f3174,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2006]) ).
fof(f2006,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( X0 != X1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
inference(rectify,[],[f997]) ).
fof(f997,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> ( X13 != X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14658,plain,
spl263_909,
inference(avatar_split_clause,[],[f5756,f14656]) ).
fof(f14656,plain,
( spl263_909
<=> ! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK136(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_909])]) ).
fof(f5756,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK136(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4253]) ).
fof(f4253,plain,
! [X0,X1] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK136(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK136(X0,X1))) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f3165,f4252]) ).
fof(f4252,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK136(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK136(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f3165,plain,
! [X0,X1] :
( ? [X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1997]) ).
fof(f1997,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ? [X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
inference(rectify,[],[f1078]) ).
fof(f1078,axiom,
! [X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ? [X118] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X118) = X23
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X118)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14654,plain,
spl263_908,
inference(avatar_split_clause,[],[f5738,f14652]) ).
fof(f14652,plain,
( spl263_908
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_908])]) ).
fof(f5738,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f3146]) ).
fof(f3146,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(flattening,[],[f3145]) ).
fof(f3145,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(ennf_transformation,[],[f1982]) ).
fof(f1982,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
=> X0 = X1 ) ),
inference(rectify,[],[f1154]) ).
fof(f1154,axiom,
! [X97,X134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X97),X134))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X134),X97))
=> X97 = X134 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14650,plain,
spl263_907,
inference(avatar_split_clause,[],[f5731,f14648]) ).
fof(f14648,plain,
( spl263_907
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_907])]) ).
fof(f5731,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f3137]) ).
fof(f3137,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(flattening,[],[f3136]) ).
fof(f3136,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(ennf_transformation,[],[f1976]) ).
fof(f1976,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
=> X0 = X1 ) ),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X38,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X38),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X38))
=> X10 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14646,plain,
spl263_906,
inference(avatar_split_clause,[],[f5723,f14644]) ).
fof(f14644,plain,
( spl263_906
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_906])]) ).
fof(f5723,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f3126]) ).
fof(f3126,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
inference(flattening,[],[f3125]) ).
fof(f3125,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
inference(ennf_transformation,[],[f1969]) ).
fof(f1969,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
=> X0 = X1 ) ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X4,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X4))
=> X4 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14642,plain,
spl263_905,
inference(avatar_split_clause,[],[f5692,f14640]) ).
fof(f14640,plain,
( spl263_905
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK133(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_905])]) ).
fof(f5692,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK133(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(cnf_transformation,[],[f4241]) ).
fof(f4241,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ( ~ hBOOL(hAPP_nat_bool(X0,sK133(X0)))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK133(X0)))) )
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f3086,f4240]) ).
fof(f4240,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK133(X0)))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK133(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f3086,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(flattening,[],[f3085]) ).
fof(f3085,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(ennf_transformation,[],[f1942]) ).
fof(f1942,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
=> ( ! [X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2)))
=> hBOOL(hAPP_nat_bool(X0,X2)) )
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
inference(rectify,[],[f1081]) ).
fof(f1081,axiom,
! [X12,X15] :
( hBOOL(hAPP_nat_bool(X12,X15))
=> ( ! [X28] :
( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(suc,X28)))
=> hBOOL(hAPP_nat_bool(X12,X28)) )
=> hBOOL(hAPP_nat_bool(X12,zero_zero_nat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14638,plain,
spl263_904,
inference(avatar_split_clause,[],[f5691,f14636]) ).
fof(f14636,plain,
( spl263_904
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK132(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_904])]) ).
fof(f5691,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK132(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4239]) ).
fof(f4239,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK132(X1))))
& hBOOL(hAPP_nat_bool(X1,sK132(X1))) )
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f3084,f4238]) ).
fof(f4238,plain,
! [X1] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
& hBOOL(hAPP_nat_bool(X1,X2)) )
=> ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK132(X1))))
& hBOOL(hAPP_nat_bool(X1,sK132(X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f3084,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
& hBOOL(hAPP_nat_bool(X1,X2)) )
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(flattening,[],[f3083]) ).
fof(f3083,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
& hBOOL(hAPP_nat_bool(X1,X2)) )
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(ennf_transformation,[],[f1941]) ).
fof(f1941,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
=> ( ! [X2] :
( hBOOL(hAPP_nat_bool(X1,X2))
=> hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2))) )
=> hBOOL(hAPP_nat_bool(X1,X0)) ) ),
inference(rectify,[],[f1083]) ).
fof(f1083,axiom,
! [X16,X12] :
( hBOOL(hAPP_nat_bool(X12,zero_zero_nat))
=> ( ! [X28] :
( hBOOL(hAPP_nat_bool(X12,X28))
=> hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(suc,X28))) )
=> hBOOL(hAPP_nat_bool(X12,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14634,plain,
spl263_903,
inference(avatar_split_clause,[],[f5416,f14632]) ).
fof(f14632,plain,
( spl263_903
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_903])]) ).
fof(f5416,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2823]) ).
fof(f2823,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1 ),
inference(flattening,[],[f2822]) ).
fof(f2822,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f1749]) ).
fof(f1749,plain,
! [X0,X1] :
( X0 != X1
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ) ),
inference(rectify,[],[f967]) ).
fof(f967,axiom,
! [X17,X18] :
( X17 != X18
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14630,plain,
spl263_902,
inference(avatar_split_clause,[],[f5413,f14628]) ).
fof(f14628,plain,
( spl263_902
<=> ! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_902])]) ).
fof(f5413,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2817]) ).
fof(f2817,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(flattening,[],[f2816]) ).
fof(f2816,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f1746]) ).
fof(f1746,plain,
! [X0,X1] :
( is_fun_a_bool(X1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1 ) ),
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X7,X4] :
( is_fun_a_bool(X4)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),X4))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X4) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14626,plain,
spl263_901,
inference(avatar_split_clause,[],[f5390,f14624]) ).
fof(f14624,plain,
( spl263_901
<=> ! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_901])]) ).
fof(f5390,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2800]) ).
fof(f2800,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(flattening,[],[f2799]) ).
fof(f2799,plain,
! [X0,X1] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1 ) ),
inference(rectify,[],[f507]) ).
fof(f507,axiom,
! [X7,X4] :
( is_fun_pname_bool(X4)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),X4))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X4) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14622,plain,
( spl263_900
| ~ spl263_145
| ~ spl263_853 ),
inference(avatar_split_clause,[],[f14253,f13408,f8483,f14620]) ).
fof(f14620,plain,
( spl263_900
<=> ! [X0,X1] : sP34(X0,bot_bot_fun_int_bool,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_900])]) ).
fof(f13408,plain,
( spl263_853
<=> ! [X2,X0,X1] :
( sP34(X2,X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_853])]) ).
fof(f14253,plain,
( ! [X0,X1] : sP34(X0,bot_bot_fun_int_bool,X1)
| ~ spl263_145
| ~ spl263_853 ),
inference(resolution,[],[f13409,f8484]) ).
fof(f13409,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
| sP34(X2,X0,X1) )
| ~ spl263_853 ),
inference(avatar_component_clause,[],[f13408]) ).
fof(f14618,plain,
spl263_899,
inference(avatar_split_clause,[],[f5343,f14616]) ).
fof(f14616,plain,
( spl263_899
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_899])]) ).
fof(f5343,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
| X0 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(rectify,[],[f1156]) ).
fof(f1156,axiom,
! [X17,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X18),X17))
| X17 = X18
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14614,plain,
spl263_898,
inference(avatar_split_clause,[],[f5309,f14612]) ).
fof(f14612,plain,
( spl263_898
<=> ! [X0,X1] :
( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_898])]) ).
fof(f5309,plain,
! [X0,X1] :
( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2757]) ).
fof(f14610,plain,
spl263_897,
inference(avatar_split_clause,[],[f5270,f14608]) ).
fof(f14608,plain,
( spl263_897
<=> ! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_897])]) ).
fof(f5270,plain,
! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)),
inference(cnf_transformation,[],[f1666]) ).
fof(f1666,plain,
! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)),
inference(rectify,[],[f926]) ).
fof(f926,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(suc,X13)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14606,plain,
spl263_896,
inference(avatar_split_clause,[],[f5269,f14604]) ).
fof(f14604,plain,
( spl263_896
<=> ! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_896])]) ).
fof(f5269,plain,
! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1),
inference(cnf_transformation,[],[f1665]) ).
fof(f1665,plain,
! [X0,X1] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1),
inference(rectify,[],[f927]) ).
fof(f927,axiom,
! [X14,X13] : hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X14)),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14602,plain,
spl263_895,
inference(avatar_split_clause,[],[f5268,f14600]) ).
fof(f14600,plain,
( spl263_895
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_895])]) ).
fof(f5268,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)),
inference(cnf_transformation,[],[f1664]) ).
fof(f1664,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)),
inference(rectify,[],[f279]) ).
fof(f279,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X14)),hAPP_nat_nat(suc,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14598,plain,
spl263_894,
inference(avatar_split_clause,[],[f5267,f14596]) ).
fof(f14596,plain,
( spl263_894
<=> ! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_894])]) ).
fof(f5267,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),
inference(cnf_transformation,[],[f1663]) ).
fof(f1663,plain,
! [X0,X1] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),
inference(rectify,[],[f489]) ).
fof(f489,axiom,
! [X10,X4] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14594,plain,
spl263_893,
inference(avatar_split_clause,[],[f5073,f14592]) ).
fof(f14592,plain,
( spl263_893
<=> ! [X0] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_893])]) ).
fof(f5073,plain,
! [X0] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f2741]) ).
fof(f2741,plain,
! [X0] :
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(ennf_transformation,[],[f1568]) ).
fof(f1568,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0 ),
inference(rectify,[],[f1074]) ).
fof(f1074,axiom,
! [X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),one_one_nat)) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14581,plain,
spl263_892,
inference(avatar_split_clause,[],[f4811,f14578]) ).
fof(f14578,plain,
( spl263_892
<=> hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_892])]) ).
fof(f4811,plain,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
inference(cnf_transformation,[],[f1412]) ).
fof(f1412,axiom,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14565,plain,
( spl263_891
| ~ spl263_413
| ~ spl263_853 ),
inference(avatar_split_clause,[],[f14252,f13408,f9895,f14563]) ).
fof(f14563,plain,
( spl263_891
<=> ! [X0,X1] : sP34(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_891])]) ).
fof(f9895,plain,
( spl263_413
<=> ! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_413])]) ).
fof(f14252,plain,
( ! [X0,X1] : sP34(X0,X0,X1)
| ~ spl263_413
| ~ spl263_853 ),
inference(resolution,[],[f13409,f9896]) ).
fof(f9896,plain,
( ! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
| ~ spl263_413 ),
inference(avatar_component_clause,[],[f9895]) ).
fof(f14481,plain,
( spl263_890
| ~ spl263_144
| ~ spl263_851 ),
inference(avatar_split_clause,[],[f14234,f13400,f8479,f14479]) ).
fof(f14479,plain,
( spl263_890
<=> ! [X0,X1] : sP33(X0,bot_bot_fun_a_bool,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_890])]) ).
fof(f13400,plain,
( spl263_851
<=> ! [X2,X0,X1] :
( sP33(X2,X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_851])]) ).
fof(f14234,plain,
( ! [X0,X1] : sP33(X0,bot_bot_fun_a_bool,X1)
| ~ spl263_144
| ~ spl263_851 ),
inference(resolution,[],[f13401,f8480]) ).
fof(f13401,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
| sP33(X2,X0,X1) )
| ~ spl263_851 ),
inference(avatar_component_clause,[],[f13400]) ).
fof(f14278,plain,
( spl263_889
| ~ spl263_410
| ~ spl263_851 ),
inference(avatar_split_clause,[],[f14233,f13400,f9883,f14276]) ).
fof(f14276,plain,
( spl263_889
<=> ! [X0,X1] : sP33(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_889])]) ).
fof(f9883,plain,
( spl263_410
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_410])]) ).
fof(f14233,plain,
( ! [X0,X1] : sP33(X0,X0,X1)
| ~ spl263_410
| ~ spl263_851 ),
inference(resolution,[],[f13401,f9884]) ).
fof(f9884,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
| ~ spl263_410 ),
inference(avatar_component_clause,[],[f9883]) ).
fof(f14170,plain,
( spl263_888
| ~ spl263_36
| ~ spl263_113 ),
inference(avatar_split_clause,[],[f8398,f8310,f7956,f14168]) ).
fof(f14168,plain,
( spl263_888
<=> ! [X0] :
( ~ sP10(X0)
| sP3(sK111(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_888])]) ).
fof(f8398,plain,
( ! [X0] :
( ~ sP10(X0)
| sP3(sK111(X0)) )
| ~ spl263_36
| ~ spl263_113 ),
inference(resolution,[],[f8311,f7957]) ).
fof(f13890,plain,
( spl263_887
| ~ spl263_37
| ~ spl263_111 ),
inference(avatar_split_clause,[],[f8397,f8302,f7960,f13888]) ).
fof(f13888,plain,
( spl263_887
<=> ! [X0] :
( ~ sP9(X0)
| sP5(sK94(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_887])]) ).
fof(f8302,plain,
( spl263_111
<=> ! [X0] :
( is_fun_a_bool(sK94(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_111])]) ).
fof(f8397,plain,
( ! [X0] :
( ~ sP9(X0)
| sP5(sK94(X0)) )
| ~ spl263_37
| ~ spl263_111 ),
inference(resolution,[],[f8303,f7961]) ).
fof(f8303,plain,
( ! [X0] :
( is_fun_a_bool(sK94(X0))
| ~ sP9(X0) )
| ~ spl263_111 ),
inference(avatar_component_clause,[],[f8302]) ).
fof(f13833,plain,
( spl263_886
| ~ spl263_38
| ~ spl263_111 ),
inference(avatar_split_clause,[],[f8396,f8302,f7964,f13831]) ).
fof(f13831,plain,
( spl263_886
<=> ! [X0] :
( ~ sP9(X0)
| sP7(sK94(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_886])]) ).
fof(f8396,plain,
( ! [X0] :
( ~ sP9(X0)
| sP7(sK94(X0)) )
| ~ spl263_38
| ~ spl263_111 ),
inference(resolution,[],[f8303,f7965]) ).
fof(f13793,plain,
( spl263_885
| ~ spl263_35
| ~ spl263_109 ),
inference(avatar_split_clause,[],[f8395,f8294,f7952,f13791]) ).
fof(f13791,plain,
( spl263_885
<=> ! [X0] :
( ~ sP8(X0)
| sP1(sK91(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_885])]) ).
fof(f8294,plain,
( spl263_109
<=> ! [X0] :
( is_fun_pname_bool(sK91(X0))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_109])]) ).
fof(f8395,plain,
( ! [X0] :
( ~ sP8(X0)
| sP1(sK91(X0)) )
| ~ spl263_35
| ~ spl263_109 ),
inference(resolution,[],[f8295,f7953]) ).
fof(f8295,plain,
( ! [X0] :
( is_fun_pname_bool(sK91(X0))
| ~ sP8(X0) )
| ~ spl263_109 ),
inference(avatar_component_clause,[],[f8294]) ).
fof(f13783,plain,
( spl263_884
| ~ spl263_36
| ~ spl263_109 ),
inference(avatar_split_clause,[],[f8394,f8294,f7956,f13781]) ).
fof(f13781,plain,
( spl263_884
<=> ! [X0] :
( ~ sP8(X0)
| sP3(sK91(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_884])]) ).
fof(f8394,plain,
( ! [X0] :
( ~ sP8(X0)
| sP3(sK91(X0)) )
| ~ spl263_36
| ~ spl263_109 ),
inference(resolution,[],[f8295,f7957]) ).
fof(f13658,plain,
( spl263_883
| ~ spl263_37
| ~ spl263_107 ),
inference(avatar_split_clause,[],[f8393,f8286,f7960,f13656]) ).
fof(f13656,plain,
( spl263_883
<=> ! [X0] :
( ~ sP4(X0)
| sP5(sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_883])]) ).
fof(f8286,plain,
( spl263_107
<=> ! [X0] :
( is_fun_a_bool(sK49(X0))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_107])]) ).
fof(f8393,plain,
( ! [X0] :
( ~ sP4(X0)
| sP5(sK49(X0)) )
| ~ spl263_37
| ~ spl263_107 ),
inference(resolution,[],[f8287,f7961]) ).
fof(f8287,plain,
( ! [X0] :
( is_fun_a_bool(sK49(X0))
| ~ sP4(X0) )
| ~ spl263_107 ),
inference(avatar_component_clause,[],[f8286]) ).
fof(f13554,plain,
( spl263_882
| ~ spl263_38
| ~ spl263_107 ),
inference(avatar_split_clause,[],[f8392,f8286,f7964,f13552]) ).
fof(f13552,plain,
( spl263_882
<=> ! [X0] :
( ~ sP4(X0)
| sP7(sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_882])]) ).
fof(f8392,plain,
( ! [X0] :
( ~ sP4(X0)
| sP7(sK49(X0)) )
| ~ spl263_38
| ~ spl263_107 ),
inference(resolution,[],[f8287,f7965]) ).
fof(f13526,plain,
spl263_881,
inference(avatar_split_clause,[],[f7706,f13524]) ).
fof(f13524,plain,
( spl263_881
<=> ! [X2,X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_881])]) ).
fof(f7706,plain,
! [X2,X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(forward_demodulation,[],[f6558,f7396]) ).
fof(f6558,plain,
! [X2,X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f3608]) ).
fof(f3608,plain,
! [X0,X1,X2] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f2442]) ).
fof(f2442,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2) ),
inference(rectify,[],[f772]) ).
fof(f772,axiom,
! [X31,X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> image_nat_int(cOMBK_int_nat(X31),X4) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),bot_bot_fun_int_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13522,plain,
spl263_880,
inference(avatar_split_clause,[],[f7703,f13520]) ).
fof(f13520,plain,
( spl263_880
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X1),X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_880])]) ).
fof(f7703,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X1),X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(forward_demodulation,[],[f7702,f6154]) ).
fof(f6154,plain,
! [X2,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2220]) ).
fof(f2220,plain,
! [X0,X1,X2] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)),
inference(rectify,[],[f1341]) ).
fof(f1341,axiom,
! [X158,X159,X160] : hAPP_a_bool(cOMBS_a_bool_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X158,X160),hAPP_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7702,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X1),X0),hAPP_a_bool(X2,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(forward_demodulation,[],[f6530,f6102]) ).
fof(f6102,plain,
! [X2,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2168]) ).
fof(f2168,plain,
! [X0,X1,X2] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)),
inference(rectify,[],[f1366]) ).
fof(f1366,axiom,
! [X158,X159,X160] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6530,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X0)),hAPP_a_bool(X2,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f3561]) ).
fof(f3561,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X0)),hAPP_a_bool(X2,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f2414]) ).
fof(f2414,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X0)),hAPP_a_bool(X2,X0))) ),
inference(rectify,[],[f556]) ).
fof(f556,axiom,
! [X10,X8,X68] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),X68))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X8,X10)),hAPP_a_bool(X68,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13518,plain,
spl263_879,
inference(avatar_split_clause,[],[f7686,f13516]) ).
fof(f13516,plain,
( spl263_879
<=> ! [X2,X0,X1] :
( hAPP_fun_a_bool_a(X2,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0
| ~ hBOOL(finite_folding_one_a(X1,X2))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_879])]) ).
fof(f7686,plain,
! [X2,X0,X1] :
( hAPP_fun_a_bool_a(X2,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0
| ~ hBOOL(finite_folding_one_a(X1,X2))
| ~ is_a(X0) ),
inference(forward_demodulation,[],[f6207,f4966]) ).
fof(f6207,plain,
! [X2,X0,X1] :
( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0
| ~ hBOOL(finite_folding_one_a(X1,X2))
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f3288]) ).
fof(f3288,plain,
! [X0,X1,X2] :
( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0
| ~ hBOOL(finite_folding_one_a(X1,X2))
| ~ is_a(X0) ),
inference(flattening,[],[f3287]) ).
fof(f3287,plain,
! [X0,X1,X2] :
( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0
| ~ hBOOL(finite_folding_one_a(X1,X2))
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2266]) ).
fof(f2266,plain,
! [X0,X1,X2] :
( is_a(X0)
=> ( hBOOL(finite_folding_one_a(X1,X2))
=> hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ) ),
inference(rectify,[],[f855]) ).
fof(f855,axiom,
! [X10,X8,X6] :
( is_a(X10)
=> ( hBOOL(finite_folding_one_a(X8,X6))
=> hAPP_fun_a_bool_a(X6,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool)) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13514,plain,
( spl263_878
| ~ spl263_37
| ~ spl263_105 ),
inference(avatar_split_clause,[],[f8389,f8278,f7960,f13512]) ).
fof(f13512,plain,
( spl263_878
<=> ! [X0] :
( ~ is_fun_a_bool(X0)
| sP5(collect_a(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_878])]) ).
fof(f8278,plain,
( spl263_105
<=> ! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_105])]) ).
fof(f8389,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| sP5(collect_a(X0)) )
| ~ spl263_37
| ~ spl263_105 ),
inference(resolution,[],[f8279,f7961]) ).
fof(f8279,plain,
( ! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) )
| ~ spl263_105 ),
inference(avatar_component_clause,[],[f8278]) ).
fof(f13510,plain,
spl263_877,
inference(avatar_split_clause,[],[f7626,f13508]) ).
fof(f13508,plain,
( spl263_877
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_877])]) ).
fof(f7626,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
inference(forward_demodulation,[],[f6014,f4957]) ).
fof(f4957,plain,
! [X0] : hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),
inference(cnf_transformation,[],[f1503]) ).
fof(f1503,plain,
! [X0] : hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),
inference(rectify,[],[f1020]) ).
fof(f1020,axiom,
! [X29] : hAPP_n1699378549t_bool(ord_less_nat,X29) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6014,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f4395]) ).
fof(f4395,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) )
& ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
inference(nnf_transformation,[],[f2133]) ).
fof(f2133,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
<=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
inference(rectify,[],[f596]) ).
fof(f596,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X24)),X16))
<=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X24)),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13506,plain,
spl263_876,
inference(avatar_split_clause,[],[f7625,f13504]) ).
fof(f13504,plain,
( spl263_876
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_876])]) ).
fof(f7625,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
inference(forward_demodulation,[],[f6015,f4957]) ).
fof(f6015,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
inference(cnf_transformation,[],[f4395]) ).
fof(f13502,plain,
spl263_875,
inference(avatar_split_clause,[],[f7472,f13500]) ).
fof(f13500,plain,
( spl263_875
<=> ! [X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X1)
| bot_bo844097828e_bool = X1
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_875])]) ).
fof(f7472,plain,
! [X0,X1] :
( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X1)
| bot_bo844097828e_bool = X1
| ~ is_fun_pname_bool(X1) ),
inference(forward_demodulation,[],[f5379,f4966]) ).
fof(f5379,plain,
! [X0,X1] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1)
| bot_bo844097828e_bool = X1
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2794]) ).
fof(f2794,plain,
! [X0,X1] :
( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1)
| bot_bo844097828e_bool = X1 )
& ( bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X0),X1)
| bot_bo844097828e_bool != X1 ) )
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f1737]) ).
fof(f1737,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( ( bot_bo844097828e_bool != X1
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1) )
& ( bot_bo844097828e_bool = X1
=> bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X0),X1) ) ) ),
inference(rectify,[],[f775]) ).
fof(f775,axiom,
! [X31,X4] :
( is_fun_pname_bool(X4)
=> ( ( bot_bo844097828e_bool != X4
=> image_pname_a(cOMBK_a_pname(X31),X4) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),bot_bot_fun_a_bool) )
& ( bot_bo844097828e_bool = X4
=> bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X31),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13498,plain,
spl263_874,
inference(avatar_split_clause,[],[f7404,f13496]) ).
fof(f13496,plain,
( spl263_874
<=> ! [X0] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)) = image_nat_int(semiri1621563631at_int,cOMBB_int_bool_nat(X0,semiri1621563631at_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_874])]) ).
fof(f7404,plain,
! [X0] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)) = image_nat_int(semiri1621563631at_int,cOMBB_int_bool_nat(X0,semiri1621563631at_int)),
inference(forward_demodulation,[],[f7037,f4876]) ).
fof(f7037,plain,
! [X0] : image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)),
inference(definition_unfolding,[],[f4979,f4830]) ).
fof(f4979,plain,
! [X0] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X0)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))),
inference(cnf_transformation,[],[f1525]) ).
fof(f1525,plain,
! [X0] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X0)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))),
inference(rectify,[],[f1224]) ).
fof(f1224,axiom,
! [X12] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X12)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X12,semiri1621563631at_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13491,plain,
( spl263_873
| ~ spl263_239
| ~ spl263_528
| ~ spl263_872 ),
inference(avatar_split_clause,[],[f13487,f13484,f10617,f8904,f13489]) ).
fof(f13489,plain,
( spl263_873
<=> ! [X0,X1] :
( pls != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_873])]) ).
fof(f8904,plain,
( spl263_239
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_239])]) ).
fof(f10617,plain,
( spl263_528
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_528])]) ).
fof(f13484,plain,
( spl263_872
<=> ! [X0,X1,X3] :
( X0 = X1
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_872])]) ).
fof(f13487,plain,
( ! [X0,X1] :
( pls != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)
| X0 = X1 )
| ~ spl263_239
| ~ spl263_528
| ~ spl263_872 ),
inference(forward_demodulation,[],[f13485,f10994]) ).
fof(f10994,plain,
( ! [X0] : pls = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X0)
| ~ spl263_239
| ~ spl263_528 ),
inference(superposition,[],[f10618,f8905]) ).
fof(f8905,plain,
( ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0
| ~ spl263_239 ),
inference(avatar_component_clause,[],[f8904]) ).
fof(f10618,plain,
( ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0
| ~ spl263_528 ),
inference(avatar_component_clause,[],[f10617]) ).
fof(f13485,plain,
( ! [X3,X0,X1] :
( X0 = X1
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) )
| ~ spl263_872 ),
inference(avatar_component_clause,[],[f13484]) ).
fof(f13486,plain,
spl263_872,
inference(avatar_split_clause,[],[f7354,f13484]) ).
fof(f7354,plain,
! [X3,X0,X1] :
( X0 = X1
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) ),
inference(equality_resolution,[],[f6960]) ).
fof(f6960,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X2 != X3
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ),
inference(cnf_transformation,[],[f4773]) ).
fof(f4773,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X1
| X2 != X3 )
& ( X2 = X3
| X0 != X1 ) )
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ),
inference(nnf_transformation,[],[f3889]) ).
fof(f3889,plain,
! [X0,X1,X2,X3] :
( ( X0 = X1
<=> X2 = X3 )
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ),
inference(ennf_transformation,[],[f2665]) ).
fof(f2665,plain,
! [X0,X1,X2,X3] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3)
=> ( X0 = X1
<=> X2 = X3 ) ),
inference(rectify,[],[f776]) ).
fof(f776,axiom,
! [X7,X30,X31,X72] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X7),X30) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X31),X72)
=> ( X7 = X30
<=> X31 = X72 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13482,plain,
spl263_871,
inference(avatar_split_clause,[],[f7260,f13480]) ).
fof(f13480,plain,
( spl263_871
<=> ! [X2,X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_871])]) ).
fof(f7260,plain,
! [X2,X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))),
inference(equality_resolution,[],[f5937]) ).
fof(f5937,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 ),
inference(cnf_transformation,[],[f4340]) ).
fof(f13478,plain,
spl263_870,
inference(avatar_split_clause,[],[f7152,f13476]) ).
fof(f13476,plain,
( spl263_870
<=> ! [X2,X1] :
( sP6(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_870])]) ).
fof(f7152,plain,
! [X2,X1] :
( sP6(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ),
inference(equality_resolution,[],[f5040]) ).
fof(f5040,plain,
! [X2,X0,X1] :
( sP6(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f4018]) ).
fof(f4018,plain,
! [X0] :
( ( sP6(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) )
& bot_bot_fun_a_bool != X0 ) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK50(X0)))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK51(X0)),sK50(X0)) = X0
& is_a(sK51(X0))
& is_fun_a_bool(sK50(X0)) )
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f4016,f4017]) ).
fof(f4017,plain,
! [X0] :
( ? [X3,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X3) = X0
& is_a(X4)
& is_fun_a_bool(X3) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK50(X0)))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK51(X0)),sK50(X0)) = X0
& is_a(sK51(X0))
& is_fun_a_bool(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4016,plain,
! [X0] :
( ( sP6(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) )
& bot_bot_fun_a_bool != X0 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X3) = X0
& is_a(X4)
& is_fun_a_bool(X3) )
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
inference(rectify,[],[f4015]) ).
fof(f4015,plain,
! [X0] :
( ( sP6(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) )
& bot_bot_fun_a_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0
& is_a(X2)
& is_fun_a_bool(X1) )
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
inference(flattening,[],[f4014]) ).
fof(f4014,plain,
! [X0] :
( ( sP6(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) )
& bot_bot_fun_a_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0
& is_a(X2)
& is_fun_a_bool(X1) )
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f3920]) ).
fof(f3920,plain,
! [X0] :
( sP6(X0)
<=> ( ? [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0
& is_a(X2)
& is_fun_a_bool(X1) )
| bot_bot_fun_a_bool = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f13474,plain,
spl263_869,
inference(avatar_split_clause,[],[f7146,f13472]) ).
fof(f13472,plain,
( spl263_869
<=> ! [X2,X1] :
( sP2(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_869])]) ).
fof(f7146,plain,
! [X2,X1] :
( sP2(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ),
inference(equality_resolution,[],[f5013]) ).
fof(f5013,plain,
! [X2,X0,X1] :
( sP2(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f3999]) ).
fof(f3999,plain,
! [X0] :
( ( sP2(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) )
& bot_bo844097828e_bool != X0 ) )
& ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(X0)))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK45(X0)),sK44(X0)) = X0
& is_pname(sK45(X0))
& is_fun_pname_bool(sK44(X0)) )
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f3997,f3998]) ).
fof(f3998,plain,
! [X0] :
( ? [X3,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X3) = X0
& is_pname(X4)
& is_fun_pname_bool(X3) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(X0)))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK45(X0)),sK44(X0)) = X0
& is_pname(sK45(X0))
& is_fun_pname_bool(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3997,plain,
! [X0] :
( ( sP2(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) )
& bot_bo844097828e_bool != X0 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X3) = X0
& is_pname(X4)
& is_fun_pname_bool(X3) )
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
inference(rectify,[],[f3996]) ).
fof(f3996,plain,
! [X0] :
( ( sP2(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) )
& bot_bo844097828e_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0
& is_pname(X2)
& is_fun_pname_bool(X1) )
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
inference(flattening,[],[f3995]) ).
fof(f3995,plain,
! [X0] :
( ( sP2(X0)
| ( ! [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) )
& bot_bo844097828e_bool != X0 ) )
& ( ? [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0
& is_pname(X2)
& is_fun_pname_bool(X1) )
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f3914]) ).
fof(f3914,plain,
! [X0] :
( sP2(X0)
<=> ( ? [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0
& is_pname(X2)
& is_fun_pname_bool(X1) )
| bot_bo844097828e_bool = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f13470,plain,
( spl263_868
| ~ spl263_38
| ~ spl263_105 ),
inference(avatar_split_clause,[],[f8388,f8278,f7964,f13468]) ).
fof(f13468,plain,
( spl263_868
<=> ! [X0] :
( ~ is_fun_a_bool(X0)
| sP7(collect_a(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_868])]) ).
fof(f8388,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| sP7(collect_a(X0)) )
| ~ spl263_38
| ~ spl263_105 ),
inference(resolution,[],[f8279,f7965]) ).
fof(f13466,plain,
spl263_867,
inference(avatar_split_clause,[],[f7139,f13464]) ).
fof(f13464,plain,
( spl263_867
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,pls))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_867])]) ).
fof(f7139,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,pls))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ sP36(X0,X1,X2) ),
inference(definition_unfolding,[],[f6846,f4830]) ).
fof(f6846,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f4736]) ).
fof(f13462,plain,
spl263_866,
inference(avatar_split_clause,[],[f7138,f13460]) ).
fof(f13460,plain,
( spl263_866
<=> ! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,pls))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_866])]) ).
fof(f7138,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,pls))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(definition_unfolding,[],[f6849,f4830]) ).
fof(f6849,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f4736]) ).
fof(f13458,plain,
spl263_865,
inference(avatar_split_clause,[],[f7134,f13456]) ).
fof(f13456,plain,
( spl263_865
<=> ! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(X2)
| ~ sP28(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_865])]) ).
fof(f7134,plain,
! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(X2)
| ~ sP28(X0,X1,X2) ),
inference(definition_unfolding,[],[f6723,f4830]) ).
fof(f6723,plain,
! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ sP28(X0,X1,X2) ),
inference(cnf_transformation,[],[f4642]) ).
fof(f4642,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ( ~ hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ( ~ hBOOL(X2)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) )
| ~ sP28(X0,X1,X2) ),
inference(rectify,[],[f4641]) ).
fof(f4641,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ( ~ hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ( ~ hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) )
| ~ sP28(X0,X2,X1) ),
inference(flattening,[],[f4640]) ).
fof(f4640,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ( ~ hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
& ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ( ~ hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) )
| ~ sP28(X0,X2,X1) ),
inference(nnf_transformation,[],[f3962]) ).
fof(f3962,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP28(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f13454,plain,
spl263_864,
inference(avatar_split_clause,[],[f7132,f13452]) ).
fof(f13452,plain,
( spl263_864
<=> ! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(X0)
| ~ sP28(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_864])]) ).
fof(f7132,plain,
! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(X0)
| ~ sP28(X0,X1,X2) ),
inference(definition_unfolding,[],[f6725,f4830]) ).
fof(f6725,plain,
! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X0)
| ~ sP28(X0,X1,X2) ),
inference(cnf_transformation,[],[f4642]) ).
fof(f13450,plain,
spl263_863,
inference(avatar_split_clause,[],[f7129,f13448]) ).
fof(f13448,plain,
( spl263_863
<=> ! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_863])]) ).
fof(f7129,plain,
! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP27(X0,X1,X2) ),
inference(definition_unfolding,[],[f6716,f4830]) ).
fof(f6716,plain,
! [X2,X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f4637]) ).
fof(f4637,plain,
! [X0,X1,X2] :
( ( ( ( hBOOL(X2)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP27(X0,X1,X2) ),
inference(rectify,[],[f4636]) ).
fof(f4636,plain,
! [X0,X2,X1] :
( ( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
& ( ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP27(X0,X2,X1) ),
inference(flattening,[],[f4635]) ).
fof(f4635,plain,
! [X0,X2,X1] :
( ( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
& ( ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP27(X0,X2,X1) ),
inference(nnf_transformation,[],[f3960]) ).
fof(f3960,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP27(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f13446,plain,
spl263_862,
inference(avatar_split_clause,[],[f7127,f13444]) ).
fof(f13444,plain,
( spl263_862
<=> ! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_862])]) ).
fof(f7127,plain,
! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP27(X0,X1,X2) ),
inference(definition_unfolding,[],[f6718,f4830]) ).
fof(f6718,plain,
! [X2,X0,X1] :
( hBOOL(X2)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f4637]) ).
fof(f13442,plain,
spl263_861,
inference(avatar_split_clause,[],[f7074,f13440]) ).
fof(f13440,plain,
( spl263_861
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_861])]) ).
fof(f7074,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
inference(definition_unfolding,[],[f5167,f4830]) ).
fof(f5167,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))) ),
inference(cnf_transformation,[],[f4125]) ).
fof(f4125,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))) ) ),
inference(nnf_transformation,[],[f1613]) ).
fof(f1613,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(rectify,[],[f1233]) ).
fof(f1233,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13438,plain,
spl263_860,
inference(avatar_split_clause,[],[f7073,f13436]) ).
fof(f13436,plain,
( spl263_860
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_860])]) ).
fof(f7073,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(definition_unfolding,[],[f5168,f4830]) ).
fof(f5168,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f4125]) ).
fof(f13434,plain,
spl263_859,
inference(avatar_split_clause,[],[f6852,f13432]) ).
fof(f6852,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
| ~ sP36(X0,X2,X1) ),
inference(cnf_transformation,[],[f4737]) ).
fof(f4737,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
| ~ sP36(X0,X2,X1) )
& ( sP36(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ) ),
inference(nnf_transformation,[],[f3979]) ).
fof(f3979,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
<=> sP36(X0,X2,X1) ),
inference(definition_folding,[],[f3818,f3978]) ).
fof(f3818,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
<=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
inference(ennf_transformation,[],[f2601]) ).
fof(f2601,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_int_bool(X0,zero_zero_int)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
=> hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))) ) ) ),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X12,X10,X38] :
( hBOOL(hAPP_int_bool(X12,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X10),X38))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X10),X38))
=> hBOOL(hAPP_int_bool(X12,zero_zero_int)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X38),X10))
=> hBOOL(hAPP_int_bool(X12,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X10)),hAPP_nat_int(semiri1621563631at_int,X38)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13430,plain,
spl263_858,
inference(avatar_split_clause,[],[f6851,f13428]) ).
fof(f13428,plain,
( spl263_858
<=> ! [X2,X0,X1] :
( sP36(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_858])]) ).
fof(f6851,plain,
! [X2,X0,X1] :
( sP36(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ),
inference(cnf_transformation,[],[f4737]) ).
fof(f13426,plain,
( spl263_857
| ~ spl263_35
| ~ spl263_103 ),
inference(avatar_split_clause,[],[f8387,f8270,f7952,f13424]) ).
fof(f13424,plain,
( spl263_857
<=> ! [X0] :
( ~ sP0(X0)
| sP1(sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_857])]) ).
fof(f8270,plain,
( spl263_103
<=> ! [X0] :
( is_fun_pname_bool(sK43(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_103])]) ).
fof(f8387,plain,
( ! [X0] :
( ~ sP0(X0)
| sP1(sK43(X0)) )
| ~ spl263_35
| ~ spl263_103 ),
inference(resolution,[],[f8271,f7953]) ).
fof(f8271,plain,
( ! [X0] :
( is_fun_pname_bool(sK43(X0))
| ~ sP0(X0) )
| ~ spl263_103 ),
inference(avatar_component_clause,[],[f8270]) ).
fof(f13422,plain,
spl263_856,
inference(avatar_split_clause,[],[f6841,f13420]) ).
fof(f13420,plain,
( spl263_856
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
| ~ sP35(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_856])]) ).
fof(f6841,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
| ~ sP35(X2,X0,X1) ),
inference(cnf_transformation,[],[f4731]) ).
fof(f4731,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
| ~ sP35(X2,X0,X1) )
& ( sP35(X2,X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
inference(nnf_transformation,[],[f3977]) ).
fof(f3977,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
<=> sP35(X2,X0,X1) ),
inference(definition_folding,[],[f3817,f3976]) ).
fof(f3817,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ) ),
inference(ennf_transformation,[],[f2599]) ).
fof(f2599,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
<=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2)) ) ) ),
inference(rectify,[],[f674]) ).
fof(f674,axiom,
! [X4,X10,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),X9)))
<=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool))),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13418,plain,
spl263_855,
inference(avatar_split_clause,[],[f6840,f13416]) ).
fof(f6840,plain,
! [X2,X0,X1] :
( sP35(X2,X0,X1)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
inference(cnf_transformation,[],[f4731]) ).
fof(f13414,plain,
spl263_854,
inference(avatar_split_clause,[],[f6824,f13412]) ).
fof(f13412,plain,
( spl263_854
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
| ~ sP34(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_854])]) ).
fof(f6824,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
| ~ sP34(X2,X0,X1) ),
inference(cnf_transformation,[],[f4721]) ).
fof(f4721,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
| ~ sP34(X2,X0,X1) )
& ( sP34(X2,X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
inference(nnf_transformation,[],[f3975]) ).
fof(f3975,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
<=> sP34(X2,X0,X1) ),
inference(definition_folding,[],[f3816,f3974]) ).
fof(f3816,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ) ),
inference(ennf_transformation,[],[f2595]) ).
fof(f2595,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
<=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2)) ) ) ),
inference(rectify,[],[f673]) ).
fof(f673,axiom,
! [X4,X10,X9] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),X9)))
<=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool))),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13410,plain,
spl263_853,
inference(avatar_split_clause,[],[f6823,f13408]) ).
fof(f6823,plain,
! [X2,X0,X1] :
( sP34(X2,X0,X1)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
inference(cnf_transformation,[],[f4721]) ).
fof(f13406,plain,
spl263_852,
inference(avatar_split_clause,[],[f6807,f13404]) ).
fof(f13404,plain,
( spl263_852
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
| ~ sP33(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_852])]) ).
fof(f6807,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
| ~ sP33(X2,X0,X1) ),
inference(cnf_transformation,[],[f4711]) ).
fof(f4711,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
| ~ sP33(X2,X0,X1) )
& ( sP33(X2,X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ) ),
inference(nnf_transformation,[],[f3973]) ).
fof(f3973,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
<=> sP33(X2,X0,X1) ),
inference(definition_folding,[],[f3815,f3972]) ).
fof(f3815,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ) ),
inference(ennf_transformation,[],[f2591]) ).
fof(f2591,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
<=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2)) ) ) ),
inference(rectify,[],[f672]) ).
fof(f672,axiom,
! [X4,X10,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),X9)))
<=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool))),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13402,plain,
spl263_851,
inference(avatar_split_clause,[],[f6806,f13400]) ).
fof(f6806,plain,
! [X2,X0,X1] :
( sP33(X2,X0,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
inference(cnf_transformation,[],[f4711]) ).
fof(f13398,plain,
spl263_850,
inference(avatar_split_clause,[],[f6790,f13396]) ).
fof(f13396,plain,
( spl263_850
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
| ~ sP32(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_850])]) ).
fof(f6790,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
| ~ sP32(X2,X0,X1) ),
inference(cnf_transformation,[],[f4701]) ).
fof(f4701,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
| ~ sP32(X2,X0,X1) )
& ( sP32(X2,X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ) ),
inference(nnf_transformation,[],[f3971]) ).
fof(f3971,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
<=> sP32(X2,X0,X1) ),
inference(definition_folding,[],[f3814,f3970]) ).
fof(f3814,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
<=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ) ),
inference(ennf_transformation,[],[f2587]) ).
fof(f2587,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
<=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2)) ) ) ),
inference(rectify,[],[f675]) ).
fof(f675,axiom,
! [X4,X10,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),X9)))
<=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X10),bot_bo844097828e_bool))),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13394,plain,
spl263_849,
inference(avatar_split_clause,[],[f6789,f13392]) ).
fof(f13392,plain,
( spl263_849
<=> ! [X2,X0,X1] :
( sP32(X2,X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_849])]) ).
fof(f6789,plain,
! [X2,X0,X1] :
( sP32(X2,X0,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
inference(cnf_transformation,[],[f4701]) ).
fof(f13390,plain,
spl263_848,
inference(avatar_split_clause,[],[f6773,f13388]) ).
fof(f13388,plain,
( spl263_848
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_848])]) ).
fof(f6773,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f13386,plain,
spl263_847,
inference(avatar_split_clause,[],[f6765,f13384]) ).
fof(f13384,plain,
( spl263_847
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ sP30(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_847])]) ).
fof(f6765,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f13382,plain,
( spl263_846
| ~ spl263_36
| ~ spl263_103 ),
inference(avatar_split_clause,[],[f8386,f8270,f7956,f13380]) ).
fof(f13380,plain,
( spl263_846
<=> ! [X0] :
( ~ sP0(X0)
| sP3(sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_846])]) ).
fof(f8386,plain,
( ! [X0] :
( ~ sP0(X0)
| sP3(sK43(X0)) )
| ~ spl263_36
| ~ spl263_103 ),
inference(resolution,[],[f8271,f7957]) ).
fof(f13378,plain,
spl263_845,
inference(avatar_split_clause,[],[f6680,f13376]) ).
fof(f13376,plain,
( spl263_845
<=> ! [X2,X0,X1] :
( X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_845])]) ).
fof(f6680,plain,
! [X2,X0,X1] :
( X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
inference(cnf_transformation,[],[f3748]) ).
fof(f3748,plain,
! [X0,X1,X2] :
( X0 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
inference(ennf_transformation,[],[f2543]) ).
fof(f2543,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)
=> X0 = X2 ),
inference(rectify,[],[f904]) ).
fof(f904,axiom,
! [X94,X95,X96] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X94),X95) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X96),X95)
=> X94 = X96 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13374,plain,
spl263_844,
inference(avatar_split_clause,[],[f6679,f13372]) ).
fof(f13372,plain,
( spl263_844
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_844])]) ).
fof(f6679,plain,
! [X2,X0,X1] :
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ),
inference(cnf_transformation,[],[f3747]) ).
fof(f3747,plain,
! [X0,X1,X2] :
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ),
inference(ennf_transformation,[],[f2542]) ).
fof(f2542,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)
=> X1 = X2 ),
inference(rectify,[],[f902]) ).
fof(f902,axiom,
! [X91,X92,X93] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X91),X92) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X91),X93)
=> X92 = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13370,plain,
spl263_843,
inference(avatar_split_clause,[],[f6678,f13368]) ).
fof(f13368,plain,
( spl263_843
<=> ! [X2,X0,X1] :
( X0 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_843])]) ).
fof(f6678,plain,
! [X2,X0,X1] :
( X0 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ),
inference(cnf_transformation,[],[f3746]) ).
fof(f3746,plain,
! [X0,X1,X2] :
( X0 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ),
inference(ennf_transformation,[],[f2541]) ).
fof(f2541,plain,
! [X0,X1,X2] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1)
=> X0 = X2 ),
inference(rectify,[],[f903]) ).
fof(f903,axiom,
! [X94,X95,X96] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X94),X95) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X96),X95)
=> X94 = X96 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13366,plain,
spl263_842,
inference(avatar_split_clause,[],[f6676,f13364]) ).
fof(f13364,plain,
( spl263_842
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_842])]) ).
fof(f6676,plain,
! [X2,X0,X1] :
( X1 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ),
inference(cnf_transformation,[],[f3744]) ).
fof(f3744,plain,
! [X0,X1,X2] :
( X1 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ),
inference(ennf_transformation,[],[f2539]) ).
fof(f2539,plain,
! [X0,X1,X2] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)
=> X1 = X2 ),
inference(rectify,[],[f899]) ).
fof(f899,axiom,
! [X88,X89,X90] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X88),X89) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X88),X90)
=> X89 = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13362,plain,
spl263_841,
inference(avatar_split_clause,[],[f6195,f13360]) ).
fof(f6195,plain,
! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| hBOOL(X2) ),
inference(cnf_transformation,[],[f3281]) ).
fof(f3281,plain,
! [X0,X1,X2] :
( ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| hBOOL(X2) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f2260]) ).
fof(f2260,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(X2)
=> hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
& ( hBOOL(X2)
=> hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) ) ),
inference(rectify,[],[f1245]) ).
fof(f1245,axiom,
! [X10,X38,X12] :
( ( ~ hBOOL(X12)
=> hAPP_nat_int(semiri1621563631at_int,X38) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X12),X10),X38)) )
& ( hBOOL(X12)
=> hAPP_nat_int(semiri1621563631at_int,X10) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X12),X10),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13358,plain,
spl263_840,
inference(avatar_split_clause,[],[f6194,f13356]) ).
fof(f13356,plain,
( spl263_840
<=> ! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_840])]) ).
fof(f6194,plain,
! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1))
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f3281]) ).
fof(f13354,plain,
spl263_839,
inference(avatar_split_clause,[],[f6051,f13352]) ).
fof(f13352,plain,
( spl263_839
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_839])]) ).
fof(f6051,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4417]) ).
fof(f13350,plain,
spl263_838,
inference(avatar_split_clause,[],[f6050,f13348]) ).
fof(f13348,plain,
( spl263_838
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_838])]) ).
fof(f6050,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4417]) ).
fof(f13346,plain,
spl263_837,
inference(avatar_split_clause,[],[f6048,f13344]) ).
fof(f13344,plain,
( spl263_837
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_837])]) ).
fof(f6048,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4415]) ).
fof(f13342,plain,
spl263_836,
inference(avatar_split_clause,[],[f6047,f13340]) ).
fof(f13340,plain,
( spl263_836
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_836])]) ).
fof(f6047,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4415]) ).
fof(f13338,plain,
( spl263_835
| ~ spl263_35
| ~ spl263_101 ),
inference(avatar_split_clause,[],[f8385,f8262,f7952,f13336]) ).
fof(f13336,plain,
( spl263_835
<=> ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP1(collect_pname(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_835])]) ).
fof(f8262,plain,
( spl263_101
<=> ! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_101])]) ).
fof(f8385,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP1(collect_pname(X0)) )
| ~ spl263_35
| ~ spl263_101 ),
inference(resolution,[],[f8263,f7953]) ).
fof(f8263,plain,
( ! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) )
| ~ spl263_101 ),
inference(avatar_component_clause,[],[f8262]) ).
fof(f13334,plain,
spl263_834,
inference(avatar_split_clause,[],[f6045,f13332]) ).
fof(f13332,plain,
( spl263_834
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_834])]) ).
fof(f6045,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4413]) ).
fof(f13330,plain,
spl263_833,
inference(avatar_split_clause,[],[f6044,f13328]) ).
fof(f13328,plain,
( spl263_833
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_833])]) ).
fof(f6044,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4413]) ).
fof(f13326,plain,
spl263_832,
inference(avatar_split_clause,[],[f6042,f13324]) ).
fof(f13324,plain,
( spl263_832
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_832])]) ).
fof(f6042,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4411]) ).
fof(f13322,plain,
spl263_831,
inference(avatar_split_clause,[],[f6041,f13320]) ).
fof(f13320,plain,
( spl263_831
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_831])]) ).
fof(f6041,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4411]) ).
fof(f13318,plain,
spl263_830,
inference(avatar_split_clause,[],[f6039,f13316]) ).
fof(f13316,plain,
( spl263_830
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_830])]) ).
fof(f6039,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4409]) ).
fof(f13314,plain,
spl263_829,
inference(avatar_split_clause,[],[f6038,f13312]) ).
fof(f13312,plain,
( spl263_829
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_829])]) ).
fof(f6038,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4409]) ).
fof(f13310,plain,
spl263_828,
inference(avatar_split_clause,[],[f6036,f13308]) ).
fof(f13308,plain,
( spl263_828
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_828])]) ).
fof(f6036,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4407]) ).
fof(f13306,plain,
spl263_827,
inference(avatar_split_clause,[],[f6035,f13304]) ).
fof(f13304,plain,
( spl263_827
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_827])]) ).
fof(f6035,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4407]) ).
fof(f13302,plain,
spl263_826,
inference(avatar_split_clause,[],[f6000,f13300]) ).
fof(f13300,plain,
( spl263_826
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_826])]) ).
fof(f6000,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f4384]) ).
fof(f4384,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
inference(nnf_transformation,[],[f2128]) ).
fof(f2128,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f1009]) ).
fof(f1009,axiom,
! [X24,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),hAPP_nat_nat(suc,X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13298,plain,
spl263_825,
inference(avatar_split_clause,[],[f5907,f13296]) ).
fof(f13296,plain,
( spl263_825
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_825])]) ).
fof(f5907,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ),
inference(cnf_transformation,[],[f4313]) ).
fof(f4313,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2085]) ).
fof(f2085,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ),
inference(rectify,[],[f972]) ).
fof(f972,axiom,
! [X24,X16] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X16))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),hAPP_nat_nat(suc,X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13294,plain,
( spl263_824
| ~ spl263_36
| ~ spl263_101 ),
inference(avatar_split_clause,[],[f8384,f8262,f7956,f13292]) ).
fof(f13292,plain,
( spl263_824
<=> ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP3(collect_pname(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_824])]) ).
fof(f8384,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| sP3(collect_pname(X0)) )
| ~ spl263_36
| ~ spl263_101 ),
inference(resolution,[],[f8263,f7957]) ).
fof(f13290,plain,
spl263_823,
inference(avatar_split_clause,[],[f5906,f13288]) ).
fof(f13288,plain,
( spl263_823
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_823])]) ).
fof(f5906,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4313]) ).
fof(f13286,plain,
spl263_822,
inference(avatar_split_clause,[],[f5860,f13284]) ).
fof(f13284,plain,
( spl263_822
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_822])]) ).
fof(f5860,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4286]) ).
fof(f4286,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147])],[f3277,f4285]) ).
fof(f4285,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3277,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f2071]) ).
fof(f2071,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ),
inference(rectify,[],[f585]) ).
fof(f585,axiom,
! [X9,X4] :
( ! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X9)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13282,plain,
spl263_821,
inference(avatar_split_clause,[],[f5859,f13280]) ).
fof(f13280,plain,
( spl263_821
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_821])]) ).
fof(f5859,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK147(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4286]) ).
fof(f13278,plain,
spl263_820,
inference(avatar_split_clause,[],[f5858,f13276]) ).
fof(f13276,plain,
( spl263_820
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_820])]) ).
fof(f5858,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4284]) ).
fof(f4284,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X0))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK146])],[f3276,f4283]) ).
fof(f4283,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X0))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3276,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
& hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
inference(ennf_transformation,[],[f2070]) ).
fof(f2070,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0)) ),
inference(rectify,[],[f584]) ).
fof(f584,axiom,
! [X9,X4] :
( ! [X29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X9)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13274,plain,
spl263_819,
inference(avatar_split_clause,[],[f5857,f13272]) ).
fof(f13272,plain,
( spl263_819
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_819])]) ).
fof(f5857,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK146(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4284]) ).
fof(f13270,plain,
spl263_818,
inference(avatar_split_clause,[],[f5853,f13268]) ).
fof(f13268,plain,
( spl263_818
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_818])]) ).
fof(f5853,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4278]) ).
fof(f4278,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X1))
& is_pname(sK144(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK144])],[f3274,f4277]) ).
fof(f4277,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X1))
& is_pname(sK144(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3274,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) ) ),
inference(flattening,[],[f3273]) ).
fof(f3273,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
& is_pname(X2) ) ),
inference(ennf_transformation,[],[f2068]) ).
fof(f2068,plain,
! [X0,X1] :
( ! [X2] :
( is_pname(X2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ),
inference(rectify,[],[f587]) ).
fof(f587,axiom,
! [X9,X4] :
( ! [X29] :
( is_pname(X29)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X9)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13266,plain,
spl263_817,
inference(avatar_split_clause,[],[f5852,f13264]) ).
fof(f13264,plain,
( spl263_817
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_817])]) ).
fof(f5852,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK144(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4278]) ).
fof(f13262,plain,
spl263_816,
inference(avatar_split_clause,[],[f5850,f13260]) ).
fof(f13260,plain,
( spl263_816
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_816])]) ).
fof(f5850,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4276]) ).
fof(f4276,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X1))
& is_a(sK143(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143])],[f3272,f4275]) ).
fof(f4275,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
& is_a(X2) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X1))
& is_a(sK143(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3272,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
& is_a(X2) ) ),
inference(flattening,[],[f3271]) ).
fof(f3271,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ? [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
& is_a(X2) ) ),
inference(ennf_transformation,[],[f2067]) ).
fof(f2067,plain,
! [X0,X1] :
( ! [X2] :
( is_a(X2)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ),
inference(rectify,[],[f586]) ).
fof(f586,axiom,
! [X9,X4] :
( ! [X29] :
( is_a(X29)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X4))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X9)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13258,plain,
spl263_815,
inference(avatar_split_clause,[],[f5849,f13256]) ).
fof(f13256,plain,
( spl263_815
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_815])]) ).
fof(f5849,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK143(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4276]) ).
fof(f13254,plain,
spl263_814,
inference(avatar_split_clause,[],[f5836,f13252]) ).
fof(f13252,plain,
( spl263_814
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_814])]) ).
fof(f5836,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f3263,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
inference(ennf_transformation,[],[f2059]) ).
fof(f2059,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0)))) ),
inference(rectify,[],[f218]) ).
fof(f218,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X11)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13250,plain,
( spl263_813
| ~ spl263_37
| ~ spl263_100 ),
inference(avatar_split_clause,[],[f8383,f8258,f7960,f13248]) ).
fof(f13248,plain,
( spl263_813
<=> ! [X0] :
( ~ is_bool(X0)
| sP5(cOMBK_bool_a(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_813])]) ).
fof(f8258,plain,
( spl263_100
<=> ! [X0] :
( is_fun_a_bool(cOMBK_bool_a(X0))
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_100])]) ).
fof(f8383,plain,
( ! [X0] :
( ~ is_bool(X0)
| sP5(cOMBK_bool_a(X0)) )
| ~ spl263_37
| ~ spl263_100 ),
inference(resolution,[],[f8259,f7961]) ).
fof(f8259,plain,
( ! [X0] :
( is_fun_a_bool(cOMBK_bool_a(X0))
| ~ is_bool(X0) )
| ~ spl263_100 ),
inference(avatar_component_clause,[],[f8258]) ).
fof(f13246,plain,
spl263_812,
inference(avatar_split_clause,[],[f5835,f13244]) ).
fof(f13244,plain,
( spl263_812
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_812])]) ).
fof(f5835,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f13242,plain,
spl263_811,
inference(avatar_split_clause,[],[f5834,f13240]) ).
fof(f13240,plain,
( spl263_811
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_811])]) ).
fof(f5834,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(cnf_transformation,[],[f3262]) ).
fof(f3262,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
inference(ennf_transformation,[],[f2058]) ).
fof(f2058,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0)))) ),
inference(rectify,[],[f223]) ).
fof(f223,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X11)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13238,plain,
spl263_810,
inference(avatar_split_clause,[],[f5833,f13236]) ).
fof(f13236,plain,
( spl263_810
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_810])]) ).
fof(f5833,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(cnf_transformation,[],[f3262]) ).
fof(f13234,plain,
spl263_809,
inference(avatar_split_clause,[],[f5832,f13232]) ).
fof(f13232,plain,
( spl263_809
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_809])]) ).
fof(f5832,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(cnf_transformation,[],[f3261]) ).
fof(f3261,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
inference(ennf_transformation,[],[f2057]) ).
fof(f2057,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f221]) ).
fof(f221,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X11)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13230,plain,
spl263_808,
inference(avatar_split_clause,[],[f5831,f13228]) ).
fof(f13228,plain,
( spl263_808
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_808])]) ).
fof(f5831,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(cnf_transformation,[],[f3261]) ).
fof(f13226,plain,
spl263_807,
inference(avatar_split_clause,[],[f5830,f13224]) ).
fof(f13224,plain,
( spl263_807
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_807])]) ).
fof(f5830,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(cnf_transformation,[],[f3260]) ).
fof(f3260,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
inference(ennf_transformation,[],[f2056]) ).
fof(f2056,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f222]) ).
fof(f222,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X11)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13222,plain,
spl263_806,
inference(avatar_split_clause,[],[f5829,f13220]) ).
fof(f13220,plain,
( spl263_806
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_806])]) ).
fof(f5829,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(cnf_transformation,[],[f3260]) ).
fof(f13218,plain,
spl263_805,
inference(avatar_split_clause,[],[f5828,f13216]) ).
fof(f13216,plain,
( spl263_805
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_805])]) ).
fof(f5828,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(cnf_transformation,[],[f3259]) ).
fof(f3259,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ) ),
inference(ennf_transformation,[],[f2055]) ).
fof(f2055,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X11)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13214,plain,
spl263_804,
inference(avatar_split_clause,[],[f5827,f13212]) ).
fof(f13212,plain,
( spl263_804
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_804])]) ).
fof(f5827,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(cnf_transformation,[],[f3259]) ).
fof(f13210,plain,
spl263_803,
inference(avatar_split_clause,[],[f5826,f13208]) ).
fof(f13208,plain,
( spl263_803
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_803])]) ).
fof(f5826,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ),
inference(cnf_transformation,[],[f3258]) ).
fof(f3258,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
& ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ) ),
inference(ennf_transformation,[],[f2054]) ).
fof(f2054,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) )
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f219]) ).
fof(f219,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X11)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X12))) )
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13206,plain,
( spl263_802
| ~ spl263_38
| ~ spl263_100 ),
inference(avatar_split_clause,[],[f8382,f8258,f7964,f13204]) ).
fof(f13204,plain,
( spl263_802
<=> ! [X0] :
( ~ is_bool(X0)
| sP7(cOMBK_bool_a(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_802])]) ).
fof(f8382,plain,
( ! [X0] :
( ~ is_bool(X0)
| sP7(cOMBK_bool_a(X0)) )
| ~ spl263_38
| ~ spl263_100 ),
inference(resolution,[],[f8259,f7965]) ).
fof(f13202,plain,
spl263_801,
inference(avatar_split_clause,[],[f5825,f13200]) ).
fof(f13200,plain,
( spl263_801
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_801])]) ).
fof(f5825,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ),
inference(cnf_transformation,[],[f3258]) ).
fof(f13198,plain,
spl263_800,
inference(avatar_split_clause,[],[f5795,f13196]) ).
fof(f13196,plain,
( spl263_800
<=> ! [X0,X1] :
( X0 = X1
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_800])]) ).
fof(f5795,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ),
inference(cnf_transformation,[],[f3214]) ).
fof(f3214,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ),
inference(ennf_transformation,[],[f2033]) ).
fof(f2033,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)
=> X0 = X1 ),
inference(rectify,[],[f697]) ).
fof(f697,axiom,
! [X7,X30] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),bot_bot_fun_nat_bool)
=> X7 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13194,plain,
spl263_799,
inference(avatar_split_clause,[],[f5794,f13192]) ).
fof(f13192,plain,
( spl263_799
<=> ! [X0,X1] :
( X0 = X1
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_799])]) ).
fof(f5794,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ),
inference(cnf_transformation,[],[f3213]) ).
fof(f3213,plain,
! [X0,X1] :
( X0 = X1
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ),
inference(ennf_transformation,[],[f2032]) ).
fof(f2032,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)
=> X0 = X1 ),
inference(rectify,[],[f698]) ).
fof(f698,axiom,
! [X7,X30] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),bot_bot_fun_int_bool)
=> X7 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13190,plain,
spl263_798,
inference(avatar_split_clause,[],[f5783,f13188]) ).
fof(f13188,plain,
( spl263_798
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_798])]) ).
fof(f5783,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f3201]) ).
fof(f3201,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(ennf_transformation,[],[f2022]) ).
fof(f2022,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(rectify,[],[f981]) ).
fof(f981,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X14)),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13186,plain,
spl263_797,
inference(avatar_split_clause,[],[f5759,f13184]) ).
fof(f13184,plain,
( spl263_797
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_797])]) ).
fof(f5759,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3168]) ).
fof(f3168,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f2000]) ).
fof(f2000,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(rectify,[],[f273]) ).
fof(f273,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(suc,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13182,plain,
spl263_796,
inference(avatar_split_clause,[],[f5758,f13180]) ).
fof(f13180,plain,
( spl263_796
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_796])]) ).
fof(f5758,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3167]) ).
fof(f3167,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1999]) ).
fof(f1999,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(rectify,[],[f1011]) ).
fof(f1011,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13178,plain,
spl263_795,
inference(avatar_split_clause,[],[f5755,f13176]) ).
fof(f13176,plain,
( spl263_795
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK136(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_795])]) ).
fof(f5755,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK136(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4253]) ).
fof(f13174,plain,
spl263_794,
inference(avatar_split_clause,[],[f5748,f13172]) ).
fof(f13172,plain,
( spl263_794
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_794])]) ).
fof(f5748,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3157]) ).
fof(f3157,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1991]) ).
fof(f1991,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(rectify,[],[f977]) ).
fof(f977,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13170,plain,
spl263_793,
inference(avatar_split_clause,[],[f5684,f13168]) ).
fof(f13168,plain,
( spl263_793
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_793])]) ).
fof(f5684,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3075]) ).
fof(f3075,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f3074]) ).
fof(f3074,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1936]) ).
fof(f1936,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X4,X9] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X9))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13166,plain,
spl263_792,
inference(avatar_split_clause,[],[f5641,f13164]) ).
fof(f13164,plain,
( spl263_792
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_792])]) ).
fof(f5641,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3035]) ).
fof(f3035,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(flattening,[],[f3034]) ).
fof(f3034,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1907]) ).
fof(f1907,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X4,X9] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X9))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X9))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13162,plain,
spl263_791,
inference(avatar_split_clause,[],[f5603,f13160]) ).
fof(f13160,plain,
( spl263_791
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_791])]) ).
fof(f5603,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f3000]) ).
fof(f3000,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f2999]) ).
fof(f2999,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1882]) ).
fof(f1882,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X9))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13158,plain,
spl263_790,
inference(avatar_split_clause,[],[f5598,f13156]) ).
fof(f13156,plain,
( spl263_790
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| sP13(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_790])]) ).
fof(f5598,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| sP13(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f3934]) ).
fof(f3934,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| sP13(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_folding,[],[f2990,f3933]) ).
fof(f2990,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f2989]) ).
fof(f2989,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1877]) ).
fof(f1877,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
=> ( ! [X2,X3] :
( ( is_fun_a_bool(X3)
& is_a(X2) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,X3))
=> hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool)) ) ) ),
inference(rectify,[],[f790]) ).
fof(f790,axiom,
! [X12,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,X4))
=> ( ! [X77,X80] :
( ( is_fun_a_bool(X80)
& is_a(X77) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X80))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X77),X80))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,X80))
=> hBOOL(hAPP_fun_a_bool_bool(X12,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X80),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X77),bot_bot_fun_a_bool)))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X12,bot_bot_fun_a_bool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13154,plain,
spl263_789,
inference(avatar_split_clause,[],[f5591,f13152]) ).
fof(f13152,plain,
( spl263_789
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP12(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_789])]) ).
fof(f5591,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP12(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f3932]) ).
fof(f3932,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| sP12(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_folding,[],[f2988,f3931]) ).
fof(f3931,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2988,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f2987]) ).
fof(f2987,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1876]) ).
fof(f1876,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
=> ( ! [X2,X3] :
( ( is_fun_a_bool(X3)
& is_a(X2) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
=> ( hBOOL(hAPP_fun_a_bool_bool(X0,X3))
=> hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ) ),
inference(rectify,[],[f794]) ).
fof(f794,axiom,
! [X12,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,bot_bot_fun_a_bool))
=> ( ! [X29,X78] :
( ( is_fun_a_bool(X78)
& is_a(X29) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X78))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X78))
=> ( hBOOL(hAPP_fun_a_bool_bool(X12,X78))
=> hBOOL(hAPP_fun_a_bool_bool(X12,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),X78))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X12,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13150,plain,
spl263_788,
inference(avatar_split_clause,[],[f5560,f13148]) ).
fof(f13148,plain,
( spl263_788
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_788])]) ).
fof(f5560,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2960]) ).
fof(f2960,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f2959]) ).
fof(f2959,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1854]) ).
fof(f1854,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13146,plain,
spl263_787,
inference(avatar_split_clause,[],[f5558,f13144]) ).
fof(f13144,plain,
( spl263_787
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| sP11(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_787])]) ).
fof(f5558,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| sP11(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f3930]) ).
fof(f3930,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| sP11(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_folding,[],[f2956,f3929]) ).
fof(f2956,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f2955]) ).
fof(f2955,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1852]) ).
fof(f1852,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
=> ( ! [X2,X3] :
( ( is_fun_pname_bool(X3)
& is_pname(X2) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,X3))
=> hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool)) ) ) ),
inference(rectify,[],[f793]) ).
fof(f793,axiom,
! [X12,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,X4))
=> ( ! [X77,X80] :
( ( is_fun_pname_bool(X80)
& is_pname(X77) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X80))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X77),X80))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,X80))
=> hBOOL(hAPP_f1664156314l_bool(X12,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X80),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X77),bot_bo844097828e_bool)))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X12,bot_bo844097828e_bool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13142,plain,
spl263_786,
inference(avatar_split_clause,[],[f5551,f13140]) ).
fof(f13140,plain,
( spl263_786
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP10(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_786])]) ).
fof(f5551,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP10(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f3928]) ).
fof(f3928,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| sP10(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_folding,[],[f2954,f3927]) ).
fof(f3927,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f2954,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f2953]) ).
fof(f2953,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,X1))
| ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1851]) ).
fof(f1851,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
=> ( ! [X2,X3] :
( ( is_fun_pname_bool(X3)
& is_pname(X2) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
=> ( hBOOL(hAPP_f1664156314l_bool(X0,X3))
=> hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ) ),
inference(rectify,[],[f797]) ).
fof(f797,axiom,
! [X12,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,bot_bo844097828e_bool))
=> ( ! [X29,X78] :
( ( is_fun_pname_bool(X78)
& is_pname(X29) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X78))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X78))
=> ( hBOOL(hAPP_f1664156314l_bool(X12,X78))
=> hBOOL(hAPP_f1664156314l_bool(X12,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X29),X78))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X12,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13138,plain,
spl263_785,
inference(avatar_split_clause,[],[f5518,f13136]) ).
fof(f13136,plain,
( spl263_785
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_785])]) ).
fof(f5518,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2922]) ).
fof(f2922,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(flattening,[],[f2921]) ).
fof(f2921,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X4,X9] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4),X9))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13134,plain,
spl263_784,
inference(avatar_split_clause,[],[f5517,f13132]) ).
fof(f13132,plain,
( spl263_784
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_784])]) ).
fof(f5517,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2920]) ).
fof(f2920,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(flattening,[],[f2919]) ).
fof(f2919,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1825]) ).
fof(f1825,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
inference(rectify,[],[f264]) ).
fof(f264,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4),X9))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13130,plain,
spl263_783,
inference(avatar_split_clause,[],[f5516,f13128]) ).
fof(f13128,plain,
( spl263_783
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_783])]) ).
fof(f5516,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2918]) ).
fof(f2918,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(flattening,[],[f2917]) ).
fof(f2917,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1824]) ).
fof(f1824,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X4,X9] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4),X9))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13126,plain,
spl263_782,
inference(avatar_split_clause,[],[f5515,f13124]) ).
fof(f13124,plain,
( spl263_782
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_782])]) ).
fof(f5515,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2916]) ).
fof(f2916,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(flattening,[],[f2915]) ).
fof(f2915,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1823]) ).
fof(f1823,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X4,X9] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X9))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4),X9))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13122,plain,
( spl263_781
| ~ spl263_157
| ~ spl263_767 ),
inference(avatar_split_clause,[],[f13065,f12666,f8531,f13120]) ).
fof(f8531,plain,
( spl263_157
<=> ! [X0] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_157])]) ).
fof(f12666,plain,
( spl263_767
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK221(X0,X1))))
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_767])]) ).
fof(f13065,plain,
( ! [X0] : ~ sP24(bot_bot_fun_int_bool,X0)
| ~ spl263_157
| ~ spl263_767 ),
inference(resolution,[],[f12667,f8532]) ).
fof(f8532,plain,
( ! [X0] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
| ~ spl263_157 ),
inference(avatar_component_clause,[],[f8531]) ).
fof(f12667,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK221(X0,X1))))
| ~ sP24(X0,X1) )
| ~ spl263_767 ),
inference(avatar_component_clause,[],[f12666]) ).
fof(f13118,plain,
spl263_780,
inference(avatar_split_clause,[],[f5470,f13116]) ).
fof(f13116,plain,
( spl263_780
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,sK109(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_780])]) ).
fof(f5470,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,sK109(X0,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4198]) ).
fof(f13114,plain,
spl263_779,
inference(avatar_split_clause,[],[f5442,f13112]) ).
fof(f13112,plain,
( spl263_779
<=> ! [X0,X1] :
( is_pname(sK97(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_779])]) ).
fof(f5442,plain,
! [X0,X1] :
( is_pname(sK97(X0,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f4174]) ).
fof(f13110,plain,
spl263_778,
inference(avatar_split_clause,[],[f5307,f13108]) ).
fof(f13108,plain,
( spl263_778
<=> ! [X0,X1] :
( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_778])]) ).
fof(f5307,plain,
! [X0,X1] :
( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0))
| hBOOL(hAPP_a_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2756]) ).
fof(f13106,plain,
spl263_777,
inference(avatar_split_clause,[],[f5037,f13104]) ).
fof(f13104,plain,
( spl263_777
<=> ! [X0] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK51(X0)),sK50(X0)) = X0
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_777])]) ).
fof(f5037,plain,
! [X0] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK51(X0)),sK50(X0)) = X0
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f4018]) ).
fof(f13102,plain,
spl263_776,
inference(avatar_split_clause,[],[f5010,f13100]) ).
fof(f13100,plain,
( spl263_776
<=> ! [X0] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK45(X0)),sK44(X0)) = X0
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_776])]) ).
fof(f5010,plain,
! [X0] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK45(X0)),sK44(X0)) = X0
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f3999]) ).
fof(f13098,plain,
spl263_775,
inference(avatar_split_clause,[],[f4978,f13096]) ).
fof(f13096,plain,
( spl263_775
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_775])]) ).
fof(f4978,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))),
inference(cnf_transformation,[],[f1524]) ).
fof(f1524,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))),
inference(rectify,[],[f1096]) ).
fof(f1096,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X14)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13094,plain,
spl263_774,
inference(avatar_split_clause,[],[f4977,f13092]) ).
fof(f13092,plain,
( spl263_774
<=> ! [X0] : hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_774])]) ).
fof(f4977,plain,
! [X0] : hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
inference(cnf_transformation,[],[f1523]) ).
fof(f1523,plain,
! [X0] : hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
inference(rectify,[],[f891]) ).
fof(f891,axiom,
! [X84] : hAPP_f22106695ol_nat(the_elem_nat,X84) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X84),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13090,plain,
spl263_773,
inference(avatar_split_clause,[],[f4976,f13088]) ).
fof(f13088,plain,
( spl263_773
<=> ! [X0] : hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_773])]) ).
fof(f4976,plain,
! [X0] : hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
inference(cnf_transformation,[],[f1522]) ).
fof(f1522,plain,
! [X0] : hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
inference(rectify,[],[f890]) ).
fof(f890,axiom,
! [X84] : hAPP_fun_a_bool_a(the_elem_a,X84) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X84),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13086,plain,
spl263_772,
inference(avatar_split_clause,[],[f4975,f13084]) ).
fof(f13084,plain,
( spl263_772
<=> ! [X0] : hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_772])]) ).
fof(f4975,plain,
! [X0] : hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
inference(cnf_transformation,[],[f1521]) ).
fof(f1521,plain,
! [X0] : hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
inference(rectify,[],[f892]) ).
fof(f892,axiom,
! [X84] : hAPP_f1594865479ol_int(the_elem_int,X84) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X84),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f13064,plain,
( spl263_771
| ~ spl263_142
| ~ spl263_757 ),
inference(avatar_split_clause,[],[f12895,f12625,f8471,f13062]) ).
fof(f13062,plain,
( spl263_771
<=> ! [X0,X1] : ~ sP39(X0,zero_zero_nat,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_771])]) ).
fof(f8471,plain,
( spl263_142
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_142])]) ).
fof(f12625,plain,
( spl263_757
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK261(X0,X1,X2)),X1))
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_757])]) ).
fof(f12895,plain,
( ! [X0,X1] : ~ sP39(X0,zero_zero_nat,X1)
| ~ spl263_142
| ~ spl263_757 ),
inference(resolution,[],[f12626,f8472]) ).
fof(f8472,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
| ~ spl263_142 ),
inference(avatar_component_clause,[],[f8471]) ).
fof(f12626,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK261(X0,X1,X2)),X1))
| ~ sP39(X0,X1,X2) )
| ~ spl263_757 ),
inference(avatar_component_clause,[],[f12625]) ).
fof(f12887,plain,
( spl263_770
| ~ spl263_37
| ~ spl263_92 ),
inference(avatar_split_clause,[],[f8374,f8225,f7960,f12884]) ).
fof(f12884,plain,
( spl263_770
<=> sP5(undefined_fun_a_bool(fun(x_a,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_770])]) ).
fof(f8225,plain,
( spl263_92
<=> is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_92])]) ).
fof(f8374,plain,
( sP5(undefined_fun_a_bool(fun(x_a,bool)))
| ~ spl263_37
| ~ spl263_92 ),
inference(resolution,[],[f8227,f7961]) ).
fof(f8227,plain,
( is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool)))
| ~ spl263_92 ),
inference(avatar_component_clause,[],[f8225]) ).
fof(f12849,plain,
( spl263_769
| ~ spl263_38
| ~ spl263_92 ),
inference(avatar_split_clause,[],[f8373,f8225,f7964,f12846]) ).
fof(f12846,plain,
( spl263_769
<=> sP7(undefined_fun_a_bool(fun(x_a,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_769])]) ).
fof(f8373,plain,
( sP7(undefined_fun_a_bool(fun(x_a,bool)))
| ~ spl263_38
| ~ spl263_92 ),
inference(resolution,[],[f8227,f7965]) ).
fof(f12788,plain,
( spl263_768
| ~ spl263_35
| ~ spl263_91 ),
inference(avatar_split_clause,[],[f8372,f8220,f7952,f12785]) ).
fof(f12785,plain,
( spl263_768
<=> sP1(undefi17486888e_bool(fun(pname,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_768])]) ).
fof(f8220,plain,
( spl263_91
<=> is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_91])]) ).
fof(f8372,plain,
( sP1(undefi17486888e_bool(fun(pname,bool)))
| ~ spl263_35
| ~ spl263_91 ),
inference(resolution,[],[f8222,f7953]) ).
fof(f8222,plain,
( is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool)))
| ~ spl263_91 ),
inference(avatar_component_clause,[],[f8220]) ).
fof(f12668,plain,
spl263_767,
inference(avatar_split_clause,[],[f7692,f12666]) ).
fof(f7692,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK221(X0,X1))))
| ~ sP24(X0,X1) ),
inference(forward_demodulation,[],[f6472,f5254]) ).
fof(f5254,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0),
inference(cnf_transformation,[],[f1650]) ).
fof(f1650,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0),
inference(rectify,[],[f1150]) ).
fof(f1150,axiom,
! [X97,X134] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X97),X134) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X134),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6472,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK221(X0,X1)),one_one_int)))
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f4569]) ).
fof(f4569,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK221(X0,X1)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1))) )
| ~ sP24(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK221])],[f4567,f4568]) ).
fof(f4568,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) )
=> ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK221(X0,X1)),one_one_int)))
& hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f4567,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
& hBOOL(hAPP_int_bool(X0,X2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) )
| ~ sP24(X0,X1) ),
inference(rectify,[],[f4566]) ).
fof(f4566,plain,
! [X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
& hBOOL(hAPP_int_bool(X1,X3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
| ~ sP24(X1,X2) ),
inference(nnf_transformation,[],[f3954]) ).
fof(f12664,plain,
spl263_766,
inference(avatar_split_clause,[],[f7587,f12662]) ).
fof(f12662,plain,
( spl263_766
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_766])]) ).
fof(f7587,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ sP17(X0,X1) ),
inference(forward_demodulation,[],[f7586,f4875]) ).
fof(f7586,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP17(X0,X1) ),
inference(forward_demodulation,[],[f7098,f4875]) ).
fof(f7098,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP17(X0,X1) ),
inference(definition_unfolding,[],[f5888,f4830]) ).
fof(f5888,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f4306]) ).
fof(f4306,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ( ~ sP16(X1,X0)
& ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
& hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
& ( ( ( sP16(X1,X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
| ~ sP17(X0,X1) ) ),
inference(flattening,[],[f4305]) ).
fof(f4305,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ( ~ sP16(X1,X0)
& ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
& hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
& ( ( ( sP16(X1,X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
| ~ sP17(X0,X1) ) ),
inference(nnf_transformation,[],[f3940]) ).
fof(f3940,plain,
! [X0,X1] :
( sP17(X0,X1)
<=> ( ( sP16(X1,X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f12660,plain,
( spl263_765
| ~ spl263_36
| ~ spl263_91 ),
inference(avatar_split_clause,[],[f8371,f8220,f7956,f12657]) ).
fof(f12657,plain,
( spl263_765
<=> sP3(undefi17486888e_bool(fun(pname,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_765])]) ).
fof(f8371,plain,
( sP3(undefi17486888e_bool(fun(pname,bool)))
| ~ spl263_36
| ~ spl263_91 ),
inference(resolution,[],[f8222,f7957]) ).
fof(f12655,plain,
spl263_764,
inference(avatar_split_clause,[],[f7584,f12653]) ).
fof(f12653,plain,
( spl263_764
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_764])]) ).
fof(f7584,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP17(X0,X1) ),
inference(forward_demodulation,[],[f7583,f4875]) ).
fof(f7583,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP17(X0,X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
inference(forward_demodulation,[],[f7097,f4875]) ).
fof(f7097,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
inference(definition_unfolding,[],[f5891,f4830]) ).
fof(f5891,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(cnf_transformation,[],[f4306]) ).
fof(f12651,plain,
spl263_763,
inference(avatar_split_clause,[],[f7461,f12649]) ).
fof(f12649,plain,
( spl263_763
<=> ! [X0,X1] :
( bot_bot_fun_nat_bool = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)
| hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_763])]) ).
fof(f7461,plain,
! [X0,X1] :
( bot_bot_fun_nat_bool = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)
| hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5315,f4876]) ).
fof(f5315,plain,
! [X0,X1] :
( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0))
| hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2760]) ).
fof(f12647,plain,
spl263_762,
inference(avatar_split_clause,[],[f7453,f12645]) ).
fof(f12645,plain,
( spl263_762
<=> ! [X0,X1] :
( bot_bot_fun_int_bool = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)
| hBOOL(hAPP_int_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_762])]) ).
fof(f7453,plain,
! [X0,X1] :
( bot_bot_fun_int_bool = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)
| hBOOL(hAPP_int_bool(X0,X1)) ),
inference(forward_demodulation,[],[f5311,f4874]) ).
fof(f5311,plain,
! [X0,X1] :
( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0))
| hBOOL(hAPP_int_bool(X0,X1)) ),
inference(cnf_transformation,[],[f2758]) ).
fof(f12643,plain,
spl263_761,
inference(avatar_split_clause,[],[f7084,f12641]) ).
fof(f12641,plain,
( spl263_761
<=> ! [X0,X1] :
( pls = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_761])]) ).
fof(f7084,plain,
! [X0,X1] :
( pls = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(definition_unfolding,[],[f5321,f4830]) ).
fof(f5321,plain,
! [X0,X1] :
( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f2763]) ).
fof(f12639,plain,
spl263_760,
inference(avatar_split_clause,[],[f7081,f12637]) ).
fof(f12637,plain,
( spl263_760
<=> ! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK86(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_760])]) ).
fof(f7081,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK86(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(definition_unfolding,[],[f5187,f4830]) ).
fof(f5187,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK86(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f4154]) ).
fof(f12635,plain,
spl263_759,
inference(avatar_split_clause,[],[f7080,f12633]) ).
fof(f12633,plain,
( spl263_759
<=> ! [X0,X3] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK83(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_759])]) ).
fof(f7080,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK83(X0))) ),
inference(definition_unfolding,[],[f5179,f4830]) ).
fof(f5179,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK83(X0))) ),
inference(cnf_transformation,[],[f4141]) ).
fof(f12631,plain,
spl263_758,
inference(avatar_split_clause,[],[f7045,f12629]) ).
fof(f12629,plain,
( spl263_758
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK56(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_758])]) ).
fof(f7045,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK56(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f5067,f4830]) ).
fof(f5067,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK56(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4034]) ).
fof(f4034,plain,
! [X0] :
( ( hAPP_nat_int(semiri1621563631at_int,sK56(X0)) = X0
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK56(X0))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f2736,f4033]) ).
fof(f4033,plain,
! [X0] :
( ? [X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = X0
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
=> ( hAPP_nat_int(semiri1621563631at_int,sK56(X0)) = X0
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK56(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f2736,plain,
! [X0] :
( ? [X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = X0
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1563]) ).
fof(f1563,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
=> ? [X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = X0
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
inference(rectify,[],[f1238]) ).
fof(f1238,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X21))
=> ? [X28] :
( hAPP_nat_int(semiri1621563631at_int,X28) = X21
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X28)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12627,plain,
spl263_757,
inference(avatar_split_clause,[],[f6973,f12625]) ).
fof(f6973,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK261(X0,X1,X2)),X1))
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f4783]) ).
fof(f4783,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK261(X0,X1,X2)),one_one_nat))),hAPP_nat_int(X0,sK261(X0,X1,X2))))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK261(X0,X1,X2)),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK261(X0,X1,X2))) )
| ~ sP39(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK261])],[f4781,f4782]) ).
fof(f4782,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),one_one_nat))),hAPP_nat_int(X0,X3)))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK261(X0,X1,X2)),one_one_nat))),hAPP_nat_int(X0,sK261(X0,X1,X2))))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK261(X0,X1,X2)),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK261(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f4781,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),one_one_nat))),hAPP_nat_int(X0,X3)))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
| ~ sP39(X0,X1,X2) ),
inference(rectify,[],[f4780]) ).
fof(f4780,plain,
! [X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X4),one_one_nat))),hAPP_nat_int(X1,X4)))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) )
| ~ sP39(X1,X2,X3) ),
inference(nnf_transformation,[],[f3983]) ).
fof(f3983,plain,
! [X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X4),one_one_nat))),hAPP_nat_int(X1,X4)))),one_one_int))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) )
| ~ sP39(X1,X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f12623,plain,
spl263_756,
inference(avatar_split_clause,[],[f6972,f12621]) ).
fof(f12621,plain,
( spl263_756
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK261(X0,X1,X2)))
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_756])]) ).
fof(f6972,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK261(X0,X1,X2)))
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f4783]) ).
fof(f12619,plain,
spl263_755,
inference(avatar_split_clause,[],[f6971,f12617]) ).
fof(f12617,plain,
( spl263_755
<=> ! [X0,X3,X2,X1] :
( sP38(X0,X3,X1,X2)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_755])]) ).
fof(f6971,plain,
! [X2,X3,X0,X1] :
( sP38(X0,X3,X1,X2)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f3982]) ).
fof(f3982,plain,
! [X0,X1,X2,X3] :
( sP38(X0,X3,X1,X2)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(definition_folding,[],[f3892,f3981,f3980]) ).
fof(f3980,plain,
! [X2,X1,X3,X0] :
( sP37(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f3981,plain,
! [X0,X3,X1,X2] :
( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))
<=> sP37(X2,X1,X3,X0) )
| ~ sP38(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f3892,plain,
! [X0,X1,X2,X3] :
( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) )
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f3891]) ).
fof(f3891,plain,
! [X0,X1,X2,X3] :
( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) )
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2667]) ).
fof(f2667,plain,
! [X0,X1,X2,X3] :
( ( is_a(X3)
& is_a(X2)
& is_a(X1)
& is_a(X0) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 ) ) ) ),
inference(rectify,[],[f703]) ).
fof(f703,axiom,
! [X7,X30,X31,X72] :
( ( is_a(X72)
& is_a(X31)
& is_a(X30)
& is_a(X7) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X72),bot_bot_fun_a_bool))
<=> ( ( X30 = X31
& X7 = X72 )
| ( X30 = X72
& X7 = X31 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12614,plain,
spl263_754,
inference(avatar_split_clause,[],[f6742,f12612]) ).
fof(f12612,plain,
( spl263_754
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| is_pname(sK247(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_754])]) ).
fof(f6742,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| is_pname(sK247(X0,X1,X2)) ),
inference(cnf_transformation,[],[f4662]) ).
fof(f12610,plain,
spl263_753,
inference(avatar_split_clause,[],[f6433,f12608]) ).
fof(f12608,plain,
( spl263_753
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),sK210(X0,X1)))
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_753])]) ).
fof(f6433,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),sK210(X0,X1)))
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f4549]) ).
fof(f12606,plain,
spl263_752,
inference(avatar_split_clause,[],[f6395,f12604]) ).
fof(f12604,plain,
( spl263_752
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),sK201(X0,X1)))
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_752])]) ).
fof(f6395,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),sK201(X0,X1)))
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f4531]) ).
fof(f12602,plain,
spl263_751,
inference(avatar_split_clause,[],[f6384,f12600]) ).
fof(f12600,plain,
( spl263_751
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),sK199(X0,X1)))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_751])]) ).
fof(f6384,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),sK199(X0,X1)))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f12598,plain,
spl263_750,
inference(avatar_split_clause,[],[f6368,f12596]) ).
fof(f12596,plain,
( spl263_750
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),sK197(X0,X1)))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_750])]) ).
fof(f6368,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),sK197(X0,X1)))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f12594,plain,
spl263_749,
inference(avatar_split_clause,[],[f6160,f12592]) ).
fof(f6160,plain,
! [X2,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)),
inference(cnf_transformation,[],[f2226]) ).
fof(f2226,plain,
! [X0,X1,X2] : hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)),
inference(rectify,[],[f1356]) ).
fof(f1356,axiom,
! [X158,X159,X160] : hAPP_nat_bool(cOMBS_nat_bool_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_n1006566506l_bool(X158,X160),hAPP_nat_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12590,plain,
spl263_748,
inference(avatar_split_clause,[],[f6159,f12588]) ).
fof(f6159,plain,
! [X2,X0,X1] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)),
inference(cnf_transformation,[],[f2225]) ).
fof(f2225,plain,
! [X0,X1,X2] : hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)),
inference(rectify,[],[f1355]) ).
fof(f1355,axiom,
! [X158,X159,X160] : hAPP_int_bool(cOMBS_int_bool_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_i68813070l_bool(X158,X160),hAPP_int_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12586,plain,
spl263_747,
inference(avatar_split_clause,[],[f6158,f12584]) ).
fof(f12584,plain,
( spl263_747
<=> ! [X2,X0,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_747])]) ).
fof(f6158,plain,
! [X2,X0,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)),
inference(cnf_transformation,[],[f2224]) ).
fof(f2224,plain,
! [X0,X1,X2] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)),
inference(rectify,[],[f1380]) ).
fof(f1380,axiom,
! [X158,X159,X160] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_f1748468828l_bool(X158,X160),hAPP_f54304608l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12582,plain,
spl263_746,
inference(avatar_split_clause,[],[f6157,f12580]) ).
fof(f12580,plain,
( spl263_746
<=> ! [X2,X0,X1] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_746])]) ).
fof(f6157,plain,
! [X2,X0,X1] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)),
inference(cnf_transformation,[],[f2223]) ).
fof(f2223,plain,
! [X0,X1,X2] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)),
inference(rectify,[],[f1379]) ).
fof(f1379,axiom,
! [X158,X159,X160] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_f1721100032l_bool(X158,X160),hAPP_f448129468l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12578,plain,
spl263_745,
inference(avatar_split_clause,[],[f6156,f12576]) ).
fof(f12576,plain,
( spl263_745
<=> ! [X2,X0,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_745])]) ).
fof(f6156,plain,
! [X2,X0,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)),
inference(cnf_transformation,[],[f2222]) ).
fof(f2222,plain,
! [X0,X1,X2] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)),
inference(rectify,[],[f1367]) ).
fof(f1367,axiom,
! [X158,X159,X160] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_f198738859l_bool(X158,X160),hAPP_fun_a_bool_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12573,plain,
spl263_744,
inference(avatar_split_clause,[],[f6155,f12571]) ).
fof(f12571,plain,
( spl263_744
<=> ! [X2,X0,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_744])]) ).
fof(f6155,plain,
! [X2,X0,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)),
inference(cnf_transformation,[],[f2221]) ).
fof(f2221,plain,
! [X0,X1,X2] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)),
inference(rectify,[],[f1384]) ).
fof(f1384,axiom,
! [X158,X159,X160] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_f1476298914l_bool(X158,X160),hAPP_f1664156314l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12569,plain,
spl263_743,
inference(avatar_split_clause,[],[f6154,f12567]) ).
fof(f12565,plain,
spl263_742,
inference(avatar_split_clause,[],[f6153,f12563]) ).
fof(f12563,plain,
( spl263_742
<=> ! [X2,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_742])]) ).
fof(f6153,plain,
! [X2,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)),
inference(cnf_transformation,[],[f2219]) ).
fof(f2219,plain,
! [X0,X1,X2] : hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)),
inference(rectify,[],[f1358]) ).
fof(f1358,axiom,
! [X158,X159,X160] : hAPP_pname_bool(cOMBS_568398431l_bool(X158,X159),X160) = hAPP_bool_bool(hAPP_p393069232l_bool(X158,X160),hAPP_pname_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12561,plain,
spl263_741,
inference(avatar_split_clause,[],[f5961,f12559]) ).
fof(f12559,plain,
( spl263_741
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_741])]) ).
fof(f5961,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ),
inference(cnf_transformation,[],[f4364]) ).
fof(f4364,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f2109]) ).
fof(f2109,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f1062]) ).
fof(f1062,axiom,
! [X24,X16] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X16)
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12557,plain,
spl263_740,
inference(avatar_split_clause,[],[f5958,f12555]) ).
fof(f12555,plain,
( spl263_740
<=> ! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_740])]) ).
fof(f5958,plain,
! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ),
inference(cnf_transformation,[],[f4363]) ).
fof(f4363,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
| ( zero_zero_nat != X1
& zero_zero_nat != X0 ) )
& ( zero_zero_nat = X1
| zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
inference(flattening,[],[f4362]) ).
fof(f4362,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
| ( zero_zero_nat != X1
& zero_zero_nat != X0 ) )
& ( zero_zero_nat = X1
| zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f2108]) ).
fof(f2108,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
<=> ( zero_zero_nat = X1
| zero_zero_nat = X0 ) ),
inference(rectify,[],[f1087]) ).
fof(f1087,axiom,
! [X24,X16] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X16)
<=> ( zero_zero_nat = X16
| zero_zero_nat = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12553,plain,
spl263_739,
inference(avatar_split_clause,[],[f5812,f12551]) ).
fof(f12551,plain,
( spl263_739
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_739])]) ).
fof(f5812,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f3243]) ).
fof(f3243,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f3242]) ).
fof(f3242,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f2046]) ).
fof(f2046,plain,
! [X0,X1] :
( ( is_fun_a_bool(X1)
& is_fun_a_bool(X0) )
=> ( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ) ),
inference(rectify,[],[f1337]) ).
fof(f1337,axiom,
! [X17,X18] :
( ( is_fun_a_bool(X18)
& is_fun_a_bool(X17) )
=> ( X17 = X18
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X17),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12549,plain,
spl263_738,
inference(avatar_split_clause,[],[f5809,f12547]) ).
fof(f12547,plain,
( spl263_738
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_738])]) ).
fof(f5809,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f3237]) ).
fof(f3237,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f3236]) ).
fof(f3236,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f2044]) ).
fof(f2044,plain,
! [X0,X1] :
( ( is_fun_pname_bool(X1)
& is_fun_pname_bool(X0) )
=> ( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ) ),
inference(rectify,[],[f1347]) ).
fof(f1347,axiom,
! [X17,X18] :
( ( is_fun_pname_bool(X18)
& is_fun_pname_bool(X17) )
=> ( X17 = X18
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X17),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12545,plain,
spl263_737,
inference(avatar_split_clause,[],[f5802,f12543]) ).
fof(f12543,plain,
( spl263_737
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ~ is_pname(X1)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_737])]) ).
fof(f5802,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f3225]) ).
fof(f3225,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(flattening,[],[f3224]) ).
fof(f3224,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(ennf_transformation,[],[f2039]) ).
fof(f2039,plain,
! [X0,X1] :
( ( is_pname(X1)
& is_pname(X0) )
=> ( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ) ),
inference(rectify,[],[f1329]) ).
fof(f1329,axiom,
! [X17,X18] :
( ( is_pname(X18)
& is_pname(X17) )
=> ( X17 = X18
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X17),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12541,plain,
spl263_736,
inference(avatar_split_clause,[],[f5797,f12539]) ).
fof(f12539,plain,
( spl263_736
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ~ is_a(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_736])]) ).
fof(f5797,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f3217]) ).
fof(f3217,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f3216]) ).
fof(f3216,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f2035]) ).
fof(f2035,plain,
! [X0,X1] :
( ( is_a(X1)
& is_a(X0) )
=> ( X0 = X1
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ) ),
inference(rectify,[],[f1319]) ).
fof(f1319,axiom,
! [X17,X18] :
( ( is_a(X18)
& is_a(X17) )
=> ( X17 = X18
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X17),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12537,plain,
spl263_735,
inference(avatar_split_clause,[],[f5774,f12535]) ).
fof(f12535,plain,
( spl263_735
<=> ! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_735])]) ).
fof(f5774,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ),
inference(cnf_transformation,[],[f3186]) ).
fof(f3186,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ),
inference(flattening,[],[f3185]) ).
fof(f3185,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ),
inference(ennf_transformation,[],[f2013]) ).
fof(f2013,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = X0
=> ( zero_zero_nat = X0
| one_one_nat = X1 ) ),
inference(rectify,[],[f1114]) ).
fof(f1114,axiom,
! [X14,X13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13) = X14
=> ( zero_zero_nat = X14
| one_one_nat = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12533,plain,
( spl263_734
| ~ spl263_158
| ~ spl263_690 ),
inference(avatar_split_clause,[],[f12279,f11714,f8535,f12531]) ).
fof(f11714,plain,
( spl263_690
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_690])]) ).
fof(f12279,plain,
( ! [X0,X1] : sP31(bot_bot_fun_nat_bool,X0,X1)
| ~ spl263_158
| ~ spl263_690 ),
inference(resolution,[],[f11715,f8536]) ).
fof(f11715,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| sP31(X0,X1,X2) )
| ~ spl263_690 ),
inference(avatar_component_clause,[],[f11714]) ).
fof(f12529,plain,
spl263_733,
inference(avatar_split_clause,[],[f5757,f12527]) ).
fof(f12527,plain,
( spl263_733
<=> ! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_733])]) ).
fof(f5757,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3166]) ).
fof(f3166,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1998]) ).
fof(f1998,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ),
inference(rectify,[],[f1063]) ).
fof(f1063,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13) = zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12525,plain,
spl263_732,
inference(avatar_split_clause,[],[f5728,f12523]) ).
fof(f12523,plain,
( spl263_732
<=> ! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_732])]) ).
fof(f5728,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3132]) ).
fof(f3132,plain,
! [X0,X1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1973]) ).
fof(f1973,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1 ),
inference(rectify,[],[f506]) ).
fof(f506,axiom,
! [X7,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),X4))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12521,plain,
spl263_731,
inference(avatar_split_clause,[],[f5720,f12519]) ).
fof(f12519,plain,
( spl263_731
<=> ! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_731])]) ).
fof(f5720,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(cnf_transformation,[],[f3121]) ).
fof(f3121,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(ennf_transformation,[],[f1966]) ).
fof(f1966,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1 ),
inference(rectify,[],[f505]) ).
fof(f505,axiom,
! [X7,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),X4))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12517,plain,
spl263_730,
inference(avatar_split_clause,[],[f5693,f12515]) ).
fof(f12515,plain,
( spl263_730
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X0,sK133(X0)))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_730])]) ).
fof(f5693,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X0,sK133(X0)))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(cnf_transformation,[],[f4241]) ).
fof(f12513,plain,
spl263_729,
inference(avatar_split_clause,[],[f5690,f12511]) ).
fof(f12511,plain,
( spl263_729
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,sK132(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_729])]) ).
fof(f5690,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| hBOOL(hAPP_nat_bool(X1,sK132(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(cnf_transformation,[],[f4239]) ).
fof(f12509,plain,
spl263_728,
inference(avatar_split_clause,[],[f5189,f12507]) ).
fof(f12507,plain,
( spl263_728
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK88(X0))),hAPP_nat_int(semiri1621563631at_int,sK89(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_728])]) ).
fof(f5189,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK88(X0))),hAPP_nat_int(semiri1621563631at_int,sK89(X0))) = X0,
inference(cnf_transformation,[],[f4156]) ).
fof(f4156,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK88(X0))),hAPP_nat_int(semiri1621563631at_int,sK89(X0))) = X0,
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88,sK89])],[f2752,f4155]) ).
fof(f4155,plain,
! [X0] :
( ? [X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = X0
=> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK88(X0))),hAPP_nat_int(semiri1621563631at_int,sK89(X0))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2752,plain,
! [X0] :
? [X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = X0,
inference(ennf_transformation,[],[f1623]) ).
fof(f1623,plain,
! [X0] :
~ ! [X1,X2] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) != X0,
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X97] :
~ ! [X34,X28] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X34)),hAPP_nat_int(semiri1621563631at_int,X28)) != X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12505,plain,
spl263_727,
inference(avatar_split_clause,[],[f4974,f12503]) ).
fof(f12503,plain,
( spl263_727
<=> ! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_727])]) ).
fof(f4974,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1520]) ).
fof(f1520,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f1231]) ).
fof(f1231,axiom,
! [X14] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X14)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12501,plain,
( spl263_726
| ~ spl263_158
| ~ spl263_688 ),
inference(avatar_split_clause,[],[f12225,f11706,f8535,f12499]) ).
fof(f11706,plain,
( spl263_688
<=> ! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_688])]) ).
fof(f12225,plain,
( ! [X0,X1] : sP30(bot_bot_fun_nat_bool,X0,X1)
| ~ spl263_158
| ~ spl263_688 ),
inference(resolution,[],[f11707,f8536]) ).
fof(f11707,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| sP30(X0,X1,X2) )
| ~ spl263_688 ),
inference(avatar_component_clause,[],[f11706]) ).
fof(f12141,plain,
( ~ spl263_725
| ~ spl263_146
| ~ spl263_643 ),
inference(avatar_split_clause,[],[f11987,f11524,f8487,f12138]) ).
fof(f12138,plain,
( spl263_725
<=> sP15(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_725])]) ).
fof(f11524,plain,
( spl263_643
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK125(X0)),sK126(X0))))
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_643])]) ).
fof(f11987,plain,
( ~ sP15(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool))
| ~ spl263_146
| ~ spl263_643 ),
inference(resolution,[],[f11525,f8488]) ).
fof(f11525,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK125(X0)),sK126(X0))))
| ~ sP15(X0) )
| ~ spl263_643 ),
inference(avatar_component_clause,[],[f11524]) ).
fof(f12070,plain,
( ~ spl263_724
| ~ spl263_145
| ~ spl263_641 ),
inference(avatar_split_clause,[],[f11982,f11516,f8483,f12067]) ).
fof(f12067,plain,
( spl263_724
<=> sP14(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_724])]) ).
fof(f11516,plain,
( spl263_641
<=> ! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK118(X0)),sK119(X0))))
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_641])]) ).
fof(f11982,plain,
( ~ sP14(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool))
| ~ spl263_145
| ~ spl263_641 ),
inference(resolution,[],[f11517,f8484]) ).
fof(f11517,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK118(X0)),sK119(X0))))
| ~ sP14(X0) )
| ~ spl263_641 ),
inference(avatar_component_clause,[],[f11516]) ).
fof(f12026,plain,
( ~ spl263_723
| ~ spl263_144
| ~ spl263_639 ),
inference(avatar_split_clause,[],[f11975,f11508,f8479,f12023]) ).
fof(f12023,plain,
( spl263_723
<=> sP12(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_723])]) ).
fof(f11508,plain,
( spl263_639
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK114(X0)),sK115(X0))))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_639])]) ).
fof(f11975,plain,
( ~ sP12(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool))
| ~ spl263_144
| ~ spl263_639 ),
inference(resolution,[],[f11509,f8480]) ).
fof(f11509,plain,
( ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK114(X0)),sK115(X0))))
| ~ sP12(X0) )
| ~ spl263_639 ),
inference(avatar_component_clause,[],[f11508]) ).
fof(f11961,plain,
( ~ spl263_722
| ~ spl263_144
| ~ spl263_630 ),
inference(avatar_split_clause,[],[f11953,f11472,f8479,f11958]) ).
fof(f11958,plain,
( spl263_722
<=> sP9(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_722])]) ).
fof(f11472,plain,
( spl263_630
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK93(X0)),sK94(X0))))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_630])]) ).
fof(f11953,plain,
( ~ sP9(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool))
| ~ spl263_144
| ~ spl263_630 ),
inference(resolution,[],[f11473,f8480]) ).
fof(f11473,plain,
( ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK93(X0)),sK94(X0))))
| ~ sP9(X0) )
| ~ spl263_630 ),
inference(avatar_component_clause,[],[f11472]) ).
fof(f11875,plain,
( spl263_721
| ~ spl263_129
| ~ spl263_518 ),
inference(avatar_split_clause,[],[f10883,f10575,f8412,f11872]) ).
fof(f11872,plain,
( spl263_721
<=> hBOOL(wt(the_com(body(pn)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_721])]) ).
fof(f10575,plain,
( spl263_518
<=> ! [X0] :
( hBOOL(wt(the_com(body(X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_518])]) ).
fof(f10883,plain,
( hBOOL(wt(the_com(body(pn))))
| ~ spl263_129
| ~ spl263_518 ),
inference(resolution,[],[f10576,f8414]) ).
fof(f8414,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl263_129 ),
inference(avatar_component_clause,[],[f8412]) ).
fof(f10576,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u))
| hBOOL(wt(the_com(body(X0)))) )
| ~ spl263_518 ),
inference(avatar_component_clause,[],[f10575]) ).
fof(f11847,plain,
spl263_720,
inference(avatar_split_clause,[],[f7661,f11845]) ).
fof(f11845,plain,
( spl263_720
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_720])]) ).
fof(f7661,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(forward_demodulation,[],[f7660,f4876]) ).
fof(f7660,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f6056,f4876]) ).
fof(f6056,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4421]) ).
fof(f11843,plain,
spl263_719,
inference(avatar_split_clause,[],[f7659,f11841]) ).
fof(f11841,plain,
( spl263_719
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_719])]) ).
fof(f7659,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f7658,f4876]) ).
fof(f7658,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f6057,f4876]) ).
fof(f6057,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4421]) ).
fof(f11839,plain,
spl263_718,
inference(avatar_split_clause,[],[f7654,f11837]) ).
fof(f11837,plain,
( spl263_718
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_718])]) ).
fof(f7654,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
inference(forward_demodulation,[],[f7653,f4874]) ).
fof(f7653,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f6053,f4874]) ).
fof(f6053,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4419]) ).
fof(f11835,plain,
spl263_717,
inference(avatar_split_clause,[],[f7652,f11833]) ).
fof(f11833,plain,
( spl263_717
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_717])]) ).
fof(f7652,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(forward_demodulation,[],[f7651,f4874]) ).
fof(f7651,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f6054,f4874]) ).
fof(f6054,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f4419]) ).
fof(f11831,plain,
spl263_716,
inference(avatar_split_clause,[],[f7596,f11829]) ).
fof(f11829,plain,
( spl263_716
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_716])]) ).
fof(f7596,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(forward_demodulation,[],[f5908,f4957]) ).
fof(f5908,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4314]) ).
fof(f4314,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2086]) ).
fof(f2086,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X24,X16] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X16)),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11827,plain,
spl263_715,
inference(avatar_split_clause,[],[f7595,f11825]) ).
fof(f11825,plain,
( spl263_715
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_715])]) ).
fof(f7595,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(forward_demodulation,[],[f5909,f4957]) ).
fof(f5909,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
inference(cnf_transformation,[],[f4314]) ).
fof(f11823,plain,
spl263_714,
inference(avatar_split_clause,[],[f7581,f11821]) ).
fof(f11821,plain,
( spl263_714
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| sP17(X0,X1)
| ~ sP16(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_714])]) ).
fof(f7581,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| sP17(X0,X1)
| ~ sP16(X1,X0) ),
inference(forward_demodulation,[],[f7096,f4875]) ).
fof(f7096,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ sP16(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
inference(definition_unfolding,[],[f5893,f4830]) ).
fof(f5893,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ sP16(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(cnf_transformation,[],[f4306]) ).
fof(f11819,plain,
spl263_713,
inference(avatar_split_clause,[],[f7573,f11817]) ).
fof(f11817,plain,
( spl263_713
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_713])]) ).
fof(f7573,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f7572,f4876]) ).
fof(f7572,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(forward_demodulation,[],[f5839,f4876]) ).
fof(f5839,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(cnf_transformation,[],[f3265]) ).
fof(f3265,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ) ),
inference(ennf_transformation,[],[f2061]) ).
fof(f2061,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))) ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X11)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11815,plain,
spl263_712,
inference(avatar_split_clause,[],[f7571,f11813]) ).
fof(f11813,plain,
( spl263_712
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_712])]) ).
fof(f7571,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f7570,f4876]) ).
fof(f7570,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f5840,f4876]) ).
fof(f5840,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(cnf_transformation,[],[f3265]) ).
fof(f11811,plain,
spl263_711,
inference(avatar_split_clause,[],[f7569,f11809]) ).
fof(f11809,plain,
( spl263_711
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_711])]) ).
fof(f7569,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f7568,f4874]) ).
fof(f7568,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
inference(forward_demodulation,[],[f5837,f4874]) ).
fof(f5837,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
inference(cnf_transformation,[],[f3264]) ).
fof(f3264,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ) ),
inference(ennf_transformation,[],[f2060]) ).
fof(f2060,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) )
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
! [X11,X12] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X11)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X12))) )
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X12),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11807,plain,
spl263_710,
inference(avatar_split_clause,[],[f7567,f11805]) ).
fof(f11805,plain,
( spl263_710
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_710])]) ).
fof(f7567,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f7566,f4874]) ).
fof(f7566,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
inference(forward_demodulation,[],[f5838,f4874]) ).
fof(f5838,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
inference(cnf_transformation,[],[f3264]) ).
fof(f11803,plain,
spl263_709,
inference(avatar_split_clause,[],[f7553,f11801]) ).
fof(f11801,plain,
( spl263_709
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| hAPP_nat_nat(suc,sK138(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_709])]) ).
fof(f7553,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| hAPP_nat_nat(suc,sK138(X1)) = X1 ),
inference(forward_demodulation,[],[f5788,f4957]) ).
fof(f5788,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK138(X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f4259]) ).
fof(f4259,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK138(X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138])],[f3205,f4258]) ).
fof(f4258,plain,
! [X1] :
( ? [X2] : hAPP_nat_nat(suc,X2) = X1
=> hAPP_nat_nat(suc,sK138(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3205,plain,
! [X0,X1] :
( ? [X2] : hAPP_nat_nat(suc,X2) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(ennf_transformation,[],[f2026]) ).
fof(f2026,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
=> ? [X2] : hAPP_nat_nat(suc,X2) = X1 ),
inference(rectify,[],[f407]) ).
fof(f407,axiom,
! [X13,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X13)),X33))
=> ? [X34] : hAPP_nat_nat(suc,X34) = X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11799,plain,
spl263_708,
inference(avatar_split_clause,[],[f7415,f11797]) ).
fof(f11797,plain,
( spl263_708
<=> ! [X0] :
( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_708])]) ).
fof(f7415,plain,
! [X0] :
( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(forward_demodulation,[],[f4987,f4958]) ).
fof(f4987,plain,
! [X0] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f2696]) ).
fof(f11795,plain,
spl263_707,
inference(avatar_split_clause,[],[f7334,f11793]) ).
fof(f7334,plain,
! [X2,X0,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP31(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ),
inference(equality_resolution,[],[f6774]) ).
fof(f6774,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f4695]) ).
fof(f11791,plain,
spl263_706,
inference(avatar_split_clause,[],[f7333,f11789]) ).
fof(f7333,plain,
! [X2,X0,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP30(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ),
inference(equality_resolution,[],[f6766]) ).
fof(f6766,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f4689]) ).
fof(f11787,plain,
spl263_705,
inference(avatar_split_clause,[],[f7261,f11785]) ).
fof(f11785,plain,
( spl263_705
<=> ! [X2,X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_705])]) ).
fof(f7261,plain,
! [X2,X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(equality_resolution,[],[f5939]) ).
fof(f5939,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 ),
inference(cnf_transformation,[],[f4344]) ).
fof(f11783,plain,
spl263_704,
inference(avatar_split_clause,[],[f7167,f11781]) ).
fof(f11781,plain,
( spl263_704
<=> ! [X2,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_704])]) ).
fof(f7167,plain,
! [X2,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(equality_resolution,[],[f5120]) ).
fof(f5120,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ),
inference(cnf_transformation,[],[f4091]) ).
fof(f11779,plain,
spl263_703,
inference(avatar_split_clause,[],[f7165,f11777]) ).
fof(f11777,plain,
( spl263_703
<=> ! [X2,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_703])]) ).
fof(f7165,plain,
! [X2,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(equality_resolution,[],[f5114]) ).
fof(f5114,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ),
inference(cnf_transformation,[],[f4085]) ).
fof(f11775,plain,
spl263_702,
inference(avatar_split_clause,[],[f7060,f11773]) ).
fof(f11773,plain,
( spl263_702
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_702])]) ).
fof(f7060,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
inference(definition_unfolding,[],[f5149,f4830]) ).
fof(f5149,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
inference(cnf_transformation,[],[f4113]) ).
fof(f4113,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
inference(nnf_transformation,[],[f1604]) ).
fof(f1604,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(rectify,[],[f1143]) ).
fof(f1143,axiom,
! [X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X55))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11771,plain,
spl263_701,
inference(avatar_split_clause,[],[f7059,f11769]) ).
fof(f11769,plain,
( spl263_701
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_701])]) ).
fof(f7059,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f5150,f4830]) ).
fof(f5150,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4113]) ).
fof(f11767,plain,
spl263_700,
inference(avatar_split_clause,[],[f7049,f11765]) ).
fof(f11765,plain,
( spl263_700
<=> ! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK59(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_700])]) ).
fof(f7049,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK59(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5072,f4830]) ).
fof(f5072,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK59(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4040]) ).
fof(f4040,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK59(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f2740,f4039]) ).
fof(f4039,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
=> hAPP_nat_int(semiri1621563631at_int,sK59(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2740,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1567]) ).
fof(f1567,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0 ),
inference(rectify,[],[f1249]) ).
fof(f1249,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ? [X28] : hAPP_nat_int(semiri1621563631at_int,X28) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11763,plain,
spl263_699,
inference(avatar_split_clause,[],[f7048,f11761]) ).
fof(f11761,plain,
( spl263_699
<=> ! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK58(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_699])]) ).
fof(f7048,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK58(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5071,f4830]) ).
fof(f5071,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK58(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4038]) ).
fof(f4038,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK58(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f2739,f4037]) ).
fof(f4037,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
=> hAPP_nat_int(semiri1621563631at_int,sK58(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2739,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1566]) ).
fof(f1566,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ~ ! [X1] : hAPP_nat_int(semiri1621563631at_int,X1) != X0 ),
inference(rectify,[],[f1247]) ).
fof(f1247,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ~ ! [X28] : hAPP_nat_int(semiri1621563631at_int,X28) != X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11759,plain,
spl263_698,
inference(avatar_split_clause,[],[f7047,f11757]) ).
fof(f11757,plain,
( spl263_698
<=> ! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK57(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_698])]) ).
fof(f7047,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK57(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5070,f4830]) ).
fof(f5070,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK57(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4036]) ).
fof(f4036,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK57(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f2738,f4035]) ).
fof(f4035,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
=> hAPP_nat_int(semiri1621563631at_int,sK57(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2738,plain,
! [X0] :
( ? [X1] : hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(ennf_transformation,[],[f1565]) ).
fof(f1565,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> ~ ! [X1] : hAPP_nat_int(semiri1621563631at_int,X1) != X0 ),
inference(rectify,[],[f1248]) ).
fof(f1248,axiom,
! [X97] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X97))
=> ~ ! [X34] : hAPP_nat_int(semiri1621563631at_int,X34) != X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11755,plain,
spl263_697,
inference(avatar_split_clause,[],[f7044,f11753]) ).
fof(f11753,plain,
( spl263_697
<=> ! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK56(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_697])]) ).
fof(f7044,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK56(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f5068,f4830]) ).
fof(f5068,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,sK56(X0)) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4034]) ).
fof(f11749,plain,
( spl263_696
| ~ spl263_242
| ~ spl263_525
| ~ spl263_695 ),
inference(avatar_split_clause,[],[f11744,f11738,f10603,f8916,f11746]) ).
fof(f11746,plain,
( spl263_696
<=> one_one_nat = number_number_of_nat(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_696])]) ).
fof(f8916,plain,
( spl263_242
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_242])]) ).
fof(f10603,plain,
( spl263_525
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_525])]) ).
fof(f11738,plain,
( spl263_695
<=> one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_695])]) ).
fof(f11744,plain,
( one_one_nat = number_number_of_nat(one_one_int)
| ~ spl263_242
| ~ spl263_525
| ~ spl263_695 ),
inference(forward_demodulation,[],[f11743,f8917]) ).
fof(f8917,plain,
( ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0
| ~ spl263_242 ),
inference(avatar_component_clause,[],[f8916]) ).
fof(f11743,plain,
( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls))
| ~ spl263_525
| ~ spl263_695 ),
inference(forward_demodulation,[],[f11742,f10604]) ).
fof(f10604,plain,
( ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)
| ~ spl263_525 ),
inference(avatar_component_clause,[],[f10603]) ).
fof(f11742,plain,
( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))
| ~ spl263_695 ),
inference(forward_demodulation,[],[f11740,f7020]) ).
fof(f11740,plain,
( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))
| ~ spl263_695 ),
inference(avatar_component_clause,[],[f11738]) ).
fof(f11741,plain,
spl263_695,
inference(avatar_split_clause,[],[f7016,f11738]) ).
fof(f7016,plain,
one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)),
inference(definition_unfolding,[],[f4846,f4973]) ).
fof(f4846,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11733,plain,
spl263_694,
inference(avatar_split_clause,[],[f7015,f11730]) ).
fof(f11730,plain,
( spl263_694
<=> one_one_int = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_694])]) ).
fof(f7015,plain,
one_one_int = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)),
inference(definition_unfolding,[],[f4843,f4973]) ).
fof(f4843,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(cnf_transformation,[],[f1282]) ).
fof(f1282,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11728,plain,
spl263_693,
inference(avatar_split_clause,[],[f6782,f11726]) ).
fof(f11726,plain,
( spl263_693
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_693])]) ).
fof(f6782,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f4697]) ).
fof(f4697,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) )
& ( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ) ),
inference(nnf_transformation,[],[f2586]) ).
fof(f2586,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
<=> hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rectify,[],[f771]) ).
fof(f771,axiom,
! [X75,X76,X19] :
( hBOOL(hAPP_nat_bool(nat_case_bool(X75,X76),hAPP_nat_nat(suc,X19)))
<=> hBOOL(hAPP_nat_bool(X76,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11724,plain,
spl263_692,
inference(avatar_split_clause,[],[f6781,f11722]) ).
fof(f11722,plain,
( spl263_692
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_692])]) ).
fof(f6781,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ),
inference(cnf_transformation,[],[f4697]) ).
fof(f11720,plain,
spl263_691,
inference(avatar_split_clause,[],[f6780,f11718]) ).
fof(f11718,plain,
( spl263_691
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_691])]) ).
fof(f6780,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f4696]) ).
fof(f4696,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP31(X0,X1,X2) )
& ( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
inference(nnf_transformation,[],[f3969]) ).
fof(f3969,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> sP31(X0,X1,X2) ),
inference(definition_folding,[],[f3813,f3968]) ).
fof(f3813,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2585]) ).
fof(f2585,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> ~ ( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(rectify,[],[f1069]) ).
fof(f1069,axiom,
! [X12,X7,X30] :
( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X7),X30)))
<=> ~ ( ? [X129] :
( ~ hBOOL(hAPP_nat_bool(X12,X129))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X30),X129) = X7 )
| ( ~ hBOOL(hAPP_nat_bool(X12,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7),X30)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11716,plain,
spl263_690,
inference(avatar_split_clause,[],[f6779,f11714]) ).
fof(f6779,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(cnf_transformation,[],[f4696]) ).
fof(f11712,plain,
spl263_689,
inference(avatar_split_clause,[],[f6772,f11710]) ).
fof(f11710,plain,
( spl263_689
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP30(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_689])]) ).
fof(f6772,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f4690]) ).
fof(f4690,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ sP30(X0,X1,X2) )
& ( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
inference(nnf_transformation,[],[f3967]) ).
fof(f3967,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> sP30(X0,X1,X2) ),
inference(definition_folding,[],[f3812,f3966]) ).
fof(f3812,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2584]) ).
fof(f2584,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
<=> ( ! [X3] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1
=> hBOOL(hAPP_nat_bool(X0,X3)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
inference(rectify,[],[f1068]) ).
fof(f1068,axiom,
! [X12,X7,X30] :
( hBOOL(hAPP_nat_bool(X12,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X7),X30)))
<=> ( ! [X129] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X30),X129) = X7
=> hBOOL(hAPP_nat_bool(X12,X129)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7),X30))
=> hBOOL(hAPP_nat_bool(X12,zero_zero_nat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11708,plain,
spl263_688,
inference(avatar_split_clause,[],[f6771,f11706]) ).
fof(f6771,plain,
! [X2,X0,X1] :
( sP30(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(cnf_transformation,[],[f4690]) ).
fof(f11704,plain,
spl263_687,
inference(avatar_split_clause,[],[f6503,f11702]) ).
fof(f11702,plain,
( spl263_687
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK230(X0,X1,X2)),X2))
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_687])]) ).
fof(f6503,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK230(X0,X1,X2)),X2))
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f4601]) ).
fof(f11700,plain,
spl263_686,
inference(avatar_split_clause,[],[f6498,f11698]) ).
fof(f11698,plain,
( spl263_686
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_686])]) ).
fof(f6498,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK226(X0,X1,X2)))
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f4591]) ).
fof(f11696,plain,
spl263_685,
inference(avatar_split_clause,[],[f6152,f11694]) ).
fof(f11694,plain,
( spl263_685
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_685])]) ).
fof(f6152,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2218]) ).
fof(f2218,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1),
inference(rectify,[],[f1352]) ).
fof(f1352,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X158),X159),X160) = hAPP_nat_bool(hAPP_n1699378549t_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11692,plain,
spl263_684,
inference(avatar_split_clause,[],[f6151,f11690]) ).
fof(f11690,plain,
( spl263_684
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_684])]) ).
fof(f6151,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2217]) ).
fof(f2217,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1),
inference(rectify,[],[f1376]) ).
fof(f1376,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X158),X159),X160) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11688,plain,
( spl263_683
| ~ spl263_154
| ~ spl263_367 ),
inference(avatar_split_clause,[],[f10926,f9614,f8519,f11685]) ).
fof(f11685,plain,
( spl263_683
<=> bot_bot_fun_a_bool = collect_a(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_683])]) ).
fof(f8519,plain,
( spl263_154
<=> ! [X0] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_154])]) ).
fof(f9614,plain,
( spl263_367
<=> ! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| hBOOL(hAPP_a_bool(X0,sK65(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_367])]) ).
fof(f10926,plain,
( bot_bot_fun_a_bool = collect_a(bot_bot_fun_a_bool)
| ~ spl263_154
| ~ spl263_367 ),
inference(resolution,[],[f8520,f9615]) ).
fof(f9615,plain,
( ! [X0] :
( hBOOL(hAPP_a_bool(X0,sK65(X0)))
| bot_bot_fun_a_bool = collect_a(X0) )
| ~ spl263_367 ),
inference(avatar_component_clause,[],[f9614]) ).
fof(f8520,plain,
( ! [X0] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
| ~ spl263_154 ),
inference(avatar_component_clause,[],[f8519]) ).
fof(f11683,plain,
spl263_682,
inference(avatar_split_clause,[],[f6150,f11681]) ).
fof(f11681,plain,
( spl263_682
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_682])]) ).
fof(f6150,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2216]) ).
fof(f2216,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1),
inference(rectify,[],[f1351]) ).
fof(f1351,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X158),X159),X160) = hAPP_int_bool(hAPP_n1082236369t_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11679,plain,
spl263_681,
inference(avatar_split_clause,[],[f6149,f11677]) ).
fof(f11677,plain,
( spl263_681
<=> ! [X2,X0,X1] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_681])]) ).
fof(f6149,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2215]) ).
fof(f2215,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1),
inference(rectify,[],[f1375]) ).
fof(f1375,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X158),X159),X160) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11675,plain,
spl263_680,
inference(avatar_split_clause,[],[f6148,f11673]) ).
fof(f6148,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2214]) ).
fof(f2214,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1),
inference(rectify,[],[f1365]) ).
fof(f1365,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X158),X159),X160) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11671,plain,
spl263_679,
inference(avatar_split_clause,[],[f6147,f11669]) ).
fof(f6147,plain,
! [X2,X0,X1] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2213]) ).
fof(f2213,plain,
! [X0,X1,X2] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1),
inference(rectify,[],[f1382]) ).
fof(f1382,axiom,
! [X158,X159,X160] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X158),X159),X160) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11667,plain,
spl263_678,
inference(avatar_split_clause,[],[f6146,f11665]) ).
fof(f11665,plain,
( spl263_678
<=> ! [X2,X0,X1] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_678])]) ).
fof(f6146,plain,
! [X2,X0,X1] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2212]) ).
fof(f2212,plain,
! [X0,X1,X2] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1),
inference(rectify,[],[f1390]) ).
fof(f1390,axiom,
! [X158,X159,X160] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X158),X159),X160) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11663,plain,
spl263_677,
inference(avatar_split_clause,[],[f6145,f11661]) ).
fof(f11661,plain,
( spl263_677
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_677])]) ).
fof(f6145,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2211]) ).
fof(f2211,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1),
inference(rectify,[],[f1350]) ).
fof(f1350,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X158),X159),X160) = hAPP_int_bool(hAPP_i1948725293t_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11659,plain,
spl263_676,
inference(avatar_split_clause,[],[f6144,f11657]) ).
fof(f11657,plain,
( spl263_676
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_676])]) ).
fof(f6144,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2210]) ).
fof(f2210,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1),
inference(rectify,[],[f1373]) ).
fof(f1373,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X158),X159),X160) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11655,plain,
spl263_675,
inference(avatar_split_clause,[],[f6143,f11653]) ).
fof(f11653,plain,
( spl263_675
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_675])]) ).
fof(f6143,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2209]) ).
fof(f2209,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1),
inference(rectify,[],[f1374]) ).
fof(f1374,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X158),X159),X160) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11651,plain,
spl263_674,
inference(avatar_split_clause,[],[f6142,f11649]) ).
fof(f11649,plain,
( spl263_674
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_674])]) ).
fof(f6142,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2208]) ).
fof(f2208,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1),
inference(rectify,[],[f1364]) ).
fof(f1364,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X158),X159),X160) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11647,plain,
spl263_673,
inference(avatar_split_clause,[],[f6141,f11645]) ).
fof(f11645,plain,
( spl263_673
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_673])]) ).
fof(f6141,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2207]) ).
fof(f2207,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1),
inference(rectify,[],[f1381]) ).
fof(f1381,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X158),X159),X160) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11643,plain,
spl263_672,
inference(avatar_split_clause,[],[f6140,f11641]) ).
fof(f11641,plain,
( spl263_672
<=> ! [X2,X0,X1] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_672])]) ).
fof(f6140,plain,
! [X2,X0,X1] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2206]) ).
fof(f2206,plain,
! [X0,X1,X2] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1),
inference(rectify,[],[f1339]) ).
fof(f1339,axiom,
! [X158,X159,X160] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X158),X159),X160) = hAPP_a_bool(hAPP_int_fun_a_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11639,plain,
spl263_671,
inference(avatar_split_clause,[],[f6139,f11637]) ).
fof(f11637,plain,
( spl263_671
<=> ! [X2,X0,X1] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_671])]) ).
fof(f6139,plain,
! [X2,X0,X1] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2205]) ).
fof(f2205,plain,
! [X0,X1,X2] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1),
inference(rectify,[],[f1392]) ).
fof(f1392,axiom,
! [X158,X159,X160] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X158),X159),X160) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11635,plain,
spl263_670,
inference(avatar_split_clause,[],[f6138,f11633]) ).
fof(f11633,plain,
( spl263_670
<=> ! [X2,X0,X1] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_670])]) ).
fof(f6138,plain,
! [X2,X0,X1] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2204]) ).
fof(f2204,plain,
! [X0,X1,X2] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1),
inference(rectify,[],[f1391]) ).
fof(f1391,axiom,
! [X158,X159,X160] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X158),X159),X160) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11631,plain,
spl263_669,
inference(avatar_split_clause,[],[f6137,f11629]) ).
fof(f11629,plain,
( spl263_669
<=> ! [X2,X0,X1] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_669])]) ).
fof(f6137,plain,
! [X2,X0,X1] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2203]) ).
fof(f2203,plain,
! [X0,X1,X2] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1),
inference(rectify,[],[f1386]) ).
fof(f1386,axiom,
! [X158,X159,X160] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X158),X159),X160) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11627,plain,
spl263_668,
inference(avatar_split_clause,[],[f6136,f11625]) ).
fof(f11625,plain,
( spl263_668
<=> ! [X2,X0,X1] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_668])]) ).
fof(f6136,plain,
! [X2,X0,X1] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2202]) ).
fof(f2202,plain,
! [X0,X1,X2] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1),
inference(rectify,[],[f1396]) ).
fof(f1396,axiom,
! [X158,X159,X160] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X158),X159),X160) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11623,plain,
spl263_667,
inference(avatar_split_clause,[],[f6135,f11621]) ).
fof(f11621,plain,
( spl263_667
<=> ! [X2,X0,X1] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_667])]) ).
fof(f6135,plain,
! [X2,X0,X1] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2201]) ).
fof(f2201,plain,
! [X0,X1,X2] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1),
inference(rectify,[],[f1389]) ).
fof(f1389,axiom,
! [X158,X159,X160] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X158),X159),X160) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11619,plain,
spl263_666,
inference(avatar_split_clause,[],[f6134,f11617]) ).
fof(f11617,plain,
( spl263_666
<=> ! [X2,X0,X1] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_666])]) ).
fof(f6134,plain,
! [X2,X0,X1] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2200]) ).
fof(f2200,plain,
! [X0,X1,X2] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1),
inference(rectify,[],[f1408]) ).
fof(f1408,axiom,
! [X158,X159,X160] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X158),X159),X160) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11615,plain,
spl263_665,
inference(avatar_split_clause,[],[f6133,f11613]) ).
fof(f11613,plain,
( spl263_665
<=> ! [X2,X0,X1] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_665])]) ).
fof(f6133,plain,
! [X2,X0,X1] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2199]) ).
fof(f2199,plain,
! [X0,X1,X2] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1),
inference(rectify,[],[f1406]) ).
fof(f1406,axiom,
! [X158,X159,X160] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X158),X159),X160) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11611,plain,
spl263_664,
inference(avatar_split_clause,[],[f6132,f11609]) ).
fof(f11609,plain,
( spl263_664
<=> ! [X2,X0,X1] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_664])]) ).
fof(f6132,plain,
! [X2,X0,X1] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2198]) ).
fof(f2198,plain,
! [X0,X1,X2] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1),
inference(rectify,[],[f1405]) ).
fof(f1405,axiom,
! [X158,X159,X160] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X158),X159),X160) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11607,plain,
spl263_663,
inference(avatar_split_clause,[],[f6131,f11605]) ).
fof(f11605,plain,
( spl263_663
<=> ! [X2,X0,X1] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_663])]) ).
fof(f6131,plain,
! [X2,X0,X1] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2197]) ).
fof(f2197,plain,
! [X0,X1,X2] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1),
inference(rectify,[],[f1407]) ).
fof(f1407,axiom,
! [X158,X159,X160] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X158),X159),X160) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11602,plain,
spl263_662,
inference(avatar_split_clause,[],[f6130,f11600]) ).
fof(f11600,plain,
( spl263_662
<=> ! [X2,X0,X1] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_662])]) ).
fof(f6130,plain,
! [X2,X0,X1] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2196]) ).
fof(f2196,plain,
! [X0,X1,X2] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1),
inference(rectify,[],[f1362]) ).
fof(f1362,axiom,
! [X158,X159,X160] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X158),X159),X160) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11598,plain,
spl263_661,
inference(avatar_split_clause,[],[f6129,f11596]) ).
fof(f11596,plain,
( spl263_661
<=> ! [X2,X0,X1] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_661])]) ).
fof(f6129,plain,
! [X2,X0,X1] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2195]) ).
fof(f2195,plain,
! [X0,X1,X2] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1),
inference(rectify,[],[f1333]) ).
fof(f1333,axiom,
! [X158,X159,X160] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X158),X159),X160) = hAPP_a_bool(hAPP_a_fun_a_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11594,plain,
spl263_660,
inference(avatar_split_clause,[],[f6128,f11592]) ).
fof(f11592,plain,
( spl263_660
<=> ! [X2,X0,X1] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_660])]) ).
fof(f6128,plain,
! [X2,X0,X1] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2194]) ).
fof(f2194,plain,
! [X0,X1,X2] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1),
inference(rectify,[],[f1370]) ).
fof(f1370,axiom,
! [X158,X159,X160] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X158),X159),X160) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11590,plain,
spl263_659,
inference(avatar_split_clause,[],[f6127,f11588]) ).
fof(f11588,plain,
( spl263_659
<=> ! [X2,X0,X1] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_659])]) ).
fof(f6127,plain,
! [X2,X0,X1] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2193]) ).
fof(f2193,plain,
! [X0,X1,X2] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1),
inference(rectify,[],[f1385]) ).
fof(f1385,axiom,
! [X158,X159,X160] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X158),X159),X160) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11586,plain,
spl263_658,
inference(avatar_split_clause,[],[f6126,f11584]) ).
fof(f11584,plain,
( spl263_658
<=> ! [X2,X0,X1] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_658])]) ).
fof(f6126,plain,
! [X2,X0,X1] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2192]) ).
fof(f2192,plain,
! [X0,X1,X2] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1),
inference(rectify,[],[f1359]) ).
fof(f1359,axiom,
! [X158,X159,X160] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X158),X159),X160) = hAPP_pname_bool(hAPP_p61793385e_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11582,plain,
spl263_657,
inference(avatar_split_clause,[],[f6125,f11580]) ).
fof(f11580,plain,
( spl263_657
<=> ! [X2,X0,X1] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_657])]) ).
fof(f6125,plain,
! [X2,X0,X1] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1),
inference(cnf_transformation,[],[f2191]) ).
fof(f2191,plain,
! [X0,X1,X2] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1),
inference(rectify,[],[f1342]) ).
fof(f1342,axiom,
! [X158,X159,X160] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X158),X159),X160) = hAPP_a_bool(hAPP_p1534023578a_bool(X158,X160),X159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11578,plain,
spl263_656,
inference(avatar_split_clause,[],[f5986,f11576]) ).
fof(f11576,plain,
( spl263_656
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_656])]) ).
fof(f5986,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ),
inference(cnf_transformation,[],[f4377]) ).
fof(f4377,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ) ),
inference(nnf_transformation,[],[f2121]) ).
fof(f2121,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rectify,[],[f252]) ).
fof(f252,axiom,
! [X7,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X4)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11574,plain,
spl263_655,
inference(avatar_split_clause,[],[f5984,f11572]) ).
fof(f11572,plain,
( spl263_655
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_655])]) ).
fof(f5984,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ),
inference(cnf_transformation,[],[f4376]) ).
fof(f4376,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ) ),
inference(nnf_transformation,[],[f2120]) ).
fof(f2120,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X7,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X4)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11570,plain,
spl263_654,
inference(avatar_split_clause,[],[f5982,f11568]) ).
fof(f11568,plain,
( spl263_654
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_654])]) ).
fof(f5982,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ),
inference(cnf_transformation,[],[f4375]) ).
fof(f4375,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ) ),
inference(nnf_transformation,[],[f2119]) ).
fof(f2119,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X7,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X4)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11566,plain,
spl263_653,
inference(avatar_split_clause,[],[f5980,f11564]) ).
fof(f11564,plain,
( spl263_653
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_653])]) ).
fof(f5980,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ),
inference(cnf_transformation,[],[f4374]) ).
fof(f4374,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ) ),
inference(nnf_transformation,[],[f2118]) ).
fof(f2118,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X4)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11562,plain,
spl263_652,
inference(avatar_split_clause,[],[f5978,f11560]) ).
fof(f11560,plain,
( spl263_652
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_652])]) ).
fof(f5978,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ),
inference(cnf_transformation,[],[f4373]) ).
fof(f4373,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ) ),
inference(nnf_transformation,[],[f2117]) ).
fof(f2117,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X7,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X7),X4)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11558,plain,
spl263_651,
inference(avatar_split_clause,[],[f5976,f11556]) ).
fof(f11556,plain,
( spl263_651
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_651])]) ).
fof(f5976,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ),
inference(cnf_transformation,[],[f4372]) ).
fof(f4372,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ) ),
inference(nnf_transformation,[],[f2116]) ).
fof(f2116,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X7),X4)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11554,plain,
spl263_650,
inference(avatar_split_clause,[],[f5974,f11552]) ).
fof(f11552,plain,
( spl263_650
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_650])]) ).
fof(f5974,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ),
inference(cnf_transformation,[],[f4371]) ).
fof(f4371,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ) ),
inference(nnf_transformation,[],[f2115]) ).
fof(f2115,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X7),X4)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11550,plain,
spl263_649,
inference(avatar_split_clause,[],[f5972,f11548]) ).
fof(f11548,plain,
( spl263_649
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_649])]) ).
fof(f5972,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ),
inference(cnf_transformation,[],[f4370]) ).
fof(f4370,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ) ),
inference(nnf_transformation,[],[f2114]) ).
fof(f2114,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
<=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X7,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X7),X4)))
<=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11546,plain,
spl263_648,
inference(avatar_split_clause,[],[f5933,f11544]) ).
fof(f11544,plain,
( spl263_648
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_648])]) ).
fof(f5933,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4336]) ).
fof(f11542,plain,
spl263_647,
inference(avatar_split_clause,[],[f5862,f11540]) ).
fof(f11540,plain,
( spl263_647
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK148(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_647])]) ).
fof(f5862,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK148(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4288]) ).
fof(f4288,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK148(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK148(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f3278,f4287]) ).
fof(f4287,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK148(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK148(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3278,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f2072]) ).
fof(f2072,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rectify,[],[f1024]) ).
fof(f1024,axiom,
! [X16,X71] :
( ! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X71))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X16)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11538,plain,
spl263_646,
inference(avatar_split_clause,[],[f5861,f11536]) ).
fof(f11536,plain,
( spl263_646
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK148(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_646])]) ).
fof(f5861,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK148(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4288]) ).
fof(f11534,plain,
spl263_645,
inference(avatar_split_clause,[],[f5777,f11532]) ).
fof(f11532,plain,
( spl263_645
<=> ! [X0,X1] :
( one_one_int = abs_abs_int(X0)
| one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_645])]) ).
fof(f5777,plain,
! [X0,X1] :
( one_one_int = abs_abs_int(X0)
| one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ),
inference(cnf_transformation,[],[f3190]) ).
fof(f3190,plain,
! [X0,X1] :
( one_one_int = abs_abs_int(X0)
| one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ),
inference(ennf_transformation,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1] :
( one_one_int = abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1))
=> one_one_int = abs_abs_int(X0) ),
inference(rectify,[],[f1257]) ).
fof(f1257,axiom,
! [X14,X13] :
( one_one_int = abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X14),X13))
=> one_one_int = abs_abs_int(X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11530,plain,
spl263_644,
inference(avatar_split_clause,[],[f5746,f11528]) ).
fof(f11528,plain,
( spl263_644
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_644])]) ).
fof(f5746,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3155]) ).
fof(f3155,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1989]) ).
fof(f1989,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f996]) ).
fof(f996,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11526,plain,
spl263_643,
inference(avatar_split_clause,[],[f5670,f11524]) ).
fof(f5670,plain,
! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK125(X0)),sK126(X0))))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f4230]) ).
fof(f4230,plain,
! [X0] :
( ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK125(X0)),sK126(X0))))
& hBOOL(hAPP_f54304608l_bool(X0,sK126(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK125(X0)),sK126(X0)))
& bot_bot_fun_nat_bool != sK126(X0)
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK126(X0))) )
| ~ sP15(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126])],[f4228,f4229]) ).
fof(f4229,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
& hBOOL(hAPP_f54304608l_bool(X0,X2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
& bot_bot_fun_nat_bool != X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK125(X0)),sK126(X0))))
& hBOOL(hAPP_f54304608l_bool(X0,sK126(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK125(X0)),sK126(X0)))
& bot_bot_fun_nat_bool != sK126(X0)
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK126(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f4228,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
& hBOOL(hAPP_f54304608l_bool(X0,X2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
& bot_bot_fun_nat_bool != X2
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) )
| ~ sP15(X0) ),
inference(rectify,[],[f4227]) ).
fof(f4227,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
& hBOOL(hAPP_f54304608l_bool(X0,X4))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& bot_bot_fun_nat_bool != X4
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f3937]) ).
fof(f11522,plain,
spl263_642,
inference(avatar_split_clause,[],[f5653,f11520]) ).
fof(f11520,plain,
( spl263_642
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_642])]) ).
fof(f5653,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3049]) ).
fof(f3049,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1918]) ).
fof(f1918,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0))) ),
inference(rectify,[],[f602]) ).
fof(f602,axiom,
! [X9,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11518,plain,
spl263_641,
inference(avatar_split_clause,[],[f5627,f11516]) ).
fof(f5627,plain,
! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK118(X0)),sK119(X0))))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f4219]) ).
fof(f4219,plain,
! [X0] :
( ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK118(X0)),sK119(X0))))
& hBOOL(hAPP_f448129468l_bool(X0,sK119(X0)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK118(X0)),sK119(X0)))
& bot_bot_fun_int_bool != sK119(X0)
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK119(X0))) )
| ~ sP14(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119])],[f4217,f4218]) ).
fof(f4218,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
& hBOOL(hAPP_f448129468l_bool(X0,X2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
& bot_bot_fun_int_bool != X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) )
=> ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK118(X0)),sK119(X0))))
& hBOOL(hAPP_f448129468l_bool(X0,sK119(X0)))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK118(X0)),sK119(X0)))
& bot_bot_fun_int_bool != sK119(X0)
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK119(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f4217,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
& hBOOL(hAPP_f448129468l_bool(X0,X2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
& bot_bot_fun_int_bool != X2
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) )
| ~ sP14(X0) ),
inference(rectify,[],[f4216]) ).
fof(f4216,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
& hBOOL(hAPP_f448129468l_bool(X0,X4))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& bot_bot_fun_int_bool != X4
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f3935]) ).
fof(f11514,plain,
spl263_640,
inference(avatar_split_clause,[],[f5611,f11512]) ).
fof(f11512,plain,
( spl263_640
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_640])]) ).
fof(f5611,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3010]) ).
fof(f3010,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1890]) ).
fof(f1890,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0))) ),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X9,X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11510,plain,
spl263_639,
inference(avatar_split_clause,[],[f5590,f11508]) ).
fof(f5590,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK114(X0)),sK115(X0))))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f4211,plain,
! [X0] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK114(X0)),sK115(X0))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK115(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK114(X0)),sK115(X0)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK115(X0)))
& is_fun_a_bool(sK115(X0))
& is_a(sK114(X0)) )
| ~ sP12(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114,sK115])],[f4209,f4210]) ).
fof(f4210,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK114(X0)),sK115(X0))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK115(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK114(X0)),sK115(X0)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK115(X0)))
& is_fun_a_bool(sK115(X0))
& is_a(sK114(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4209,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
| ~ sP12(X0) ),
inference(rectify,[],[f4208]) ).
fof(f4208,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X3))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
& is_fun_a_bool(X3)
& is_a(X2) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f3931]) ).
fof(f11506,plain,
spl263_638,
inference(avatar_split_clause,[],[f5571,f11504]) ).
fof(f11504,plain,
( spl263_638
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_638])]) ).
fof(f5571,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2975]) ).
fof(f2975,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1864]) ).
fof(f1864,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X7,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11502,plain,
spl263_637,
inference(avatar_split_clause,[],[f5550,f11500]) ).
fof(f11500,plain,
( spl263_637
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK110(X0)),sK111(X0))))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_637])]) ).
fof(f5550,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK110(X0)),sK111(X0))))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f4202,plain,
! [X0] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK110(X0)),sK111(X0))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK111(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK110(X0)),sK111(X0)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK111(X0)))
& is_fun_pname_bool(sK111(X0))
& is_pname(sK110(X0)) )
| ~ sP10(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f4200,f4201]) ).
fof(f4201,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK110(X0)),sK111(X0))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK111(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK110(X0)),sK111(X0)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK111(X0)))
& is_fun_pname_bool(sK111(X0))
& is_pname(sK110(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4200,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
| ~ sP10(X0) ),
inference(rectify,[],[f4199]) ).
fof(f4199,plain,
! [X0] :
( ? [X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
& hBOOL(hAPP_f1664156314l_bool(X0,X3))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& is_fun_pname_bool(X3)
& is_pname(X2) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f3927]) ).
fof(f11498,plain,
spl263_636,
inference(avatar_split_clause,[],[f5531,f11496]) ).
fof(f11496,plain,
( spl263_636
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_636])]) ).
fof(f5531,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2941]) ).
fof(f2941,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1839]) ).
fof(f1839,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11494,plain,
spl263_635,
inference(avatar_split_clause,[],[f5530,f11492]) ).
fof(f11492,plain,
( spl263_635
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_635])]) ).
fof(f5530,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2940]) ).
fof(f2940,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1838]) ).
fof(f1838,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0))) ),
inference(rectify,[],[f603]) ).
fof(f603,axiom,
! [X9,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11490,plain,
spl263_634,
inference(avatar_split_clause,[],[f5486,f11488]) ).
fof(f11488,plain,
( spl263_634
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_634])]) ).
fof(f5486,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2886]) ).
fof(f2886,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11486,plain,
spl263_633,
inference(avatar_split_clause,[],[f5485,f11484]) ).
fof(f11484,plain,
( spl263_633
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_633])]) ).
fof(f5485,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2885]) ).
fof(f2885,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1797]) ).
fof(f1797,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X7,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11482,plain,
spl263_632,
inference(avatar_split_clause,[],[f5484,f11480]) ).
fof(f11480,plain,
( spl263_632
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_632])]) ).
fof(f5484,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2884]) ).
fof(f2884,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1796]) ).
fof(f1796,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11478,plain,
spl263_631,
inference(avatar_split_clause,[],[f5483,f11476]) ).
fof(f11476,plain,
( spl263_631
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_631])]) ).
fof(f5483,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2883]) ).
fof(f2883,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X7,X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X7),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11474,plain,
spl263_630,
inference(avatar_split_clause,[],[f5409,f11472]) ).
fof(f5409,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK93(X0)),sK94(X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f4168,plain,
! [X0] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK93(X0)),sK94(X0))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK94(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK93(X0)),sK94(X0)))
& bot_bot_fun_a_bool != sK94(X0)
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK94(X0)))
& is_fun_a_bool(sK94(X0))
& is_a(sK93(X0)) )
| ~ sP9(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94])],[f4166,f4167]) ).
fof(f4167,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& bot_bot_fun_a_bool != X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK93(X0)),sK94(X0))))
& hBOOL(hAPP_fun_a_bool_bool(X0,sK94(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK93(X0)),sK94(X0)))
& bot_bot_fun_a_bool != sK94(X0)
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK94(X0)))
& is_fun_a_bool(sK94(X0))
& is_a(sK93(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4166,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X2))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& bot_bot_fun_a_bool != X2
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
& is_fun_a_bool(X2)
& is_a(X1) )
| ~ sP9(X0) ),
inference(rectify,[],[f4165]) ).
fof(f4165,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
& hBOOL(hAPP_fun_a_bool_bool(X0,X4))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
& bot_bot_fun_a_bool != X4
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
& is_fun_a_bool(X4)
& is_a(X3) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f3925]) ).
fof(f11470,plain,
spl263_629,
inference(avatar_split_clause,[],[f5386,f11468]) ).
fof(f11468,plain,
( spl263_629
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK90(X0)),sK91(X0))))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_629])]) ).
fof(f5386,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK90(X0)),sK91(X0))))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f4160,plain,
! [X0] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK90(X0)),sK91(X0))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK91(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK90(X0)),sK91(X0)))
& bot_bo844097828e_bool != sK91(X0)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK91(X0)))
& is_fun_pname_bool(sK91(X0))
& is_pname(sK90(X0)) )
| ~ sP8(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90,sK91])],[f4158,f4159]) ).
fof(f4159,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& bot_bo844097828e_bool != X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK90(X0)),sK91(X0))))
& hBOOL(hAPP_f1664156314l_bool(X0,sK91(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK90(X0)),sK91(X0)))
& bot_bo844097828e_bool != sK91(X0)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK91(X0)))
& is_fun_pname_bool(sK91(X0))
& is_pname(sK90(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4158,plain,
! [X0] :
( ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
& hBOOL(hAPP_f1664156314l_bool(X0,X2))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& bot_bo844097828e_bool != X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
& is_fun_pname_bool(X2)
& is_pname(X1) )
| ~ sP8(X0) ),
inference(rectify,[],[f4157]) ).
fof(f4157,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
& hBOOL(hAPP_f1664156314l_bool(X0,X4))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
& bot_bo844097828e_bool != X4
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
& is_fun_pname_bool(X4)
& is_pname(X3) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f3923]) ).
fof(f11466,plain,
spl263_628,
inference(avatar_split_clause,[],[f5346,f11464]) ).
fof(f11464,plain,
( spl263_628
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_628])]) ).
fof(f5346,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1731]) ).
fof(f1731,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X36,X37] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X37),X36))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X36),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11462,plain,
spl263_627,
inference(avatar_split_clause,[],[f5344,f11460]) ).
fof(f11460,plain,
( spl263_627
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_627])]) ).
fof(f5344,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(rectify,[],[f1152]) ).
fof(f1152,axiom,
! [X97,X134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X134),X97))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X97),X134)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11458,plain,
spl263_626,
inference(avatar_split_clause,[],[f5264,f11456]) ).
fof(f11456,plain,
( spl263_626
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_626])]) ).
fof(f5264,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))),
inference(cnf_transformation,[],[f1660]) ).
fof(f1660,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))),
inference(rectify,[],[f1015]) ).
fof(f1015,axiom,
! [X14,X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)),hAPP_nat_nat(suc,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11454,plain,
spl263_625,
inference(avatar_split_clause,[],[f5263,f11452]) ).
fof(f11452,plain,
( spl263_625
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_625])]) ).
fof(f5263,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))),
inference(cnf_transformation,[],[f1659]) ).
fof(f1659,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))),
inference(rectify,[],[f1006]) ).
fof(f1006,axiom,
! [X22,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X22)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11450,plain,
spl263_624,
inference(avatar_split_clause,[],[f5262,f11448]) ).
fof(f11448,plain,
( spl263_624
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_624])]) ).
fof(f5262,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))),
inference(cnf_transformation,[],[f1658]) ).
fof(f1658,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))),
inference(rectify,[],[f1005]) ).
fof(f1005,axiom,
! [X22,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11446,plain,
spl263_623,
inference(avatar_split_clause,[],[f5151,f11444]) ).
fof(f11444,plain,
( spl263_623
<=> ! [X0] :
( hAPP_nat_nat(suc,sK79(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_623])]) ).
fof(f5151,plain,
! [X0] :
( hAPP_nat_nat(suc,sK79(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f4117]) ).
fof(f4117,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ! [X1] : hAPP_nat_nat(suc,X1) != X0 )
& ( hAPP_nat_nat(suc,sK79(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f4115,f4116]) ).
fof(f4116,plain,
! [X0] :
( ? [X2] : hAPP_nat_nat(suc,X2) = X0
=> hAPP_nat_nat(suc,sK79(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f4115,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ! [X1] : hAPP_nat_nat(suc,X1) != X0 )
& ( ? [X2] : hAPP_nat_nat(suc,X2) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(rectify,[],[f4114]) ).
fof(f4114,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| ! [X1] : hAPP_nat_nat(suc,X1) != X0 )
& ( ? [X1] : hAPP_nat_nat(suc,X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
inference(nnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
<=> ? [X1] : hAPP_nat_nat(suc,X1) = X0 ),
inference(rectify,[],[f1053]) ).
fof(f1053,axiom,
! [X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
<=> ? [X34] : hAPP_nat_nat(suc,X34) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11442,plain,
spl263_622,
inference(avatar_split_clause,[],[f5126,f11440]) ).
fof(f11440,plain,
( spl263_622
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_622])]) ).
fof(f5126,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4101]) ).
fof(f11438,plain,
spl263_621,
inference(avatar_split_clause,[],[f5125,f11436]) ).
fof(f11436,plain,
( spl263_621
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_621])]) ).
fof(f5125,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4101]) ).
fof(f11434,plain,
spl263_620,
inference(avatar_split_clause,[],[f5123,f11432]) ).
fof(f11432,plain,
( spl263_620
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK75(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_620])]) ).
fof(f5123,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK75(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f4096]) ).
fof(f11430,plain,
spl263_619,
inference(avatar_split_clause,[],[f5122,f11428]) ).
fof(f11428,plain,
( spl263_619
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK75(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_619])]) ).
fof(f5122,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK75(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f4096]) ).
fof(f11426,plain,
spl263_618,
inference(avatar_split_clause,[],[f5118,f11424]) ).
fof(f11424,plain,
( spl263_618
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK73(X0)))
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_618])]) ).
fof(f5118,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK73(X0)))
| bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f4091]) ).
fof(f11422,plain,
spl263_617,
inference(avatar_split_clause,[],[f5112,f11420]) ).
fof(f11420,plain,
( spl263_617
<=> ! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK71(X0)))
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_617])]) ).
fof(f5112,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK71(X0)))
| bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
inference(cnf_transformation,[],[f4085]) ).
fof(f11418,plain,
spl263_616,
inference(avatar_split_clause,[],[f5082,f11416]) ).
fof(f11416,plain,
( spl263_616
<=> ! [X0] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK63(X0)),sK64(X0)) = X0
| bot_bot_fun_int_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_616])]) ).
fof(f5082,plain,
! [X0] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK63(X0)),sK64(X0)) = X0
| bot_bot_fun_int_bool = X0 ),
inference(cnf_transformation,[],[f4050]) ).
fof(f4050,plain,
! [X0] :
( ( bot_bot_fun_int_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) )
& ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK63(X0)),sK64(X0)))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK63(X0)),sK64(X0)) = X0 )
| bot_bot_fun_int_bool = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f4048,f4049]) ).
fof(f4049,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4) = X0 )
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK63(X0)),sK64(X0)))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK63(X0)),sK64(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f4048,plain,
! [X0] :
( ( bot_bot_fun_int_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) )
& ( ? [X3,X4] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4) = X0 )
| bot_bot_fun_int_bool = X0 ) ),
inference(rectify,[],[f4047]) ).
fof(f4047,plain,
! [X0] :
( ( bot_bot_fun_int_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) )
& ( ? [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X0 )
| bot_bot_fun_int_bool = X0 ) ),
inference(nnf_transformation,[],[f1575]) ).
fof(f1575,plain,
! [X0] :
( bot_bot_fun_int_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X0 ) ),
inference(rectify,[],[f807]) ).
fof(f807,axiom,
! [X4] :
( bot_bot_fun_int_bool != X4
<=> ? [X29,X82] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X82))
& hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),X82) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11414,plain,
spl263_615,
inference(avatar_split_clause,[],[f5079,f11412]) ).
fof(f11412,plain,
( spl263_615
<=> ! [X0] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK61(X0)),sK62(X0)) = X0
| bot_bot_fun_nat_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_615])]) ).
fof(f5079,plain,
! [X0] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK61(X0)),sK62(X0)) = X0
| bot_bot_fun_nat_bool = X0 ),
inference(cnf_transformation,[],[f4046]) ).
fof(f4046,plain,
! [X0] :
( ( bot_bot_fun_nat_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) )
& ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK61(X0)),sK62(X0)))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK61(X0)),sK62(X0)) = X0 )
| bot_bot_fun_nat_bool = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f4044,f4045]) ).
fof(f4045,plain,
! [X0] :
( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4) = X0 )
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK61(X0)),sK62(X0)))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK61(X0)),sK62(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f4044,plain,
! [X0] :
( ( bot_bot_fun_nat_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) )
& ( ? [X3,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4) = X0 )
| bot_bot_fun_nat_bool = X0 ) ),
inference(rectify,[],[f4043]) ).
fof(f4043,plain,
! [X0] :
( ( bot_bot_fun_nat_bool != X0
| ! [X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) )
& ( ? [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X0 )
| bot_bot_fun_nat_bool = X0 ) ),
inference(nnf_transformation,[],[f1574]) ).
fof(f1574,plain,
! [X0] :
( bot_bot_fun_nat_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X0 ) ),
inference(rectify,[],[f808]) ).
fof(f808,axiom,
! [X4] :
( bot_bot_fun_nat_bool != X4
<=> ? [X29,X82] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X82))
& hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),X82) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11410,plain,
spl263_614,
inference(avatar_split_clause,[],[f5076,f11408]) ).
fof(f11408,plain,
( spl263_614
<=> ! [X0] :
( hAPP_nat_nat(suc,sK60(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_614])]) ).
fof(f5076,plain,
! [X0] :
( hAPP_nat_nat(suc,sK60(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(cnf_transformation,[],[f4042]) ).
fof(f4042,plain,
! [X0] :
( hAPP_nat_nat(suc,sK60(X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f2744,f4041]) ).
fof(f4041,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
=> hAPP_nat_nat(suc,sK60(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2744,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(ennf_transformation,[],[f1571]) ).
fof(f1571,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
=> ? [X1] : hAPP_nat_nat(suc,X1) = X0 ),
inference(rectify,[],[f1079]) ).
fof(f1079,axiom,
! [X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
=> ? [X34] : hAPP_nat_nat(suc,X34) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11406,plain,
spl263_613,
inference(avatar_split_clause,[],[f5062,f11404]) ).
fof(f11404,plain,
( spl263_613
<=> ! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_613])]) ).
fof(f5062,plain,
! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f2731]) ).
fof(f2731,plain,
! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(ennf_transformation,[],[f1558]) ).
fof(f1558,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))) ),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11402,plain,
( spl263_612
| ~ spl263_139
| ~ spl263_568 ),
inference(avatar_split_clause,[],[f11280,f10779,f8458,f11400]) ).
fof(f11400,plain,
( spl263_612
<=> ! [X0] : ~ sP23(X0,bot_bot_fun_nat_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_612])]) ).
fof(f8458,plain,
( spl263_139
<=> ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_139])]) ).
fof(f10779,plain,
( spl263_568
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),X1))
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_568])]) ).
fof(f11280,plain,
( ! [X0] : ~ sP23(X0,bot_bot_fun_nat_bool)
| ~ spl263_139
| ~ spl263_568 ),
inference(resolution,[],[f10780,f8459]) ).
fof(f8459,plain,
( ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool))
| ~ spl263_139 ),
inference(avatar_component_clause,[],[f8458]) ).
fof(f10780,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),X1))
| ~ sP23(X0,X1) )
| ~ spl263_568 ),
inference(avatar_component_clause,[],[f10779]) ).
fof(f11398,plain,
spl263_611,
inference(avatar_split_clause,[],[f5061,f11396]) ).
fof(f11396,plain,
( spl263_611
<=> ! [X0] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_611])]) ).
fof(f5061,plain,
! [X0] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
inference(cnf_transformation,[],[f2730]) ).
fof(f2730,plain,
! [X0] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
inference(ennf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0)))) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X4] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11394,plain,
spl263_610,
inference(avatar_split_clause,[],[f5060,f11392]) ).
fof(f11392,plain,
( spl263_610
<=> ! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_610])]) ).
fof(f5060,plain,
! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
inference(cnf_transformation,[],[f2729]) ).
fof(f2729,plain,
! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
inference(ennf_transformation,[],[f1556]) ).
fof(f1556,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0)))) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11390,plain,
spl263_609,
inference(avatar_split_clause,[],[f5059,f11388]) ).
fof(f11388,plain,
( spl263_609
<=> ! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_609])]) ).
fof(f5059,plain,
! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(cnf_transformation,[],[f2728]) ).
fof(f2728,plain,
! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(ennf_transformation,[],[f1555]) ).
fof(f1555,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0)))) ),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11386,plain,
spl263_608,
inference(avatar_split_clause,[],[f5058,f11384]) ).
fof(f11384,plain,
( spl263_608
<=> ! [X0] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_608])]) ).
fof(f5058,plain,
! [X0] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
inference(cnf_transformation,[],[f2727]) ).
fof(f2727,plain,
! [X0] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
inference(ennf_transformation,[],[f1554]) ).
fof(f1554,plain,
! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0)))) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11382,plain,
spl263_607,
inference(avatar_split_clause,[],[f5057,f11380]) ).
fof(f11380,plain,
( spl263_607
<=> ! [X0] :
( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_607])]) ).
fof(f5057,plain,
! [X0] :
( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ),
inference(cnf_transformation,[],[f2726]) ).
fof(f2726,plain,
! [X0] :
( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ),
inference(ennf_transformation,[],[f1553]) ).
fof(f1553,plain,
! [X0] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
=> hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0)))) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X4] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
=> hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11378,plain,
spl263_606,
inference(avatar_split_clause,[],[f5056,f11376]) ).
fof(f11376,plain,
( spl263_606
<=> ! [X0] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_606])]) ).
fof(f5056,plain,
! [X0] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(cnf_transformation,[],[f2725]) ).
fof(f2725,plain,
! [X0] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(ennf_transformation,[],[f1552]) ).
fof(f1552,plain,
! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0)))) ),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11374,plain,
spl263_605,
inference(avatar_split_clause,[],[f5055,f11372]) ).
fof(f11372,plain,
( spl263_605
<=> ! [X0] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_605])]) ).
fof(f5055,plain,
! [X0] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
inference(cnf_transformation,[],[f2724]) ).
fof(f2724,plain,
! [X0] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
inference(ennf_transformation,[],[f1551]) ).
fof(f1551,plain,
! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0)))) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11370,plain,
spl263_604,
inference(avatar_split_clause,[],[f5051,f11368]) ).
fof(f11368,plain,
( spl263_604
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(X0)),X0))
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_604])]) ).
fof(f5051,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(X0)),X0))
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4028]) ).
fof(f4028,plain,
! [X0] :
( ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(X0)),X0))
& is_a(sK53(X0)) )
| bot_bot_fun_a_bool = X0 )
& ( bot_bot_fun_a_bool != X0
| ! [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
| ~ is_a(X2) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f4026,f4027]) ).
fof(f4027,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(X0)),X0))
& is_a(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4026,plain,
! [X0] :
( ( ( ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) )
| bot_bot_fun_a_bool = X0 )
& ( bot_bot_fun_a_bool != X0
| ! [X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
| ~ is_a(X2) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(rectify,[],[f4025]) ).
fof(f4025,plain,
! [X0] :
( ( ( ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) )
| bot_bot_fun_a_bool = X0 )
& ( bot_bot_fun_a_bool != X0
| ! [X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ is_a(X1) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(nnf_transformation,[],[f2720]) ).
fof(f2720,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) )
<=> bot_bot_fun_a_bool != X0 )
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1547]) ).
fof(f1547,plain,
! [X0] :
( is_fun_a_bool(X0)
=> ( ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) )
<=> bot_bot_fun_a_bool != X0 ) ),
inference(rectify,[],[f636]) ).
fof(f636,axiom,
! [X4] :
( is_fun_a_bool(X4)
=> ( ? [X29] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X4))
& is_a(X29) )
<=> bot_bot_fun_a_bool != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11366,plain,
spl263_603,
inference(avatar_split_clause,[],[f5047,f11364]) ).
fof(f11364,plain,
( spl263_603
<=> ! [X0] :
( bot_bot_fun_a_bool = X0
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(X0)),X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_603])]) ).
fof(f5047,plain,
! [X0] :
( bot_bot_fun_a_bool = X0
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(X0)),X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4024]) ).
fof(f4024,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ is_a(X1) )
| bot_bot_fun_a_bool != X0 )
& ( bot_bot_fun_a_bool = X0
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(X0)),X0))
& is_a(sK52(X0)) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f4022,f4023]) ).
fof(f4023,plain,
! [X0] :
( ? [X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& is_a(X2) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(X0)),X0))
& is_a(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4022,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ is_a(X1) )
| bot_bot_fun_a_bool != X0 )
& ( bot_bot_fun_a_bool = X0
| ? [X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& is_a(X2) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(rectify,[],[f4021]) ).
fof(f4021,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ is_a(X1) )
| bot_bot_fun_a_bool != X0 )
& ( bot_bot_fun_a_bool = X0
| ? [X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
& is_a(X1) ) ) )
| ~ is_fun_a_bool(X0) ),
inference(nnf_transformation,[],[f2719]) ).
fof(f2719,plain,
! [X0] :
( ( ! [X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ is_a(X1) )
<=> bot_bot_fun_a_bool = X0 )
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0] :
( is_fun_a_bool(X0)
=> ( ! [X1] :
( is_a(X1)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
<=> bot_bot_fun_a_bool = X0 ) ),
inference(rectify,[],[f640]) ).
fof(f640,axiom,
! [X4] :
( is_fun_a_bool(X4)
=> ( ! [X29] :
( is_a(X29)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X4)) )
<=> bot_bot_fun_a_bool = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11362,plain,
spl263_602,
inference(avatar_split_clause,[],[f5020,f11360]) ).
fof(f11360,plain,
( spl263_602
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK47(X0)),X0))
| bot_bo844097828e_bool = X0
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_602])]) ).
fof(f5020,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK47(X0)),X0))
| bot_bo844097828e_bool = X0
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f4007]) ).
fof(f4007,plain,
! [X0] :
( ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK47(X0)),X0))
& is_pname(sK47(X0)) )
| bot_bo844097828e_bool = X0 )
& ( bot_bo844097828e_bool != X0
| ! [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
| ~ is_pname(X2) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f4005,f4006]) ).
fof(f4006,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK47(X0)),X0))
& is_pname(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4005,plain,
! [X0] :
( ( ( ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) )
| bot_bo844097828e_bool = X0 )
& ( bot_bo844097828e_bool != X0
| ! [X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
| ~ is_pname(X2) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(rectify,[],[f4004]) ).
fof(f4004,plain,
! [X0] :
( ( ( ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) )
| bot_bo844097828e_bool = X0 )
& ( bot_bo844097828e_bool != X0
| ! [X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ is_pname(X1) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(nnf_transformation,[],[f2709]) ).
fof(f2709,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) )
<=> bot_bo844097828e_bool != X0 )
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f1539]) ).
fof(f1539,plain,
! [X0] :
( is_fun_pname_bool(X0)
=> ( ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) )
<=> bot_bo844097828e_bool != X0 ) ),
inference(rectify,[],[f637]) ).
fof(f637,axiom,
! [X4] :
( is_fun_pname_bool(X4)
=> ( ? [X29] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
& is_pname(X29) )
<=> bot_bo844097828e_bool != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11358,plain,
( spl263_601
| ~ spl263_138
| ~ spl263_567 ),
inference(avatar_split_clause,[],[f11278,f10775,f8454,f11356]) ).
fof(f11356,plain,
( spl263_601
<=> ! [X0] : ~ sP22(X0,bot_bot_fun_int_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_601])]) ).
fof(f8454,plain,
( spl263_138
<=> ! [X0] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_138])]) ).
fof(f10775,plain,
( spl263_567
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),X1))
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_567])]) ).
fof(f11278,plain,
( ! [X0] : ~ sP22(X0,bot_bot_fun_int_bool)
| ~ spl263_138
| ~ spl263_567 ),
inference(resolution,[],[f10776,f8455]) ).
fof(f8455,plain,
( ! [X0] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool))
| ~ spl263_138 ),
inference(avatar_component_clause,[],[f8454]) ).
fof(f10776,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),X1))
| ~ sP22(X0,X1) )
| ~ spl263_567 ),
inference(avatar_component_clause,[],[f10775]) ).
fof(f11354,plain,
spl263_600,
inference(avatar_split_clause,[],[f5016,f11352]) ).
fof(f11352,plain,
( spl263_600
<=> ! [X0] :
( bot_bo844097828e_bool = X0
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK46(X0)),X0))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_600])]) ).
fof(f5016,plain,
! [X0] :
( bot_bo844097828e_bool = X0
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK46(X0)),X0))
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f4003]) ).
fof(f4003,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ is_pname(X1) )
| bot_bo844097828e_bool != X0 )
& ( bot_bo844097828e_bool = X0
| ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK46(X0)),X0))
& is_pname(sK46(X0)) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f4001,f4002]) ).
fof(f4002,plain,
! [X0] :
( ? [X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& is_pname(X2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK46(X0)),X0))
& is_pname(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4001,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ is_pname(X1) )
| bot_bo844097828e_bool != X0 )
& ( bot_bo844097828e_bool = X0
| ? [X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& is_pname(X2) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(rectify,[],[f4000]) ).
fof(f4000,plain,
! [X0] :
( ( ( ! [X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ is_pname(X1) )
| bot_bo844097828e_bool != X0 )
& ( bot_bo844097828e_bool = X0
| ? [X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
& is_pname(X1) ) ) )
| ~ is_fun_pname_bool(X0) ),
inference(nnf_transformation,[],[f2708]) ).
fof(f2708,plain,
! [X0] :
( ( ! [X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ is_pname(X1) )
<=> bot_bo844097828e_bool = X0 )
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X0] :
( is_fun_pname_bool(X0)
=> ( ! [X1] :
( is_pname(X1)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
<=> bot_bo844097828e_bool = X0 ) ),
inference(rectify,[],[f641]) ).
fof(f641,axiom,
! [X4] :
( is_fun_pname_bool(X4)
=> ( ! [X29] :
( is_pname(X29)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4)) )
<=> bot_bo844097828e_bool = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11349,plain,
( spl263_599
| ~ spl263_353
| ~ spl263_598 ),
inference(avatar_split_clause,[],[f11344,f11340,f9555,f11346]) ).
fof(f11346,plain,
( spl263_599
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_599])]) ).
fof(f9555,plain,
( spl263_353
<=> ! [X0] : hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_353])]) ).
fof(f11340,plain,
( spl263_598
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_598])]) ).
fof(f11344,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl263_353
| ~ spl263_598 ),
inference(forward_demodulation,[],[f11342,f9556]) ).
fof(f9556,plain,
( ! [X0] : hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))
| ~ spl263_353 ),
inference(avatar_component_clause,[],[f9555]) ).
fof(f11342,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl263_598 ),
inference(avatar_component_clause,[],[f11340]) ).
fof(f11343,plain,
spl263_598,
inference(avatar_split_clause,[],[f4810,f11340]) ).
fof(f4810,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
inference(cnf_transformation,[],[f1411]) ).
fof(f1411,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11326,plain,
( spl263_597
| ~ spl263_137
| ~ spl263_566 ),
inference(avatar_split_clause,[],[f11275,f10771,f8450,f11324]) ).
fof(f11324,plain,
( spl263_597
<=> ! [X0] : ~ sP21(X0,bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_597])]) ).
fof(f8450,plain,
( spl263_137
<=> ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_137])]) ).
fof(f10771,plain,
( spl263_566
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),X1))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_566])]) ).
fof(f11275,plain,
( ! [X0] : ~ sP21(X0,bot_bot_fun_a_bool)
| ~ spl263_137
| ~ spl263_566 ),
inference(resolution,[],[f10772,f8451]) ).
fof(f8451,plain,
( ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool))
| ~ spl263_137 ),
inference(avatar_component_clause,[],[f8450]) ).
fof(f10772,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),X1))
| ~ sP21(X0,X1) )
| ~ spl263_566 ),
inference(avatar_component_clause,[],[f10771]) ).
fof(f11322,plain,
( spl263_596
| ~ spl263_550
| ~ spl263_584 ),
inference(avatar_split_clause,[],[f10848,f10845,f10706,f11320]) ).
fof(f11320,plain,
( spl263_596
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),pls))
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_596])]) ).
fof(f10845,plain,
( spl263_584
<=> ! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_584])]) ).
fof(f10848,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),pls))
| zero_zero_nat = X0 )
| ~ spl263_550
| ~ spl263_584 ),
inference(forward_demodulation,[],[f10846,f10707]) ).
fof(f10846,plain,
( ! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) )
| ~ spl263_584 ),
inference(avatar_component_clause,[],[f10845]) ).
fof(f11296,plain,
( spl263_595
| ~ spl263_136
| ~ spl263_565 ),
inference(avatar_split_clause,[],[f11272,f10767,f8446,f11294]) ).
fof(f11294,plain,
( spl263_595
<=> ! [X0] : ~ sP20(X0,bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_595])]) ).
fof(f8446,plain,
( spl263_136
<=> ! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_136])]) ).
fof(f10767,plain,
( spl263_565
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),X1))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_565])]) ).
fof(f11272,plain,
( ! [X0] : ~ sP20(X0,bot_bo844097828e_bool)
| ~ spl263_136
| ~ spl263_565 ),
inference(resolution,[],[f10768,f8447]) ).
fof(f8447,plain,
( ! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool))
| ~ spl263_136 ),
inference(avatar_component_clause,[],[f8446]) ).
fof(f10768,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),X1))
| ~ sP20(X0,X1) )
| ~ spl263_565 ),
inference(avatar_component_clause,[],[f10767]) ).
fof(f11212,plain,
( spl263_594
| ~ spl263_212
| ~ spl263_485 ),
inference(avatar_split_clause,[],[f10465,f10186,f8755,f11210]) ).
fof(f11210,plain,
( spl263_594
<=> ! [X0] : ~ sP29(X0,X0,fequal_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_594])]) ).
fof(f8755,plain,
( spl263_212
<=> ! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_212])]) ).
fof(f10186,plain,
( spl263_485
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_485])]) ).
fof(f10465,plain,
( ! [X0] : ~ sP29(X0,X0,fequal_nat)
| ~ spl263_212
| ~ spl263_485 ),
inference(resolution,[],[f10187,f8756]) ).
fof(f8756,plain,
( ! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1))
| ~ spl263_212 ),
inference(avatar_component_clause,[],[f8755]) ).
fof(f10187,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP29(X0,X1,X2) )
| ~ spl263_485 ),
inference(avatar_component_clause,[],[f10186]) ).
fof(f11127,plain,
( spl263_593
| ~ spl263_203
| ~ spl263_485 ),
inference(avatar_split_clause,[],[f10463,f10186,f8719,f11125]) ).
fof(f11125,plain,
( spl263_593
<=> ! [X0] : ~ sP29(X0,zero_zero_nat,ord_less_eq_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_593])]) ).
fof(f8719,plain,
( spl263_203
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_203])]) ).
fof(f10463,plain,
( ! [X0] : ~ sP29(X0,zero_zero_nat,ord_less_eq_nat)
| ~ spl263_203
| ~ spl263_485 ),
inference(resolution,[],[f10187,f8720]) ).
fof(f8720,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
| ~ spl263_203 ),
inference(avatar_component_clause,[],[f8719]) ).
fof(f11041,plain,
( spl263_592
| ~ spl263_151
| ~ spl263_485 ),
inference(avatar_split_clause,[],[f10462,f10186,f8507,f11039]) ).
fof(f11039,plain,
( spl263_592
<=> ! [X0] : ~ sP29(X0,X0,ord_less_eq_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_592])]) ).
fof(f8507,plain,
( spl263_151
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_151])]) ).
fof(f10462,plain,
( ! [X0] : ~ sP29(X0,X0,ord_less_eq_nat)
| ~ spl263_151
| ~ spl263_485 ),
inference(resolution,[],[f10187,f8508]) ).
fof(f8508,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0))
| ~ spl263_151 ),
inference(avatar_component_clause,[],[f8507]) ).
fof(f10923,plain,
( spl263_154
| ~ spl263_137
| ~ spl263_473 ),
inference(avatar_split_clause,[],[f10416,f10138,f8450,f8519]) ).
fof(f10416,plain,
( ! [X0] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
| ~ spl263_137
| ~ spl263_473 ),
inference(resolution,[],[f10139,f8451]) ).
fof(f10876,plain,
( spl263_591
| ~ spl263_136
| ~ spl263_471 ),
inference(avatar_split_clause,[],[f10400,f10130,f8446,f10874]) ).
fof(f10874,plain,
( spl263_591
<=> ! [X0] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_591])]) ).
fof(f10130,plain,
( spl263_471
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_471])]) ).
fof(f10400,plain,
( ! [X0] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X0))
| ~ spl263_136
| ~ spl263_471 ),
inference(resolution,[],[f10131,f8447]) ).
fof(f10131,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl263_471 ),
inference(avatar_component_clause,[],[f10130]) ).
fof(f10872,plain,
spl263_590,
inference(avatar_split_clause,[],[f7689,f10870]) ).
fof(f10870,plain,
( spl263_590
<=> ! [X2,X0,X1] :
( hAPP_f22106695ol_nat(X2,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0
| ~ hBOOL(finite988810631ne_nat(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_590])]) ).
fof(f7689,plain,
! [X2,X0,X1] :
( hAPP_f22106695ol_nat(X2,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0
| ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
inference(forward_demodulation,[],[f6467,f7397]) ).
fof(f6467,plain,
! [X2,X0,X1] :
( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0
| ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
inference(cnf_transformation,[],[f3504]) ).
fof(f3504,plain,
! [X0,X1,X2] :
( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0
| ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
inference(ennf_transformation,[],[f2376]) ).
fof(f2376,plain,
! [X0,X1,X2] :
( hBOOL(finite988810631ne_nat(X1,X2))
=> hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ),
inference(rectify,[],[f856]) ).
fof(f856,axiom,
! [X10,X8,X6] :
( hBOOL(finite988810631ne_nat(X8,X6))
=> hAPP_f22106695ol_nat(X6,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10868,plain,
spl263_589,
inference(avatar_split_clause,[],[f7688,f10866]) ).
fof(f10866,plain,
( spl263_589
<=> ! [X2,X0,X1] :
( hAPP_f1594865479ol_int(X2,hAPP_i1948725293t_bool(fequal_int,X0)) = X0
| ~ hBOOL(finite1626084323ne_int(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_589])]) ).
fof(f7688,plain,
! [X2,X0,X1] :
( hAPP_f1594865479ol_int(X2,hAPP_i1948725293t_bool(fequal_int,X0)) = X0
| ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
inference(forward_demodulation,[],[f6466,f7396]) ).
fof(f6466,plain,
! [X2,X0,X1] :
( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0
| ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
inference(cnf_transformation,[],[f3503]) ).
fof(f3503,plain,
! [X0,X1,X2] :
( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0
| ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
inference(ennf_transformation,[],[f2375]) ).
fof(f2375,plain,
! [X0,X1,X2] :
( hBOOL(finite1626084323ne_int(X1,X2))
=> hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ),
inference(rectify,[],[f857]) ).
fof(f857,axiom,
! [X10,X8,X6] :
( hBOOL(finite1626084323ne_int(X8,X6))
=> hAPP_f1594865479ol_int(X6,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10864,plain,
spl263_588,
inference(avatar_split_clause,[],[f7557,f10862]) ).
fof(f10862,plain,
( spl263_588
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_588])]) ).
fof(f7557,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
| X0 = X1 ),
inference(forward_demodulation,[],[f5791,f7397]) ).
fof(f5791,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(cnf_transformation,[],[f3209]) ).
fof(f3209,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
inference(ennf_transformation,[],[f2029]) ).
fof(f2029,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)))
=> X0 = X1 ),
inference(rectify,[],[f701]) ).
fof(f701,axiom,
! [X30,X7] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),bot_bot_fun_nat_bool)))
=> X7 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10860,plain,
spl263_587,
inference(avatar_split_clause,[],[f7554,f10858]) ).
fof(f10858,plain,
( spl263_587
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_587])]) ).
fof(f7554,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
| X0 = X1 ),
inference(forward_demodulation,[],[f5789,f7396]) ).
fof(f5789,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(cnf_transformation,[],[f3206]) ).
fof(f3206,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
inference(ennf_transformation,[],[f2027]) ).
fof(f2027,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)))
=> X0 = X1 ),
inference(rectify,[],[f700]) ).
fof(f700,axiom,
! [X30,X7] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),bot_bot_fun_int_bool)))
=> X7 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10856,plain,
spl263_586,
inference(avatar_split_clause,[],[f7450,f10854]) ).
fof(f10854,plain,
( spl263_586
<=> ! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X1)
| bot_bot_fun_nat_bool = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_586])]) ).
fof(f7450,plain,
! [X0,X1] :
( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X1)
| bot_bot_fun_nat_bool = X1 ),
inference(forward_demodulation,[],[f5301,f7396]) ).
fof(f5301,plain,
! [X0,X1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1)
| bot_bot_fun_nat_bool = X1 ),
inference(cnf_transformation,[],[f2753]) ).
fof(f2753,plain,
! [X0,X1] :
( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1)
| bot_bot_fun_nat_bool = X1 )
& ( bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X0),X1)
| bot_bot_fun_nat_bool != X1 ) ),
inference(ennf_transformation,[],[f1696]) ).
fof(f1696,plain,
! [X0,X1] :
( ( bot_bot_fun_nat_bool != X1
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1) )
& ( bot_bot_fun_nat_bool = X1
=> bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X0),X1) ) ),
inference(rectify,[],[f774]) ).
fof(f774,axiom,
! [X31,X4] :
( ( bot_bot_fun_nat_bool != X4
=> image_nat_int(cOMBK_int_nat(X31),X4) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),bot_bot_fun_int_bool) )
& ( bot_bot_fun_nat_bool = X4
=> bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X31),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10852,plain,
spl263_585,
inference(avatar_split_clause,[],[f7433,f10850]) ).
fof(f10850,plain,
( spl263_585
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_585])]) ).
fof(f7433,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)))),
inference(forward_demodulation,[],[f5261,f4876]) ).
fof(f5261,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))))),
inference(cnf_transformation,[],[f1657]) ).
fof(f1657,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))))),
inference(rectify,[],[f1004]) ).
fof(f1004,axiom,
! [X12,X32] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X12),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X32))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10847,plain,
spl263_584,
inference(avatar_split_clause,[],[f7076,f10845]) ).
fof(f7076,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
inference(definition_unfolding,[],[f5169,f4830]) ).
fof(f5169,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ),
inference(cnf_transformation,[],[f4126]) ).
fof(f4126,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f1614]) ).
fof(f1614,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f1228]) ).
fof(f1228,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X16)),zero_zero_int))
<=> zero_zero_nat = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10843,plain,
spl263_583,
inference(avatar_split_clause,[],[f7028,f10841]) ).
fof(f10841,plain,
( spl263_583
<=> ! [X0] : pls != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_583])]) ).
fof(f7028,plain,
! [X0] : pls != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0),
inference(definition_unfolding,[],[f4872,f4973]) ).
fof(f4872,plain,
! [X0] : pls != bit1(X0),
inference(cnf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0] : pls != bit1(X0),
inference(rectify,[],[f1289]) ).
fof(f1289,axiom,
! [X21] : pls != bit1(X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10839,plain,
spl263_582,
inference(avatar_split_clause,[],[f6989,f10837]) ).
fof(f10837,plain,
( spl263_582
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP41(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_582])]) ).
fof(f6989,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4793]) ).
fof(f4793,plain,
! [X0,X1,X2,X3] :
( ( sP41(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X1 != X2
| X0 != X3 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X1 = X2
& X0 = X3 )
| ~ sP41(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4792]) ).
fof(f4792,plain,
! [X2,X1,X3,X0] :
( ( sP41(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP41(X2,X1,X3,X0) ) ),
inference(flattening,[],[f4791]) ).
fof(f4791,plain,
! [X2,X1,X3,X0] :
( ( sP41(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP41(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f3987]) ).
fof(f10835,plain,
spl263_581,
inference(avatar_split_clause,[],[f6988,f10833]) ).
fof(f10833,plain,
( spl263_581
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP41(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_581])]) ).
fof(f6988,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4793]) ).
fof(f10830,plain,
spl263_580,
inference(avatar_split_clause,[],[f6987,f10828]) ).
fof(f10828,plain,
( spl263_580
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP41(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_580])]) ).
fof(f6987,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4793]) ).
fof(f10826,plain,
spl263_579,
inference(avatar_split_clause,[],[f6986,f10824]) ).
fof(f10824,plain,
( spl263_579
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP41(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_579])]) ).
fof(f6986,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4793]) ).
fof(f10822,plain,
spl263_578,
inference(avatar_split_clause,[],[f6981,f10820]) ).
fof(f10820,plain,
( spl263_578
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP40(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_578])]) ).
fof(f6981,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4789]) ).
fof(f4789,plain,
! [X0,X1,X2,X3] :
( ( sP40(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X1 != X2
| X0 != X3 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X1 = X2
& X0 = X3 )
| ~ sP40(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4788]) ).
fof(f4788,plain,
! [X2,X1,X3,X0] :
( ( sP40(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP40(X2,X1,X3,X0) ) ),
inference(flattening,[],[f4787]) ).
fof(f4787,plain,
! [X2,X1,X3,X0] :
( ( sP40(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP40(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f3985]) ).
fof(f10818,plain,
spl263_577,
inference(avatar_split_clause,[],[f6980,f10816]) ).
fof(f10816,plain,
( spl263_577
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP40(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_577])]) ).
fof(f6980,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4789]) ).
fof(f10814,plain,
spl263_576,
inference(avatar_split_clause,[],[f6979,f10812]) ).
fof(f10812,plain,
( spl263_576
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP40(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_576])]) ).
fof(f6979,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4789]) ).
fof(f10810,plain,
spl263_575,
inference(avatar_split_clause,[],[f6978,f10808]) ).
fof(f10808,plain,
( spl263_575
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP40(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_575])]) ).
fof(f6978,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4789]) ).
fof(f10806,plain,
spl263_574,
inference(avatar_split_clause,[],[f6968,f10804]) ).
fof(f10804,plain,
( spl263_574
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_574])]) ).
fof(f6968,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4779]) ).
fof(f4779,plain,
! [X0,X1,X2,X3] :
( ( sP37(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X1 != X2
| X0 != X3 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X1 = X2
& X0 = X3 )
| ~ sP37(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4778]) ).
fof(f4778,plain,
! [X2,X1,X3,X0] :
( ( sP37(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP37(X2,X1,X3,X0) ) ),
inference(flattening,[],[f4777]) ).
fof(f4777,plain,
! [X2,X1,X3,X0] :
( ( sP37(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X1 != X3
| X0 != X2 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X1 = X3
& X0 = X2 )
| ~ sP37(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f3980]) ).
fof(f10802,plain,
spl263_573,
inference(avatar_split_clause,[],[f6967,f10800]) ).
fof(f10800,plain,
( spl263_573
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_573])]) ).
fof(f6967,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4779]) ).
fof(f10798,plain,
spl263_572,
inference(avatar_split_clause,[],[f6966,f10796]) ).
fof(f10796,plain,
( spl263_572
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_572])]) ).
fof(f6966,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4779]) ).
fof(f10794,plain,
spl263_571,
inference(avatar_split_clause,[],[f6965,f10792]) ).
fof(f10792,plain,
( spl263_571
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_571])]) ).
fof(f6965,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4779]) ).
fof(f10790,plain,
( spl263_570
| ~ spl263_120
| ~ spl263_296 ),
inference(avatar_split_clause,[],[f9362,f9152,f8338,f10787]) ).
fof(f10787,plain,
( spl263_570
<=> pls = abs_abs_int(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_570])]) ).
fof(f8338,plain,
( spl263_120
<=> hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls ),
introduced(avatar_definition,[new_symbols(naming,[spl263_120])]) ).
fof(f9152,plain,
( spl263_296
<=> ! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_296])]) ).
fof(f9362,plain,
( pls = abs_abs_int(pls)
| ~ spl263_120
| ~ spl263_296 ),
inference(superposition,[],[f9153,f8340]) ).
fof(f8340,plain,
( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls
| ~ spl263_120 ),
inference(avatar_component_clause,[],[f8338]) ).
fof(f9153,plain,
( ! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0))
| ~ spl263_296 ),
inference(avatar_component_clause,[],[f9152]) ).
fof(f10785,plain,
spl263_569,
inference(avatar_split_clause,[],[f6470,f10783]) ).
fof(f10783,plain,
( spl263_569
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1)))
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_569])]) ).
fof(f6470,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1)))
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f4569]) ).
fof(f10781,plain,
spl263_568,
inference(avatar_split_clause,[],[f6432,f10779]) ).
fof(f6432,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK209(X0,X1)),X1))
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f4549]) ).
fof(f10777,plain,
spl263_567,
inference(avatar_split_clause,[],[f6394,f10775]) ).
fof(f6394,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK200(X0,X1)),X1))
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f4531]) ).
fof(f10773,plain,
spl263_566,
inference(avatar_split_clause,[],[f6383,f10771]) ).
fof(f6383,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK198(X0,X1)),X1))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f10769,plain,
spl263_565,
inference(avatar_split_clause,[],[f6367,f10767]) ).
fof(f6367,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK196(X0,X1)),X1))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f10765,plain,
spl263_564,
inference(avatar_split_clause,[],[f6124,f10763]) ).
fof(f10763,plain,
( spl263_564
<=> ! [X2,X0,X1] : hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_564])]) ).
fof(f6124,plain,
! [X2,X0,X1] : hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)),
inference(cnf_transformation,[],[f2190]) ).
fof(f2190,plain,
! [X0,X1,X2] : hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)),
inference(rectify,[],[f770]) ).
fof(f770,axiom,
! [X75,X76,X19] : hAPP_nat_nat(nat_case_nat(X75,X76),hAPP_nat_nat(suc,X19)) = hAPP_nat_nat(X76,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10761,plain,
spl263_563,
inference(avatar_split_clause,[],[f6123,f10759]) ).
fof(f6123,plain,
! [X2,X0,X1] : hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)),
inference(cnf_transformation,[],[f2189]) ).
fof(f2189,plain,
! [X0,X1,X2] : hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)),
inference(rectify,[],[f1354]) ).
fof(f1354,axiom,
! [X158,X159,X160] : hAPP_nat_bool(cOMBB_bool_bool_nat(X158,X159),X160) = hAPP_bool_bool(X158,hAPP_nat_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10757,plain,
spl263_562,
inference(avatar_split_clause,[],[f6122,f10755]) ).
fof(f10755,plain,
( spl263_562
<=> ! [X2,X0,X1] : hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_562])]) ).
fof(f6122,plain,
! [X2,X0,X1] : hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)),
inference(cnf_transformation,[],[f2188]) ).
fof(f2188,plain,
! [X0,X1,X2] : hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)),
inference(rectify,[],[f1349]) ).
fof(f1349,axiom,
! [X158,X159,X160] : hAPP_nat_bool(cOMBB_int_bool_nat(X158,X159),X160) = hAPP_int_bool(X158,hAPP_nat_int(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10753,plain,
spl263_561,
inference(avatar_split_clause,[],[f6121,f10751]) ).
fof(f10751,plain,
( spl263_561
<=> ! [X2,X0,X1] : hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_561])]) ).
fof(f6121,plain,
! [X2,X0,X1] : hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)),
inference(cnf_transformation,[],[f2187]) ).
fof(f2187,plain,
! [X0,X1,X2] : hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)),
inference(rectify,[],[f1372]) ).
fof(f1372,axiom,
! [X158,X159,X160] : hAPP_nat_bool(cOMBB_955900739ol_nat(X158,X159),X160) = hAPP_f54304608l_bool(X158,hAPP_n1699378549t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10749,plain,
spl263_560,
inference(avatar_split_clause,[],[f6120,f10747]) ).
fof(f10747,plain,
( spl263_560
<=> ! [X2,X0,X1] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_560])]) ).
fof(f6120,plain,
! [X2,X0,X1] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)),
inference(cnf_transformation,[],[f2186]) ).
fof(f2186,plain,
! [X0,X1,X2] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)),
inference(rectify,[],[f1369]) ).
fof(f1369,axiom,
! [X158,X159,X160] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X158,X159),X160) = hAPP_n1699378549t_bool(X158,hAPP_nat_nat(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10745,plain,
( spl263_559
| ~ spl263_86
| ~ spl263_296 ),
inference(avatar_split_clause,[],[f9361,f9152,f8195,f10742]) ).
fof(f10742,plain,
( spl263_559
<=> one_one_int = abs_abs_int(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_559])]) ).
fof(f8195,plain,
( spl263_86
<=> one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_86])]) ).
fof(f9361,plain,
( one_one_int = abs_abs_int(one_one_int)
| ~ spl263_86
| ~ spl263_296 ),
inference(superposition,[],[f9153,f8197]) ).
fof(f8197,plain,
( one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat)
| ~ spl263_86 ),
inference(avatar_component_clause,[],[f8195]) ).
fof(f10740,plain,
spl263_558,
inference(avatar_split_clause,[],[f6119,f10738]) ).
fof(f10738,plain,
( spl263_558
<=> ! [X2,X0,X1] : hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_558])]) ).
fof(f6119,plain,
! [X2,X0,X1] : hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)),
inference(cnf_transformation,[],[f2185]) ).
fof(f2185,plain,
! [X0,X1,X2] : hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)),
inference(rectify,[],[f1353]) ).
fof(f1353,axiom,
! [X158,X159,X160] : hAPP_int_bool(cOMBB_bool_bool_int(X158,X159),X160) = hAPP_bool_bool(X158,hAPP_int_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10736,plain,
spl263_557,
inference(avatar_split_clause,[],[f6118,f10734]) ).
fof(f10734,plain,
( spl263_557
<=> ! [X2,X0,X1] : hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_557])]) ).
fof(f6118,plain,
! [X2,X0,X1] : hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)),
inference(cnf_transformation,[],[f2184]) ).
fof(f2184,plain,
! [X0,X1,X2] : hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)),
inference(rectify,[],[f1371]) ).
fof(f1371,axiom,
! [X158,X159,X160] : hAPP_int_bool(cOMBB_1418110531ol_int(X158,X159),X160) = hAPP_f448129468l_bool(X158,hAPP_i1948725293t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10732,plain,
spl263_556,
inference(avatar_split_clause,[],[f6117,f10730]) ).
fof(f10730,plain,
( spl263_556
<=> ! [X2,X0,X1] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_556])]) ).
fof(f6117,plain,
! [X2,X0,X1] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)),
inference(cnf_transformation,[],[f2183]) ).
fof(f2183,plain,
! [X0,X1,X2] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)),
inference(rectify,[],[f1388]) ).
fof(f1388,axiom,
! [X158,X159,X160] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X158,X159),X160) = hAPP_n215258509l_bool(X158,hAPP_nat_nat(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10728,plain,
spl263_555,
inference(avatar_split_clause,[],[f6116,f10726]) ).
fof(f10726,plain,
( spl263_555
<=> ! [X2,X0,X1] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_555])]) ).
fof(f6116,plain,
! [X2,X0,X1] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)),
inference(cnf_transformation,[],[f2182]) ).
fof(f2182,plain,
! [X0,X1,X2] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)),
inference(rectify,[],[f1402]) ).
fof(f1402,axiom,
! [X158,X159,X160] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X158,X159),X160) = hAPP_f103356543l_bool(X158,hAPP_n1699378549t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10724,plain,
spl263_554,
inference(avatar_split_clause,[],[f6115,f10722]) ).
fof(f10722,plain,
( spl263_554
<=> ! [X2,X0,X1] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_554])]) ).
fof(f6115,plain,
! [X2,X0,X1] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)),
inference(cnf_transformation,[],[f2181]) ).
fof(f2181,plain,
! [X0,X1,X2] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)),
inference(rectify,[],[f1399]) ).
fof(f1399,axiom,
! [X158,X159,X160] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X158,X159),X160) = hAPP_f284875647l_bool(X158,hAPP_i1948725293t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10720,plain,
spl263_553,
inference(avatar_split_clause,[],[f6114,f10718]) ).
fof(f10718,plain,
( spl263_553
<=> ! [X2,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_553])]) ).
fof(f6114,plain,
! [X2,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2180]) ).
fof(f2180,plain,
! [X0,X1,X2] : hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)),
inference(rectify,[],[f1340]) ).
fof(f1340,axiom,
! [X158,X159,X160] : hAPP_a_bool(cOMBB_bool_bool_a(X158,X159),X160) = hAPP_bool_bool(X158,hAPP_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10716,plain,
spl263_552,
inference(avatar_split_clause,[],[f6113,f10714]) ).
fof(f10714,plain,
( spl263_552
<=> ! [X2,X0,X1] : hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_552])]) ).
fof(f6113,plain,
! [X2,X0,X1] : hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2179]) ).
fof(f2179,plain,
! [X0,X1,X2] : hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)),
inference(rectify,[],[f1361]) ).
fof(f1361,axiom,
! [X158,X159,X160] : hAPP_a_bool(cOMBB_1273333599bool_a(X158,X159),X160) = hAPP_fun_a_bool_bool(X158,hAPP_a_fun_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10712,plain,
spl263_551,
inference(avatar_split_clause,[],[f6112,f10710]) ).
fof(f10710,plain,
( spl263_551
<=> ! [X2,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_551])]) ).
fof(f6112,plain,
! [X2,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)),
inference(cnf_transformation,[],[f2178]) ).
fof(f2178,plain,
! [X0,X1,X2] : hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)),
inference(rectify,[],[f1357]) ).
fof(f1357,axiom,
! [X158,X159,X160] : hAPP_pname_bool(cOMBB_647938656_pname(X158,X159),X160) = hAPP_bool_bool(X158,hAPP_pname_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10708,plain,
spl263_550,
inference(avatar_split_clause,[],[f6111,f10706]) ).
fof(f6111,plain,
! [X2,X0,X1] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)),
inference(cnf_transformation,[],[f2177]) ).
fof(f2177,plain,
! [X0,X1,X2] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)),
inference(rectify,[],[f1368]) ).
fof(f1368,axiom,
! [X158,X159,X160] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X158,X159),X160) = hAPP_i1948725293t_bool(X158,hAPP_nat_int(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10704,plain,
spl263_549,
inference(avatar_split_clause,[],[f6110,f10702]) ).
fof(f10702,plain,
( spl263_549
<=> ! [X2,X0,X1] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_549])]) ).
fof(f6110,plain,
! [X2,X0,X1] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)),
inference(cnf_transformation,[],[f2176]) ).
fof(f2176,plain,
! [X0,X1,X2] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)),
inference(rectify,[],[f1360]) ).
fof(f1360,axiom,
! [X158,X159,X160] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X158,X159),X160) = hAPP_a_fun_a_bool(X158,hAPP_int_a(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10700,plain,
spl263_548,
inference(avatar_split_clause,[],[f6109,f10698]) ).
fof(f10698,plain,
( spl263_548
<=> ! [X2,X0,X1] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_548])]) ).
fof(f6109,plain,
! [X2,X0,X1] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2175]) ).
fof(f2175,plain,
! [X0,X1,X2] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)),
inference(rectify,[],[f1398]) ).
fof(f1398,axiom,
! [X158,X159,X160] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X158,X159),X160) = hAPP_f1631501043l_bool(X158,hAPP_nat_fun_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10696,plain,
spl263_547,
inference(avatar_split_clause,[],[f6108,f10694]) ).
fof(f10694,plain,
( spl263_547
<=> ! [X2,X0,X1] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_547])]) ).
fof(f6108,plain,
! [X2,X0,X1] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)),
inference(cnf_transformation,[],[f2174]) ).
fof(f2174,plain,
! [X0,X1,X2] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)),
inference(rectify,[],[f1397]) ).
fof(f1397,axiom,
! [X158,X159,X160] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X158,X159),X160) = hAPP_f1631501043l_bool(X158,hAPP_int_fun_a_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10692,plain,
spl263_546,
inference(avatar_split_clause,[],[f6107,f10690]) ).
fof(f10690,plain,
( spl263_546
<=> ! [X2,X0,X1] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_546])]) ).
fof(f6107,plain,
! [X2,X0,X1] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)),
inference(cnf_transformation,[],[f2173]) ).
fof(f2173,plain,
! [X0,X1,X2] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)),
inference(rectify,[],[f1404]) ).
fof(f1404,axiom,
! [X158,X159,X160] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X158,X159),X160) = hAPP_f434788991l_bool(X158,hAPP_n1025906991e_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10688,plain,
spl263_545,
inference(avatar_split_clause,[],[f6106,f10686]) ).
fof(f10686,plain,
( spl263_545
<=> ! [X2,X0,X1] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_545])]) ).
fof(f6106,plain,
! [X2,X0,X1] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)),
inference(cnf_transformation,[],[f2172]) ).
fof(f2172,plain,
! [X0,X1,X2] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)),
inference(rectify,[],[f1403]) ).
fof(f1403,axiom,
! [X158,X159,X160] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X158,X159),X160) = hAPP_f434788991l_bool(X158,hAPP_i7355787e_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10684,plain,
spl263_544,
inference(avatar_split_clause,[],[f6105,f10682]) ).
fof(f10682,plain,
( spl263_544
<=> ! [X2,X0,X1] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_544])]) ).
fof(f6105,plain,
! [X2,X0,X1] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)),
inference(cnf_transformation,[],[f2171]) ).
fof(f2171,plain,
! [X0,X1,X2] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)),
inference(rectify,[],[f1363]) ).
fof(f1363,axiom,
! [X158,X159,X160] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X158,X159),X160) = hAPP_a_fun_a_bool(X158,hAPP_pname_a(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10680,plain,
spl263_543,
inference(avatar_split_clause,[],[f6104,f10678]) ).
fof(f6104,plain,
! [X2,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)),
inference(cnf_transformation,[],[f2170]) ).
fof(f2170,plain,
! [X0,X1,X2] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)),
inference(rectify,[],[f1378]) ).
fof(f1378,axiom,
! [X158,X159,X160] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_nat_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10676,plain,
spl263_542,
inference(avatar_split_clause,[],[f6103,f10674]) ).
fof(f6103,plain,
! [X2,X0,X1] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)),
inference(cnf_transformation,[],[f2169]) ).
fof(f2169,plain,
! [X0,X1,X2] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)),
inference(rectify,[],[f1377]) ).
fof(f1377,axiom,
! [X158,X159,X160] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_int_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10672,plain,
spl263_541,
inference(avatar_split_clause,[],[f6102,f10670]) ).
fof(f10668,plain,
spl263_540,
inference(avatar_split_clause,[],[f6101,f10666]) ).
fof(f10666,plain,
( spl263_540
<=> ! [X2,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_540])]) ).
fof(f6101,plain,
! [X2,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)),
inference(cnf_transformation,[],[f2167]) ).
fof(f2167,plain,
! [X0,X1,X2] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)),
inference(rectify,[],[f1383]) ).
fof(f1383,axiom,
! [X158,X159,X160] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_pname_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10664,plain,
spl263_539,
inference(avatar_split_clause,[],[f6100,f10662]) ).
fof(f10662,plain,
( spl263_539
<=> ! [X2,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_539])]) ).
fof(f6100,plain,
! [X2,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)),
inference(cnf_transformation,[],[f2166]) ).
fof(f2166,plain,
! [X0,X1,X2] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)),
inference(rectify,[],[f1394]) ).
fof(f1394,axiom,
! [X158,X159,X160] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_f54304608l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10660,plain,
( spl263_538
| ~ spl263_129
| ~ spl263_470 ),
inference(avatar_split_clause,[],[f10392,f10126,f8412,f10657]) ).
fof(f10657,plain,
( spl263_538
<=> hBOOL(hAPP_pname_bool(u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_538])]) ).
fof(f10126,plain,
( spl263_470
<=> ! [X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_470])]) ).
fof(f10392,plain,
( hBOOL(hAPP_pname_bool(u,pn))
| ~ spl263_129
| ~ spl263_470 ),
inference(resolution,[],[f10127,f8414]) ).
fof(f10127,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl263_470 ),
inference(avatar_component_clause,[],[f10126]) ).
fof(f10655,plain,
spl263_537,
inference(avatar_split_clause,[],[f6099,f10653]) ).
fof(f10653,plain,
( spl263_537
<=> ! [X2,X0,X1] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_537])]) ).
fof(f6099,plain,
! [X2,X0,X1] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)),
inference(cnf_transformation,[],[f2165]) ).
fof(f2165,plain,
! [X0,X1,X2] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)),
inference(rectify,[],[f1393]) ).
fof(f1393,axiom,
! [X158,X159,X160] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_f448129468l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10651,plain,
spl263_536,
inference(avatar_split_clause,[],[f6098,f10649]) ).
fof(f10649,plain,
( spl263_536
<=> ! [X2,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_536])]) ).
fof(f6098,plain,
! [X2,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)),
inference(cnf_transformation,[],[f2164]) ).
fof(f2164,plain,
! [X0,X1,X2] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)),
inference(rectify,[],[f1387]) ).
fof(f1387,axiom,
! [X158,X159,X160] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_fun_a_bool_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10647,plain,
spl263_535,
inference(avatar_split_clause,[],[f6097,f10645]) ).
fof(f10645,plain,
( spl263_535
<=> ! [X2,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_535])]) ).
fof(f6097,plain,
! [X2,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)),
inference(cnf_transformation,[],[f2163]) ).
fof(f2163,plain,
! [X0,X1,X2] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)),
inference(rectify,[],[f1395]) ).
fof(f1395,axiom,
! [X158,X159,X160] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X158,X159),X160) = hAPP_b589554111l_bool(X158,hAPP_f1664156314l_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10643,plain,
spl263_534,
inference(avatar_split_clause,[],[f6096,f10641]) ).
fof(f10641,plain,
( spl263_534
<=> ! [X2,X0,X1] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_534])]) ).
fof(f6096,plain,
! [X2,X0,X1] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)),
inference(cnf_transformation,[],[f2162]) ).
fof(f2162,plain,
! [X0,X1,X2] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)),
inference(rectify,[],[f1400]) ).
fof(f1400,axiom,
! [X158,X159,X160] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X158,X159),X160) = hAPP_f284875647l_bool(X158,hAPP_n1082236369t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10639,plain,
spl263_533,
inference(avatar_split_clause,[],[f6095,f10637]) ).
fof(f10637,plain,
( spl263_533
<=> ! [X2,X0,X1] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_533])]) ).
fof(f6095,plain,
! [X2,X0,X1] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)),
inference(cnf_transformation,[],[f2161]) ).
fof(f2161,plain,
! [X0,X1,X2] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)),
inference(rectify,[],[f1401]) ).
fof(f1401,axiom,
! [X158,X159,X160] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X158,X159),X160) = hAPP_f103356543l_bool(X158,hAPP_i418383825t_bool(X159,X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10635,plain,
spl263_532,
inference(avatar_split_clause,[],[f5718,f10633]) ).
fof(f5718,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f3118]) ).
fof(f3118,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(ennf_transformation,[],[f1964]) ).
fof(f1964,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) ),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X2,X3] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
=> hBOOL(hAPP_fun_a_bool_bool(p(X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10631,plain,
spl263_531,
inference(avatar_split_clause,[],[f5260,f10629]) ).
fof(f10629,plain,
( spl263_531
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_531])]) ).
fof(f5260,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0,
inference(cnf_transformation,[],[f1656]) ).
fof(f1656,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0,
inference(rectify,[],[f940]) ).
fof(f940,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13)),X13) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10627,plain,
spl263_530,
inference(avatar_split_clause,[],[f5259,f10625]) ).
fof(f10625,plain,
( spl263_530
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_530])]) ).
fof(f5259,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1,
inference(cnf_transformation,[],[f1655]) ).
fof(f1655,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1,
inference(rectify,[],[f941]) ).
fof(f941,axiom,
! [X13,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14)),X13) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10623,plain,
spl263_529,
inference(avatar_split_clause,[],[f5258,f10621]) ).
fof(f10621,plain,
( spl263_529
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_529])]) ).
fof(f5258,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0,
inference(cnf_transformation,[],[f1654]) ).
fof(f1654,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0,
inference(rectify,[],[f924]) ).
fof(f924,axiom,
! [X114,X115] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X114),X115)),X115) = X114,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10619,plain,
spl263_528,
inference(avatar_split_clause,[],[f5257,f10617]) ).
fof(f5257,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0,
inference(cnf_transformation,[],[f1653]) ).
fof(f1653,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0,
inference(rectify,[],[f925]) ).
fof(f925,axiom,
! [X116,X117] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X116),X117)),X117) = X116,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10613,plain,
spl263_527,
inference(avatar_split_clause,[],[f5256,f10611]) ).
fof(f10611,plain,
( spl263_527
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_527])]) ).
fof(f5256,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0),
inference(cnf_transformation,[],[f1652]) ).
fof(f1652,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0),
inference(rectify,[],[f905]) ).
fof(f905,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10609,plain,
spl263_526,
inference(avatar_split_clause,[],[f5255,f10607]) ).
fof(f10607,plain,
( spl263_526
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_526])]) ).
fof(f5255,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0),
inference(cnf_transformation,[],[f1651]) ).
fof(f1651,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0),
inference(rectify,[],[f1123]) ).
fof(f1123,axiom,
! [X14,X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10605,plain,
spl263_525,
inference(avatar_split_clause,[],[f5254,f10603]) ).
fof(f10601,plain,
spl263_524,
inference(avatar_split_clause,[],[f5253,f10599]) ).
fof(f10599,plain,
( spl263_524
<=> ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_524])]) ).
fof(f5253,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0),
inference(cnf_transformation,[],[f1649]) ).
fof(f1649,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0),
inference(rectify,[],[f1128]) ).
fof(f1128,axiom,
! [X97,X134] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X97),X134) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X134),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10597,plain,
spl263_523,
inference(avatar_split_clause,[],[f5252,f10595]) ).
fof(f10595,plain,
( spl263_523
<=> ! [X0,X1] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_523])]) ).
fof(f5252,plain,
! [X0,X1] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),
inference(cnf_transformation,[],[f1648]) ).
fof(f1648,plain,
! [X0,X1] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),
inference(rectify,[],[f1061]) ).
fof(f1061,axiom,
! [X13,X14] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10593,plain,
spl263_522,
inference(avatar_split_clause,[],[f5188,f10591]) ).
fof(f10591,plain,
( spl263_522
<=> ! [X2,X0] :
( hBOOL(hAPP_int_bool(X0,sK86(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_522])]) ).
fof(f5188,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(X0,sK86(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f4154]) ).
fof(f10589,plain,
spl263_521,
inference(avatar_split_clause,[],[f5180,f10587]) ).
fof(f10587,plain,
( spl263_521
<=> ! [X0,X3] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK83(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_521])]) ).
fof(f5180,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK83(X0))) ),
inference(cnf_transformation,[],[f4141]) ).
fof(f10585,plain,
spl263_520,
inference(avatar_split_clause,[],[f5083,f10583]) ).
fof(f10583,plain,
( spl263_520
<=> ! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK63(X0)),sK64(X0)))
| bot_bot_fun_int_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_520])]) ).
fof(f5083,plain,
! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK63(X0)),sK64(X0)))
| bot_bot_fun_int_bool = X0 ),
inference(cnf_transformation,[],[f4050]) ).
fof(f10581,plain,
spl263_519,
inference(avatar_split_clause,[],[f5080,f10579]) ).
fof(f10579,plain,
( spl263_519
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK61(X0)),sK62(X0)))
| bot_bot_fun_nat_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_519])]) ).
fof(f5080,plain,
! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK61(X0)),sK62(X0)))
| bot_bot_fun_nat_bool = X0 ),
inference(cnf_transformation,[],[f4046]) ).
fof(f10577,plain,
spl263_518,
inference(avatar_split_clause,[],[f5064,f10575]) ).
fof(f5064,plain,
! [X0] :
( hBOOL(wt(the_com(body(X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ),
inference(cnf_transformation,[],[f2733]) ).
fof(f2733,plain,
! [X0] :
( hBOOL(wt(the_com(body(X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ),
inference(ennf_transformation,[],[f1560]) ).
fof(f1560,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u))
=> hBOOL(wt(the_com(body(X0)))) ),
inference(rectify,[],[f810]) ).
fof(f810,axiom,
! [X79] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X79),u))
=> hBOOL(wt(the_com(body(X79)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10571,plain,
spl263_517,
inference(avatar_split_clause,[],[f5029,f10569]) ).
fof(f10569,plain,
( spl263_517
<=> ! [X0] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK48(X0)),sK49(X0)) = X0
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_517])]) ).
fof(f5029,plain,
! [X0] :
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK48(X0)),sK49(X0)) = X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f4012]) ).
fof(f10567,plain,
spl263_516,
inference(avatar_split_clause,[],[f5024,f10565]) ).
fof(f10565,plain,
( spl263_516
<=> ! [X0] :
( bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_516])]) ).
fof(f5024,plain,
! [X0] :
( bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f2714]) ).
fof(f2714,plain,
! [X0] :
( bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f2713]) ).
fof(f2713,plain,
! [X0] :
( bot_bot_fun_a_bool = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1541]) ).
fof(f1541,plain,
! [X0] :
( is_fun_a_bool(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
=> bot_bot_fun_a_bool = X0 ) ),
inference(rectify,[],[f728]) ).
fof(f728,axiom,
! [X7] :
( is_fun_a_bool(X7)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),bot_bot_fun_a_bool))
=> bot_bot_fun_a_bool = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10563,plain,
spl263_515,
inference(avatar_split_clause,[],[f5002,f10561]) ).
fof(f10561,plain,
( spl263_515
<=> ! [X0] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK42(X0)),sK43(X0)) = X0
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_515])]) ).
fof(f5002,plain,
! [X0] :
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK42(X0)),sK43(X0)) = X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f10537,plain,
( spl263_514
| spl263_23
| ~ spl263_474 ),
inference(avatar_split_clause,[],[f10421,f10142,f7896,f10534]) ).
fof(f10534,plain,
( spl263_514
<=> is_a(sK149(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_514])]) ).
fof(f10142,plain,
( spl263_474
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK149(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_474])]) ).
fof(f10421,plain,
( is_a(sK149(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)))
| spl263_23
| ~ spl263_474 ),
inference(resolution,[],[f10143,f7898]) ).
fof(f10143,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK149(X0,X1)) )
| ~ spl263_474 ),
inference(avatar_component_clause,[],[f10142]) ).
fof(f10453,plain,
( spl263_513
| spl263_23
| ~ spl263_467 ),
inference(avatar_split_clause,[],[f10388,f10113,f7896,f10450]) ).
fof(f10450,plain,
( spl263_513
<=> is_a(sK143(image_pname_a(mgt_call,u),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_513])]) ).
fof(f10113,plain,
( spl263_467
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK143(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_467])]) ).
fof(f10388,plain,
( is_a(sK143(image_pname_a(mgt_call,u),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
| spl263_23
| ~ spl263_467 ),
inference(resolution,[],[f10114,f7898]) ).
fof(f10114,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK143(X0,X1)) )
| ~ spl263_467 ),
inference(avatar_component_clause,[],[f10113]) ).
fof(f10408,plain,
( spl263_512
| spl263_23
| ~ spl263_466 ),
inference(avatar_split_clause,[],[f10387,f10109,f7896,f10405]) ).
fof(f10405,plain,
( spl263_512
<=> is_a(sK142(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_512])]) ).
fof(f10109,plain,
( spl263_466
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK142(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_466])]) ).
fof(f10387,plain,
( is_a(sK142(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)))
| spl263_23
| ~ spl263_466 ),
inference(resolution,[],[f10110,f7898]) ).
fof(f10110,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK142(X0,X1)) )
| ~ spl263_466 ),
inference(avatar_component_clause,[],[f10109]) ).
fof(f10357,plain,
( spl263_511
| ~ spl263_282 ),
inference(avatar_split_clause,[],[f9119,f9077,f10355]) ).
fof(f10355,plain,
( spl263_511
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_511])]) ).
fof(f9077,plain,
( spl263_282
<=> ! [X2,X0] :
( bot_bot_fun_nat_bool != X0
| ~ hBOOL(hAPP_nat_bool(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_282])]) ).
fof(f9119,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ spl263_282 ),
inference(equality_resolution,[],[f9078]) ).
fof(f9078,plain,
( ! [X2,X0] :
( bot_bot_fun_nat_bool != X0
| ~ hBOOL(hAPP_nat_bool(X0,X2)) )
| ~ spl263_282 ),
inference(avatar_component_clause,[],[f9077]) ).
fof(f10319,plain,
( spl263_510
| ~ spl263_281 ),
inference(avatar_split_clause,[],[f9118,f9073,f10317]) ).
fof(f10317,plain,
( spl263_510
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_510])]) ).
fof(f9073,plain,
( spl263_281
<=> ! [X2,X0] :
( bot_bot_fun_int_bool != X0
| ~ hBOOL(hAPP_int_bool(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_281])]) ).
fof(f9118,plain,
( ! [X0] : ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
| ~ spl263_281 ),
inference(equality_resolution,[],[f9074]) ).
fof(f9074,plain,
( ! [X2,X0] :
( bot_bot_fun_int_bool != X0
| ~ hBOOL(hAPP_int_bool(X0,X2)) )
| ~ spl263_281 ),
inference(avatar_component_clause,[],[f9073]) ).
fof(f10286,plain,
spl263_509,
inference(avatar_split_clause,[],[f7647,f10284]) ).
fof(f10284,plain,
( spl263_509
<=> ! [X0,X1] :
( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| sP19(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_509])]) ).
fof(f7647,plain,
! [X0,X1] :
( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| sP19(X1,X0) ),
inference(forward_demodulation,[],[f6033,f4848]) ).
fof(f6033,plain,
! [X0,X1] :
( sP19(X1,X0)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ),
inference(cnf_transformation,[],[f4405]) ).
fof(f4405,plain,
! [X0,X1] :
( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP19(X1,X0) )
& ( sP19(X1,X0)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f3945]) ).
fof(f3945,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
<=> sP19(X1,X0) ),
inference(definition_folding,[],[f2136,f3944]) ).
fof(f3944,plain,
! [X1,X0] :
( sP19(X1,X0)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f2136,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ),
inference(rectify,[],[f1056]) ).
fof(f1056,axiom,
! [X24,X16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X16) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X16
& zero_zero_nat = X24 )
| ( zero_zero_nat = X16
& hAPP_nat_nat(suc,zero_zero_nat) = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10282,plain,
spl263_508,
inference(avatar_split_clause,[],[f7646,f10280]) ).
fof(f10280,plain,
( spl263_508
<=> ! [X0,X1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP19(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_508])]) ).
fof(f7646,plain,
! [X0,X1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP19(X1,X0) ),
inference(forward_demodulation,[],[f6034,f4848]) ).
fof(f6034,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP19(X1,X0) ),
inference(cnf_transformation,[],[f4405]) ).
fof(f10277,plain,
spl263_507,
inference(avatar_split_clause,[],[f7639,f10275]) ).
fof(f10275,plain,
( spl263_507
<=> ! [X0,X1] :
( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| sP18(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_507])]) ).
fof(f7639,plain,
! [X0,X1] :
( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| sP18(X1,X0) ),
inference(forward_demodulation,[],[f6025,f4848]) ).
fof(f6025,plain,
! [X0,X1] :
( sP18(X1,X0)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ),
inference(cnf_transformation,[],[f4401]) ).
fof(f4401,plain,
! [X0,X1] :
( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP18(X1,X0) )
& ( sP18(X1,X0)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f3943]) ).
fof(f3943,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
<=> sP18(X1,X0) ),
inference(definition_folding,[],[f2135,f3942]) ).
fof(f3942,plain,
! [X1,X0] :
( sP18(X1,X0)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f2135,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ),
inference(rectify,[],[f1057]) ).
fof(f1057,axiom,
! [X24,X16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X16) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( hAPP_nat_nat(suc,zero_zero_nat) = X16
& zero_zero_nat = X24 )
| ( zero_zero_nat = X16
& hAPP_nat_nat(suc,zero_zero_nat) = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10273,plain,
spl263_506,
inference(avatar_split_clause,[],[f7638,f10271]) ).
fof(f10271,plain,
( spl263_506
<=> ! [X0,X1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP18(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_506])]) ).
fof(f7638,plain,
! [X0,X1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP18(X1,X0) ),
inference(forward_demodulation,[],[f6026,f4848]) ).
fof(f6026,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| ~ sP18(X1,X0) ),
inference(cnf_transformation,[],[f4401]) ).
fof(f10269,plain,
spl263_505,
inference(avatar_split_clause,[],[f7594,f10267]) ).
fof(f10267,plain,
( spl263_505
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| pls = X1
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_505])]) ).
fof(f7594,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| pls = X1
| ~ sP16(X0,X1) ),
inference(forward_demodulation,[],[f7593,f4875]) ).
fof(f7593,plain,
! [X0,X1] :
( pls = X1
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP16(X0,X1) ),
inference(forward_demodulation,[],[f7101,f4875]) ).
fof(f7101,plain,
! [X0,X1] :
( pls = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP16(X0,X1) ),
inference(definition_unfolding,[],[f5894,f4830]) ).
fof(f5894,plain,
! [X0,X1] :
( zero_zero_int = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f4309]) ).
fof(f4309,plain,
! [X0,X1] :
( ( sP16(X0,X1)
| ( X0 != X1
& ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
| ( zero_zero_int != number_number_of_int(X1)
& hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( zero_zero_int = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
| ~ sP16(X0,X1) ) ),
inference(rectify,[],[f4308]) ).
fof(f4308,plain,
! [X1,X0] :
( ( sP16(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
| ( zero_zero_int != number_number_of_int(X0)
& hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
& ( zero_zero_int = number_number_of_int(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
| ~ sP16(X1,X0) ) ),
inference(flattening,[],[f4307]) ).
fof(f4307,plain,
! [X1,X0] :
( ( sP16(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
| ( zero_zero_int != number_number_of_int(X0)
& hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
& ( zero_zero_int = number_number_of_int(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
| ~ sP16(X1,X0) ) ),
inference(nnf_transformation,[],[f3939]) ).
fof(f3939,plain,
! [X1,X0] :
( sP16(X1,X0)
<=> ( ( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
& ( zero_zero_int = number_number_of_int(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f10265,plain,
spl263_504,
inference(avatar_split_clause,[],[f7592,f10263]) ).
fof(f10263,plain,
( spl263_504
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| X0 = X1
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_504])]) ).
fof(f7592,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| X0 = X1
| ~ sP16(X0,X1) ),
inference(forward_demodulation,[],[f5895,f4875]) ).
fof(f5895,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f4309]) ).
fof(f10261,plain,
spl263_503,
inference(avatar_split_clause,[],[f7591,f10259]) ).
fof(f10259,plain,
( spl263_503
<=> ! [X0,X1] :
( pls != X1
| ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_503])]) ).
fof(f7591,plain,
! [X0,X1] :
( pls != X1
| ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP16(X0,X1) ),
inference(forward_demodulation,[],[f7590,f4875]) ).
fof(f7590,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| sP16(X0,X1)
| pls != number_number_of_int(X1) ),
inference(forward_demodulation,[],[f7100,f4875]) ).
fof(f7100,plain,
! [X0,X1] :
( sP16(X0,X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| pls != number_number_of_int(X1) ),
inference(definition_unfolding,[],[f5897,f4830]) ).
fof(f5897,plain,
! [X0,X1] :
( sP16(X0,X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| zero_zero_int != number_number_of_int(X1) ),
inference(cnf_transformation,[],[f4309]) ).
fof(f10257,plain,
spl263_502,
inference(avatar_split_clause,[],[f7585,f10255]) ).
fof(f10255,plain,
( spl263_502
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| sP16(X1,X0)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_502])]) ).
fof(f7585,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| sP16(X1,X0)
| ~ sP17(X0,X1) ),
inference(forward_demodulation,[],[f5889,f4875]) ).
fof(f5889,plain,
! [X0,X1] :
( sP16(X1,X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f4306]) ).
fof(f10253,plain,
spl263_501,
inference(avatar_split_clause,[],[f7582,f10251]) ).
fof(f10251,plain,
( spl263_501
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| sP17(X0,X1)
| ~ sP16(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_501])]) ).
fof(f7582,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| sP17(X0,X1)
| ~ sP16(X1,X0) ),
inference(forward_demodulation,[],[f5892,f4875]) ).
fof(f5892,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ sP16(X1,X0)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f4306]) ).
fof(f10249,plain,
spl263_500,
inference(avatar_split_clause,[],[f7416,f10247]) ).
fof(f10247,plain,
( spl263_500
<=> ! [X0] :
( hAPP_fun_a_bool_a(the_elem_a,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_500])]) ).
fof(f7416,plain,
! [X0] :
( hAPP_fun_a_bool_a(the_elem_a,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0
| ~ is_a(X0) ),
inference(forward_demodulation,[],[f4991,f4966]) ).
fof(f4991,plain,
! [X0] :
( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f2697,plain,
! [X0] :
( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0] :
( is_a(X0)
=> hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ),
inference(rectify,[],[f803]) ).
fof(f803,axiom,
! [X10] :
( is_a(X10)
=> hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X10),bot_bot_fun_a_bool)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10245,plain,
spl263_499,
inference(avatar_split_clause,[],[f7413,f10243]) ).
fof(f10243,plain,
( spl263_499
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_499])]) ).
fof(f7413,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ),
inference(forward_demodulation,[],[f7042,f4875]) ).
fof(f7042,plain,
! [X0] :
( pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f4985,f4830]) ).
fof(f4985,plain,
! [X0] :
( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2695]) ).
fof(f2695,plain,
! [X0] :
( ( number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
inference(ennf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) ),
inference(rectify,[],[f1263]) ).
fof(f1263,axiom,
! [X132] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> number_number_of_int(X132) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X132)) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X132)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10241,plain,
spl263_498,
inference(avatar_split_clause,[],[f7412,f10239]) ).
fof(f10239,plain,
( spl263_498
<=> ! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_498])]) ).
fof(f7412,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 ),
inference(forward_demodulation,[],[f7411,f4875]) ).
fof(f7411,plain,
! [X0] :
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(forward_demodulation,[],[f4986,f4875]) ).
fof(f4986,plain,
! [X0] :
( number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2695]) ).
fof(f10237,plain,
spl263_497,
inference(avatar_split_clause,[],[f7410,f10235]) ).
fof(f10235,plain,
( spl263_497
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_497])]) ).
fof(f7410,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ),
inference(forward_demodulation,[],[f4983,f4875]) ).
fof(f4983,plain,
! [X0] :
( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2694]) ).
fof(f10233,plain,
spl263_496,
inference(avatar_split_clause,[],[f7403,f10231]) ).
fof(f10231,plain,
( spl263_496
<=> ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_496])]) ).
fof(f7403,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)),
inference(forward_demodulation,[],[f4972,f4876]) ).
fof(f4972,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
inference(cnf_transformation,[],[f1518]) ).
fof(f1518,plain,
! [X0] : hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
inference(rectify,[],[f228]) ).
fof(f228,axiom,
! [X16] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X16))) = hAPP_nat_nat(suc,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10229,plain,
spl263_495,
inference(avatar_split_clause,[],[f7402,f10227]) ).
fof(f10227,plain,
( spl263_495
<=> ! [X0] : collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_495])]) ).
fof(f7402,plain,
! [X0] : collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),
inference(forward_demodulation,[],[f4971,f4966]) ).
fof(f4971,plain,
! [X0] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),
inference(cnf_transformation,[],[f1517]) ).
fof(f1517,plain,
! [X0] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),
inference(rectify,[],[f743]) ).
fof(f743,axiom,
! [X7] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10225,plain,
spl263_494,
inference(avatar_split_clause,[],[f7375,f10223]) ).
fof(f10223,plain,
( spl263_494
<=> ! [X2,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1),X2))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_494])]) ).
fof(f7375,plain,
! [X2,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1),X2))
| ~ is_a(X2) ),
inference(duplicate_literal_removal,[],[f7322]) ).
fof(f7322,plain,
! [X2,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1),X2))
| ~ is_a(X2)
| ~ is_a(X2) ),
inference(equality_resolution,[],[f6694]) ).
fof(f6694,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
| X0 != X2
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f4628]) ).
fof(f10221,plain,
spl263_493,
inference(avatar_split_clause,[],[f7293,f10219]) ).
fof(f10219,plain,
( spl263_493
<=> ! [X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_493])]) ).
fof(f7293,plain,
! [X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))),
inference(equality_resolution,[],[f6067]) ).
fof(f6067,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| X0 != X1 ),
inference(cnf_transformation,[],[f4426]) ).
fof(f10217,plain,
spl263_492,
inference(avatar_split_clause,[],[f7136,f10215]) ).
fof(f10215,plain,
( spl263_492
<=> ! [X2,X0,X1] :
( sP28(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_492])]) ).
fof(f7136,plain,
! [X2,X0,X1] :
( sP28(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f6726,f4830]) ).
fof(f6726,plain,
! [X2,X0,X1] :
( sP28(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f4644]) ).
fof(f4644,plain,
! [X0,X1,X2] :
( sP28(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f4643]) ).
fof(f4643,plain,
! [X0,X1,X2] :
( sP28(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f3963]) ).
fof(f3963,plain,
! [X0,X1,X2] :
( sP28(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f3785,f3962]) ).
fof(f3785,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2567]) ).
fof(f2567,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X1) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X0) ) ) ),
inference(rectify,[],[f1197]) ).
fof(f1197,axiom,
! [X147,X12,X10] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> ( hBOOL(X12)
<=> hBOOL(X147) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> hBOOL(X12) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> hBOOL(X147) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10213,plain,
spl263_491,
inference(avatar_split_clause,[],[f7131,f10211]) ).
fof(f10211,plain,
( spl263_491
<=> ! [X2,X0,X1] :
( sP27(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_491])]) ).
fof(f7131,plain,
! [X2,X0,X1] :
( sP27(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f6719,f4830]) ).
fof(f6719,plain,
! [X2,X0,X1] :
( sP27(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f4639]) ).
fof(f4639,plain,
! [X0,X1,X2] :
( sP27(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f4638]) ).
fof(f4638,plain,
! [X0,X1,X2] :
( sP27(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f3961]) ).
fof(f3961,plain,
! [X0,X1,X2] :
( sP27(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f3784,f3960]) ).
fof(f3784,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2566]) ).
fof(f2566,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) ),
inference(rectify,[],[f1196]) ).
fof(f1196,axiom,
! [X147,X12,X10] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> ( hBOOL(X12)
<=> hBOOL(X147) ) )
=> ( ( hBOOL(X12)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10)) )
<=> ( hBOOL(X147)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10209,plain,
spl263_490,
inference(avatar_split_clause,[],[f7068,f10207]) ).
fof(f10207,plain,
( spl263_490
<=> ! [X0] :
( pls = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_490])]) ).
fof(f7068,plain,
! [X0] :
( pls = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ),
inference(definition_unfolding,[],[f5161,f4830]) ).
fof(f5161,plain,
! [X0] :
( zero_zero_int = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ),
inference(cnf_transformation,[],[f4122]) ).
fof(f4122,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| zero_zero_int != X0 )
& ( zero_zero_int = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) ),
inference(nnf_transformation,[],[f1610]) ).
fof(f1610,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
<=> zero_zero_int = X0 ),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X55)),one_one_int))
<=> zero_zero_int = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10205,plain,
spl263_489,
inference(avatar_split_clause,[],[f7054,f10203]) ).
fof(f10203,plain,
( spl263_489
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_489])]) ).
fof(f7054,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ),
inference(definition_unfolding,[],[f5127,f4830]) ).
fof(f5127,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ),
inference(cnf_transformation,[],[f4102]) ).
fof(f4102,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
inference(nnf_transformation,[],[f1593]) ).
fof(f1593,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
inference(rectify,[],[f1253]) ).
fof(f1253,axiom,
! [X152] :
( hBOOL(hAPP_int_bool(nat_neg,X152))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X152),zero_zero_int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10201,plain,
spl263_488,
inference(avatar_split_clause,[],[f7053,f10199]) ).
fof(f10199,plain,
( spl263_488
<=> ! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_488])]) ).
fof(f7053,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f5128,f4830]) ).
fof(f5128,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
inference(cnf_transformation,[],[f4102]) ).
fof(f10196,plain,
spl263_487,
inference(avatar_split_clause,[],[f7052,f10194]) ).
fof(f10194,plain,
( spl263_487
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_487])]) ).
fof(f7052,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ),
inference(definition_unfolding,[],[f5091,f4830]) ).
fof(f5091,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ),
inference(cnf_transformation,[],[f4054]) ).
fof(f4054,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
| hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
inference(nnf_transformation,[],[f1579]) ).
fof(f1579,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X10] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X10))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10192,plain,
spl263_486,
inference(avatar_split_clause,[],[f7051,f10190]) ).
fof(f10190,plain,
( spl263_486
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_486])]) ).
fof(f7051,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f5092,f4830]) ).
fof(f5092,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f4054]) ).
fof(f10188,plain,
spl263_485,
inference(avatar_split_clause,[],[f6730,f10186]) ).
fof(f6730,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f4646]) ).
fof(f4646,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ sP29(X0,X1,X2) ),
inference(rectify,[],[f4645]) ).
fof(f4645,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP29(X1,X2,X0) ),
inference(nnf_transformation,[],[f3964]) ).
fof(f10184,plain,
spl263_484,
inference(avatar_split_clause,[],[f6729,f10182]) ).
fof(f10182,plain,
( spl263_484
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_484])]) ).
fof(f6729,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f4646]) ).
fof(f10180,plain,
spl263_483,
inference(avatar_split_clause,[],[f5966,f10178]) ).
fof(f10178,plain,
( spl263_483
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_483])]) ).
fof(f5966,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ),
inference(cnf_transformation,[],[f4367]) ).
fof(f4367,plain,
! [X0,X1] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
inference(nnf_transformation,[],[f2111]) ).
fof(f2111,plain,
! [X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1239]) ).
fof(f1239,axiom,
! [X24,X16] :
( hAPP_nat_int(semiri1621563631at_int,X16) = hAPP_nat_int(semiri1621563631at_int,X24)
<=> X16 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10176,plain,
spl263_482,
inference(avatar_split_clause,[],[f5964,f10174]) ).
fof(f10174,plain,
( spl263_482
<=> ! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_482])]) ).
fof(f5964,plain,
! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ),
inference(cnf_transformation,[],[f4366]) ).
fof(f4366,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| zero_zero_nat != X1
| zero_zero_nat != X0 )
& ( ( zero_zero_nat = X1
& zero_zero_nat = X0 )
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
inference(flattening,[],[f4365]) ).
fof(f4365,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
| zero_zero_nat != X1
| zero_zero_nat != X0 )
& ( ( zero_zero_nat = X1
& zero_zero_nat = X0 )
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f2110]) ).
fof(f2110,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)
<=> ( zero_zero_nat = X1
& zero_zero_nat = X0 ) ),
inference(rectify,[],[f1039]) ).
fof(f1039,axiom,
! [X24,X16] :
( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X16)
<=> ( zero_zero_nat = X16
& zero_zero_nat = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10172,plain,
spl263_481,
inference(avatar_split_clause,[],[f5963,f10170]) ).
fof(f10170,plain,
( spl263_481
<=> ! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_481])]) ).
fof(f5963,plain,
! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ),
inference(cnf_transformation,[],[f4366]) ).
fof(f10168,plain,
spl263_480,
inference(avatar_split_clause,[],[f5953,f10166]) ).
fof(f10166,plain,
( spl263_480
<=> ! [X0,X1] :
( one_one_nat = X1
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_480])]) ).
fof(f5953,plain,
! [X0,X1] :
( one_one_nat = X1
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ),
inference(cnf_transformation,[],[f4359]) ).
fof(f4359,plain,
! [X0,X1] :
( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
| one_one_nat != X1
| one_one_nat != X0 )
& ( ( one_one_nat = X1
& one_one_nat = X0 )
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
inference(flattening,[],[f4358]) ).
fof(f4358,plain,
! [X0,X1] :
( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
| one_one_nat != X1
| one_one_nat != X0 )
& ( ( one_one_nat = X1
& one_one_nat = X0 )
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
inference(nnf_transformation,[],[f2106]) ).
fof(f2106,plain,
! [X0,X1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)
<=> ( one_one_nat = X1
& one_one_nat = X0 ) ),
inference(rectify,[],[f1100]) ).
fof(f1100,axiom,
! [X24,X16] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X16)
<=> ( one_one_nat = X16
& one_one_nat = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10164,plain,
spl263_479,
inference(avatar_split_clause,[],[f5952,f10162]) ).
fof(f10162,plain,
( spl263_479
<=> ! [X0,X1] :
( one_one_nat = X0
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_479])]) ).
fof(f5952,plain,
! [X0,X1] :
( one_one_nat = X0
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ),
inference(cnf_transformation,[],[f4359]) ).
fof(f10160,plain,
spl263_478,
inference(avatar_split_clause,[],[f5922,f10158]) ).
fof(f10158,plain,
( spl263_478
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_478])]) ).
fof(f5922,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(cnf_transformation,[],[f4326]) ).
fof(f4326,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
& ( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f2092]) ).
fof(f2092,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(rectify,[],[f484]) ).
fof(f484,axiom,
! [X10,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
<=> hBOOL(hAPP_nat_bool(X4,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10156,plain,
spl263_477,
inference(avatar_split_clause,[],[f5921,f10154]) ).
fof(f10154,plain,
( spl263_477
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_477])]) ).
fof(f5921,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f4326]) ).
fof(f10152,plain,
spl263_476,
inference(avatar_split_clause,[],[f5918,f10150]) ).
fof(f10150,plain,
( spl263_476
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_476])]) ).
fof(f5918,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(X1,X0)) ),
inference(cnf_transformation,[],[f4321]) ).
fof(f4321,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
| ~ hBOOL(hAPP_int_bool(X1,X0)) )
& ( hBOOL(hAPP_int_bool(X1,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f2090]) ).
fof(f2090,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
<=> hBOOL(hAPP_int_bool(X1,X0)) ),
inference(rectify,[],[f483]) ).
fof(f483,axiom,
! [X10,X4] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X10),X4))
<=> hBOOL(hAPP_int_bool(X4,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10148,plain,
spl263_475,
inference(avatar_split_clause,[],[f5917,f10146]) ).
fof(f10146,plain,
( spl263_475
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_475])]) ).
fof(f5917,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(X1,X0))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
inference(cnf_transformation,[],[f4321]) ).
fof(f10144,plain,
spl263_474,
inference(avatar_split_clause,[],[f5915,f10142]) ).
fof(f5915,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK149(X0,X1)) ),
inference(cnf_transformation,[],[f4320]) ).
fof(f10140,plain,
spl263_473,
inference(avatar_split_clause,[],[f5913,f10138]) ).
fof(f5913,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) ),
inference(cnf_transformation,[],[f4316]) ).
fof(f4316,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
& ( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
inference(nnf_transformation,[],[f2088]) ).
fof(f2088,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
<=> hBOOL(hAPP_a_bool(X1,X0)) ),
inference(rectify,[],[f485]) ).
fof(f485,axiom,
! [X10,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
<=> hBOOL(hAPP_a_bool(X4,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10136,plain,
spl263_472,
inference(avatar_split_clause,[],[f5912,f10134]) ).
fof(f10134,plain,
( spl263_472
<=> ! [X0,X1] :
( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_472])]) ).
fof(f5912,plain,
! [X0,X1] :
( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(cnf_transformation,[],[f4316]) ).
fof(f10132,plain,
spl263_471,
inference(avatar_split_clause,[],[f5911,f10130]) ).
fof(f5911,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(cnf_transformation,[],[f4315]) ).
fof(f4315,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
& ( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
inference(nnf_transformation,[],[f2087]) ).
fof(f2087,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
<=> hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
<=> hBOOL(hAPP_pname_bool(X4,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10128,plain,
spl263_470,
inference(avatar_split_clause,[],[f5910,f10126]) ).
fof(f5910,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f4315]) ).
fof(f10124,plain,
spl263_469,
inference(avatar_split_clause,[],[f5867,f10122]) ).
fof(f10122,plain,
( spl263_469
<=> ! [X0,X1] :
( X0 = X1
| image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_469])]) ).
fof(f5867,plain,
! [X0,X1] :
( X0 = X1
| image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) ),
inference(cnf_transformation,[],[f4291]) ).
fof(f4291,plain,
! [X0,X1] :
( ( X0 = X1
| image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) )
& ( image_nat_int(semiri1621563631at_int,X0) = image_nat_int(semiri1621563631at_int,X1)
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2074]) ).
fof(f2074,plain,
! [X0,X1] :
( X0 = X1
<=> image_nat_int(semiri1621563631at_int,X0) = image_nat_int(semiri1621563631at_int,X1) ),
inference(rectify,[],[f1243]) ).
fof(f1243,axiom,
! [X4,X9] :
( X4 = X9
<=> image_nat_int(semiri1621563631at_int,X4) = image_nat_int(semiri1621563631at_int,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10120,plain,
spl263_468,
inference(avatar_split_clause,[],[f5851,f10118]) ).
fof(f10118,plain,
( spl263_468
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| is_pname(sK144(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_468])]) ).
fof(f5851,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| is_pname(sK144(X0,X1)) ),
inference(cnf_transformation,[],[f4278]) ).
fof(f10115,plain,
spl263_467,
inference(avatar_split_clause,[],[f5848,f10113]) ).
fof(f5848,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK143(X0,X1)) ),
inference(cnf_transformation,[],[f4276]) ).
fof(f10111,plain,
spl263_466,
inference(avatar_split_clause,[],[f5846,f10109]) ).
fof(f5846,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK142(X0,X1)) ),
inference(cnf_transformation,[],[f4274]) ).
fof(f10107,plain,
spl263_465,
inference(avatar_split_clause,[],[f5776,f10105]) ).
fof(f10105,plain,
( spl263_465
<=> ! [X0,X1] :
( zero_zero_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_465])]) ).
fof(f5776,plain,
! [X0,X1] :
( zero_zero_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ),
inference(cnf_transformation,[],[f3189]) ).
fof(f3189,plain,
! [X0,X1] :
( zero_zero_nat = X1
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ),
inference(ennf_transformation,[],[f2015]) ).
fof(f2015,plain,
! [X0,X1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = X0
=> zero_zero_nat = X1 ),
inference(rectify,[],[f1038]) ).
fof(f1038,axiom,
! [X14,X13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13) = X14
=> zero_zero_nat = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10103,plain,
spl263_464,
inference(avatar_split_clause,[],[f5773,f10101]) ).
fof(f10101,plain,
( spl263_464
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_464])]) ).
fof(f5773,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ),
inference(cnf_transformation,[],[f3184]) ).
fof(f3184,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ),
inference(ennf_transformation,[],[f2012]) ).
fof(f2012,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
=> X0 = X1 ),
inference(rectify,[],[f229]) ).
fof(f229,axiom,
! [X17,X18] :
( hAPP_nat_nat(suc,X17) = hAPP_nat_nat(suc,X18)
=> X17 = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10099,plain,
spl263_463,
inference(avatar_split_clause,[],[f5668,f10097]) ).
fof(f10097,plain,
( spl263_463
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK125(X0)),sK126(X0)))
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_463])]) ).
fof(f5668,plain,
! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK125(X0)),sK126(X0)))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f4230]) ).
fof(f10095,plain,
spl263_462,
inference(avatar_split_clause,[],[f5652,f10093]) ).
fof(f10093,plain,
( spl263_462
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_462])]) ).
fof(f5652,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3048]) ).
fof(f3048,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1917]) ).
fof(f1917,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1))) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10091,plain,
spl263_461,
inference(avatar_split_clause,[],[f5651,f10089]) ).
fof(f10089,plain,
( spl263_461
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_461])]) ).
fof(f5651,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3047]) ).
fof(f3047,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1916]) ).
fof(f1916,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1))) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10087,plain,
spl263_460,
inference(avatar_split_clause,[],[f5650,f10085]) ).
fof(f10085,plain,
( spl263_460
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_460])]) ).
fof(f5650,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3046]) ).
fof(f3046,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1915]) ).
fof(f1915,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1))) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10083,plain,
spl263_459,
inference(avatar_split_clause,[],[f5649,f10081]) ).
fof(f10081,plain,
( spl263_459
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_459])]) ).
fof(f5649,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3045]) ).
fof(f3045,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1914]) ).
fof(f1914,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1))) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10079,plain,
spl263_458,
inference(avatar_split_clause,[],[f5648,f10077]) ).
fof(f10077,plain,
( spl263_458
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_458])]) ).
fof(f5648,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3044]) ).
fof(f3044,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1913]) ).
fof(f1913,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1))) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10075,plain,
spl263_457,
inference(avatar_split_clause,[],[f5647,f10073]) ).
fof(f10073,plain,
( spl263_457
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_457])]) ).
fof(f5647,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f3043]) ).
fof(f3043,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f1912]) ).
fof(f1912,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1))) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10071,plain,
spl263_456,
inference(avatar_split_clause,[],[f5625,f10069]) ).
fof(f10069,plain,
( spl263_456
<=> ! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK118(X0)),sK119(X0)))
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_456])]) ).
fof(f5625,plain,
! [X0] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK118(X0)),sK119(X0)))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f4219]) ).
fof(f10067,plain,
spl263_455,
inference(avatar_split_clause,[],[f5610,f10065]) ).
fof(f10065,plain,
( spl263_455
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_455])]) ).
fof(f5610,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3009]) ).
fof(f3009,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1889]) ).
fof(f1889,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1))) ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X5,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10063,plain,
spl263_454,
inference(avatar_split_clause,[],[f5609,f10061]) ).
fof(f10061,plain,
( spl263_454
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_454])]) ).
fof(f5609,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3008]) ).
fof(f3008,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1888]) ).
fof(f1888,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1))) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X5,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10059,plain,
spl263_453,
inference(avatar_split_clause,[],[f5608,f10057]) ).
fof(f10057,plain,
( spl263_453
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_453])]) ).
fof(f5608,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3007]) ).
fof(f3007,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1887]) ).
fof(f1887,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1))) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X5,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10055,plain,
spl263_452,
inference(avatar_split_clause,[],[f5607,f10053]) ).
fof(f10053,plain,
( spl263_452
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_452])]) ).
fof(f5607,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3006]) ).
fof(f3006,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1886]) ).
fof(f1886,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1))) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X5,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10051,plain,
spl263_451,
inference(avatar_split_clause,[],[f5606,f10049]) ).
fof(f10049,plain,
( spl263_451
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_451])]) ).
fof(f5606,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(cnf_transformation,[],[f3005]) ).
fof(f3005,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(ennf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1))) ),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X5,X6] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X6))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10047,plain,
spl263_450,
inference(avatar_split_clause,[],[f5595,f10045]) ).
fof(f10045,plain,
( spl263_450
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK116(X0)),sK117(X0)))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_450])]) ).
fof(f5595,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK116(X0)),sK117(X0)))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f10043,plain,
spl263_449,
inference(avatar_split_clause,[],[f5588,f10041]) ).
fof(f10041,plain,
( spl263_449
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK114(X0)),sK115(X0)))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_449])]) ).
fof(f5588,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK114(X0)),sK115(X0)))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f10039,plain,
spl263_448,
inference(avatar_split_clause,[],[f5570,f10037]) ).
fof(f10037,plain,
( spl263_448
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_448])]) ).
fof(f5570,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2974]) ).
fof(f2974,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1863]) ).
fof(f1863,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1))) ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X5,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10034,plain,
spl263_447,
inference(avatar_split_clause,[],[f5569,f10032]) ).
fof(f10032,plain,
( spl263_447
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_447])]) ).
fof(f5569,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2973]) ).
fof(f2973,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1862]) ).
fof(f1862,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1))) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X5,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10030,plain,
spl263_446,
inference(avatar_split_clause,[],[f5568,f10028]) ).
fof(f10028,plain,
( spl263_446
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_446])]) ).
fof(f5568,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f2972]) ).
fof(f2972,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f1861]) ).
fof(f1861,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1))) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X5,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10026,plain,
spl263_445,
inference(avatar_split_clause,[],[f5555,f10024]) ).
fof(f10024,plain,
( spl263_445
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK112(X0)),sK113(X0)))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_445])]) ).
fof(f5555,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK112(X0)),sK113(X0)))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f10022,plain,
spl263_444,
inference(avatar_split_clause,[],[f5548,f10020]) ).
fof(f10020,plain,
( spl263_444
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK110(X0)),sK111(X0)))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_444])]) ).
fof(f5548,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK110(X0)),sK111(X0)))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f10018,plain,
spl263_443,
inference(avatar_split_clause,[],[f5529,f10016]) ).
fof(f10016,plain,
( spl263_443
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_443])]) ).
fof(f5529,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2939]) ).
fof(f2939,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1837]) ).
fof(f1837,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1))) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10014,plain,
spl263_442,
inference(avatar_split_clause,[],[f5528,f10012]) ).
fof(f10012,plain,
( spl263_442
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_442])]) ).
fof(f5528,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2938]) ).
fof(f2938,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1836]) ).
fof(f1836,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1))) ),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10010,plain,
spl263_441,
inference(avatar_split_clause,[],[f5527,f10008]) ).
fof(f10008,plain,
( spl263_441
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_441])]) ).
fof(f5527,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2937]) ).
fof(f2937,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1))) ),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10006,plain,
spl263_440,
inference(avatar_split_clause,[],[f5526,f10004]) ).
fof(f10004,plain,
( spl263_440
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_440])]) ).
fof(f5526,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2936]) ).
fof(f2936,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1834]) ).
fof(f1834,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1))) ),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10002,plain,
spl263_439,
inference(avatar_split_clause,[],[f5525,f10000]) ).
fof(f10000,plain,
( spl263_439
<=> ! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_439])]) ).
fof(f5525,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f2935]) ).
fof(f2935,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f1833]) ).
fof(f1833,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1))) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9998,plain,
spl263_438,
inference(avatar_split_clause,[],[f5482,f9996]) ).
fof(f9996,plain,
( spl263_438
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_438])]) ).
fof(f5482,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2882]) ).
fof(f2882,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1794]) ).
fof(f1794,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1))) ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9994,plain,
spl263_437,
inference(avatar_split_clause,[],[f5481,f9992]) ).
fof(f9992,plain,
( spl263_437
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_437])]) ).
fof(f5481,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2881]) ).
fof(f2881,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1793]) ).
fof(f1793,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1))) ),
inference(rectify,[],[f137]) ).
fof(f137,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9990,plain,
spl263_436,
inference(avatar_split_clause,[],[f5480,f9988]) ).
fof(f9988,plain,
( spl263_436
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_436])]) ).
fof(f5480,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2880]) ).
fof(f2880,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1792]) ).
fof(f1792,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1))) ),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X5,X6] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9986,plain,
spl263_435,
inference(avatar_split_clause,[],[f5479,f9984]) ).
fof(f9984,plain,
( spl263_435
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_435])]) ).
fof(f5479,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2879]) ).
fof(f2879,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1791]) ).
fof(f1791,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1))) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X5,X6] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9982,plain,
spl263_434,
inference(avatar_split_clause,[],[f5478,f9980]) ).
fof(f9980,plain,
( spl263_434
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_434])]) ).
fof(f5478,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2878]) ).
fof(f2878,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1790]) ).
fof(f1790,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1))) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X5,X6] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9978,plain,
spl263_433,
inference(avatar_split_clause,[],[f5477,f9976]) ).
fof(f9976,plain,
( spl263_433
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_433])]) ).
fof(f5477,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2877]) ).
fof(f2877,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1))) ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X5,X6] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9974,plain,
spl263_432,
inference(avatar_split_clause,[],[f5476,f9972]) ).
fof(f9972,plain,
( spl263_432
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_432])]) ).
fof(f5476,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2876]) ).
fof(f2876,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1788]) ).
fof(f1788,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1))) ),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9970,plain,
spl263_431,
inference(avatar_split_clause,[],[f5475,f9968]) ).
fof(f9968,plain,
( spl263_431
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_431])]) ).
fof(f5475,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2875]) ).
fof(f2875,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1787]) ).
fof(f1787,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1))) ),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X6))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9966,plain,
spl263_430,
inference(avatar_split_clause,[],[f5474,f9964]) ).
fof(f9964,plain,
( spl263_430
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_430])]) ).
fof(f5474,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(cnf_transformation,[],[f2874]) ).
fof(f2874,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(ennf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X0,X1] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1))) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X5,X6] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9962,plain,
spl263_429,
inference(avatar_split_clause,[],[f5473,f9960]) ).
fof(f9960,plain,
( spl263_429
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_429])]) ).
fof(f5473,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f2873]) ).
fof(f2873,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f1785]) ).
fof(f1785,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1))) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9958,plain,
spl263_428,
inference(avatar_split_clause,[],[f5472,f9956]) ).
fof(f9956,plain,
( spl263_428
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_428])]) ).
fof(f5472,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f2872]) ).
fof(f2872,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f1784]) ).
fof(f1784,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1))) ),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X5,X6] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9953,plain,
spl263_427,
inference(avatar_split_clause,[],[f5471,f9951]) ).
fof(f9951,plain,
( spl263_427
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_427])]) ).
fof(f5471,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f2871]) ).
fof(f2871,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1))) ),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9949,plain,
spl263_426,
inference(avatar_split_clause,[],[f5407,f9947]) ).
fof(f9947,plain,
( spl263_426
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK93(X0)),sK94(X0)))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_426])]) ).
fof(f5407,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK93(X0)),sK94(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f9945,plain,
spl263_425,
inference(avatar_split_clause,[],[f5392,f9943]) ).
fof(f9943,plain,
( spl263_425
<=> ! [X0,X1] :
( bot_bo844097828e_bool = X1
| bot_bot_fun_a_bool != image_pname_a(X0,X1)
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_425])]) ).
fof(f5392,plain,
! [X0,X1] :
( bot_bo844097828e_bool = X1
| bot_bot_fun_a_bool != image_pname_a(X0,X1)
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f4163]) ).
fof(f4163,plain,
! [X0,X1] :
( ( ( bot_bot_fun_a_bool = image_pname_a(X0,X1)
| bot_bo844097828e_bool != X1 )
& ( bot_bo844097828e_bool = X1
| bot_bot_fun_a_bool != image_pname_a(X0,X1) ) )
| ~ is_fun_pname_bool(X1) ),
inference(nnf_transformation,[],[f2803]) ).
fof(f2803,plain,
! [X0,X1] :
( ( bot_bot_fun_a_bool = image_pname_a(X0,X1)
<=> bot_bo844097828e_bool = X1 )
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f1742]) ).
fof(f1742,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( bot_bot_fun_a_bool = image_pname_a(X0,X1)
<=> bot_bo844097828e_bool = X1 ) ),
inference(rectify,[],[f724]) ).
fof(f724,axiom,
! [X8,X4] :
( is_fun_pname_bool(X4)
=> ( bot_bot_fun_a_bool = image_pname_a(X8,X4)
<=> bot_bo844097828e_bool = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9941,plain,
spl263_424,
inference(avatar_split_clause,[],[f5384,f9939]) ).
fof(f9939,plain,
( spl263_424
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK90(X0)),sK91(X0)))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_424])]) ).
fof(f5384,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK90(X0)),sK91(X0)))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f9937,plain,
spl263_423,
inference(avatar_split_clause,[],[f5336,f9935]) ).
fof(f9935,plain,
( spl263_423
<=> ! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_423])]) ).
fof(f5336,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f1721]) ).
fof(f1721,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(rectify,[],[f1313]) ).
fof(f1313,axiom,
! [X158,X159] :
( hBOOL(X159)
| hBOOL(X158)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X158),X159)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9933,plain,
spl263_422,
inference(avatar_split_clause,[],[f5335,f9931]) ).
fof(f9931,plain,
( spl263_422
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_422])]) ).
fof(f5335,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f1720]) ).
fof(f1720,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(rectify,[],[f1318]) ).
fof(f1318,axiom,
! [X158,X159] :
( hBOOL(X159)
| ~ hBOOL(X158)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X158),X159)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9929,plain,
spl263_421,
inference(avatar_split_clause,[],[f5322,f9927]) ).
fof(f9927,plain,
( spl263_421
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_421])]) ).
fof(f5322,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1707]) ).
fof(f1707,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f1308]) ).
fof(f1308,axiom,
! [X159,X158] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X158),X159))
| ~ hBOOL(X159)
| ~ hBOOL(X158) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9925,plain,
spl263_420,
inference(avatar_split_clause,[],[f5251,f9923]) ).
fof(f9923,plain,
( spl263_420
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_420])]) ).
fof(f5251,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)),
inference(cnf_transformation,[],[f1647]) ).
fof(f1647,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X14,X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X13)),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9921,plain,
spl263_419,
inference(avatar_split_clause,[],[f5250,f9919]) ).
fof(f9919,plain,
( spl263_419
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_419])]) ).
fof(f5250,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))),
inference(cnf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))),
inference(rectify,[],[f929]) ).
fof(f929,axiom,
! [X13,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9917,plain,
spl263_418,
inference(avatar_split_clause,[],[f5249,f9915]) ).
fof(f9915,plain,
( spl263_418
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_418])]) ).
fof(f5249,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))),
inference(cnf_transformation,[],[f1645]) ).
fof(f1645,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))),
inference(rectify,[],[f930]) ).
fof(f930,axiom,
! [X13,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9913,plain,
spl263_417,
inference(avatar_split_clause,[],[f5248,f9911]) ).
fof(f9911,plain,
( spl263_417
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_417])]) ).
fof(f5248,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)),
inference(cnf_transformation,[],[f1644]) ).
fof(f1644,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)),
inference(rectify,[],[f694]) ).
fof(f694,axiom,
! [X4,X9] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X9)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9909,plain,
spl263_416,
inference(avatar_split_clause,[],[f5247,f9907]) ).
fof(f5247,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))),
inference(cnf_transformation,[],[f1643]) ).
fof(f1643,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))),
inference(rectify,[],[f559]) ).
fof(f559,axiom,
! [X9,X7] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9905,plain,
spl263_415,
inference(avatar_split_clause,[],[f5246,f9903]) ).
fof(f9903,plain,
( spl263_415
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_415])]) ).
fof(f5246,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))),
inference(cnf_transformation,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))),
inference(rectify,[],[f474]) ).
fof(f474,axiom,
! [X7,X9] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9901,plain,
spl263_414,
inference(avatar_split_clause,[],[f5245,f9899]) ).
fof(f9899,plain,
( spl263_414
<=> ! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_414])]) ).
fof(f5245,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)),
inference(cnf_transformation,[],[f1641]) ).
fof(f1641,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)),
inference(rectify,[],[f693]) ).
fof(f693,axiom,
! [X4,X9] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X9)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9897,plain,
spl263_413,
inference(avatar_split_clause,[],[f5244,f9895]) ).
fof(f5244,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))),
inference(cnf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))),
inference(rectify,[],[f558]) ).
fof(f558,axiom,
! [X9,X7] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9893,plain,
spl263_412,
inference(avatar_split_clause,[],[f5243,f9891]) ).
fof(f9891,plain,
( spl263_412
<=> ! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_412])]) ).
fof(f5243,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))),
inference(cnf_transformation,[],[f1639]) ).
fof(f1639,plain,
! [X0,X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X7,X9] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X7),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9889,plain,
spl263_411,
inference(avatar_split_clause,[],[f5242,f9887]) ).
fof(f9887,plain,
( spl263_411
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_411])]) ).
fof(f5242,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)),
inference(cnf_transformation,[],[f1638]) ).
fof(f1638,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)),
inference(rectify,[],[f695]) ).
fof(f695,axiom,
! [X4,X9] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X9)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9885,plain,
spl263_410,
inference(avatar_split_clause,[],[f5241,f9883]) ).
fof(f5241,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))),
inference(cnf_transformation,[],[f1637]) ).
fof(f1637,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X9,X7] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9881,plain,
spl263_409,
inference(avatar_split_clause,[],[f5240,f9879]) ).
fof(f9879,plain,
( spl263_409
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_409])]) ).
fof(f5240,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))),
inference(cnf_transformation,[],[f1636]) ).
fof(f1636,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X7,X9] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9877,plain,
spl263_408,
inference(avatar_split_clause,[],[f5239,f9875]) ).
fof(f5239,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))),
inference(cnf_transformation,[],[f1635]) ).
fof(f1635,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))),
inference(rectify,[],[f475]) ).
fof(f475,axiom,
! [X7,X9] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X7),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9872,plain,
spl263_407,
inference(avatar_split_clause,[],[f5238,f9870]) ).
fof(f9870,plain,
( spl263_407
<=> ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_407])]) ).
fof(f5238,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)),
inference(cnf_transformation,[],[f1634]) ).
fof(f1634,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)),
inference(rectify,[],[f983]) ).
fof(f983,axiom,
! [X22,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X23)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9868,plain,
spl263_406,
inference(avatar_split_clause,[],[f5237,f9866]) ).
fof(f9866,plain,
( spl263_406
<=> ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_406])]) ).
fof(f5237,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)),
inference(cnf_transformation,[],[f1633]) ).
fof(f1633,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)),
inference(rectify,[],[f984]) ).
fof(f984,axiom,
! [X23,X22] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9864,plain,
spl263_405,
inference(avatar_split_clause,[],[f5185,f9862]) ).
fof(f9862,plain,
( spl263_405
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0)),X0))
| bot_bot_fun_nat_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_405])]) ).
fof(f5185,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0)),X0))
| bot_bot_fun_nat_bool = X0 ),
inference(cnf_transformation,[],[f4149]) ).
fof(f4149,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0)),X0))
| bot_bot_fun_nat_bool = X0 )
& ( bot_bot_fun_nat_bool != X0
| ! [X2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f4147,f4148]) ).
fof(f4148,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f4147,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| bot_bot_fun_nat_bool = X0 )
& ( bot_bot_fun_nat_bool != X0
| ! [X2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(rectify,[],[f4146]) ).
fof(f4146,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| bot_bot_fun_nat_bool = X0 )
& ( bot_bot_fun_nat_bool != X0
| ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
inference(nnf_transformation,[],[f1621]) ).
fof(f1621,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
<=> bot_bot_fun_nat_bool != X0 ),
inference(rectify,[],[f635]) ).
fof(f635,axiom,
! [X4] :
( ? [X29] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4))
<=> bot_bot_fun_nat_bool != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9860,plain,
spl263_404,
inference(avatar_split_clause,[],[f5183,f9858]) ).
fof(f9858,plain,
( spl263_404
<=> ! [X0] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK84(X0)),X0))
| bot_bot_fun_int_bool = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_404])]) ).
fof(f5183,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK84(X0)),X0))
| bot_bot_fun_int_bool = X0 ),
inference(cnf_transformation,[],[f4145]) ).
fof(f4145,plain,
! [X0] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK84(X0)),X0))
| bot_bot_fun_int_bool = X0 )
& ( bot_bot_fun_int_bool != X0
| ! [X2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f4143,f4144]) ).
fof(f4144,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK84(X0)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f4143,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| bot_bot_fun_int_bool = X0 )
& ( bot_bot_fun_int_bool != X0
| ! [X2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
inference(rectify,[],[f4142]) ).
fof(f4142,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| bot_bot_fun_int_bool = X0 )
& ( bot_bot_fun_int_bool != X0
| ! [X1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
inference(nnf_transformation,[],[f1620]) ).
fof(f1620,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
<=> bot_bot_fun_int_bool != X0 ),
inference(rectify,[],[f634]) ).
fof(f634,axiom,
! [X4] :
( ? [X29] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4))
<=> bot_bot_fun_int_bool != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9856,plain,
spl263_403,
inference(avatar_split_clause,[],[f5177,f9854]) ).
fof(f9854,plain,
( spl263_403
<=> ! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_403])]) ).
fof(f5177,plain,
! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(X0)),X0)) ),
inference(cnf_transformation,[],[f4136]) ).
fof(f4136,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| bot_bot_fun_nat_bool != X0 )
& ( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(X0)),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f4134,f4135]) ).
fof(f4135,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(X0)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f4134,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| bot_bot_fun_nat_bool != X0 )
& ( bot_bot_fun_nat_bool = X0
| ? [X2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(rectify,[],[f4133]) ).
fof(f4133,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| bot_bot_fun_nat_bool != X0 )
& ( bot_bot_fun_nat_bool = X0
| ? [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
inference(nnf_transformation,[],[f1618]) ).
fof(f1618,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
<=> bot_bot_fun_nat_bool = X0 ),
inference(rectify,[],[f639]) ).
fof(f639,axiom,
! [X4] :
( ! [X29] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X4))
<=> bot_bot_fun_nat_bool = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9852,plain,
spl263_402,
inference(avatar_split_clause,[],[f5175,f9850]) ).
fof(f9850,plain,
( spl263_402
<=> ! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_402])]) ).
fof(f5175,plain,
! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0)),X0)) ),
inference(cnf_transformation,[],[f4132]) ).
fof(f4132,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| bot_bot_fun_int_bool != X0 )
& ( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0)),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f4130,f4131]) ).
fof(f4131,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f4130,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| bot_bot_fun_int_bool != X0 )
& ( bot_bot_fun_int_bool = X0
| ? [X2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
inference(rectify,[],[f4129]) ).
fof(f4129,plain,
! [X0] :
( ( ! [X1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
| bot_bot_fun_int_bool != X0 )
& ( bot_bot_fun_int_bool = X0
| ? [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
inference(nnf_transformation,[],[f1617]) ).
fof(f1617,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
<=> bot_bot_fun_int_bool = X0 ),
inference(rectify,[],[f638]) ).
fof(f638,axiom,
! [X4] :
( ! [X29] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X4))
<=> bot_bot_fun_int_bool = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9848,plain,
spl263_401,
inference(avatar_split_clause,[],[f5116,f9846]) ).
fof(f9846,plain,
( spl263_401
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_401])]) ).
fof(f5116,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ),
inference(cnf_transformation,[],[f4086]) ).
fof(f4086,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(nnf_transformation,[],[f1589]) ).
fof(f1589,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ),
inference(rectify,[],[f1221]) ).
fof(f1221,axiom,
! [X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9844,plain,
spl263_400,
inference(avatar_split_clause,[],[f5093,f9842]) ).
fof(f9842,plain,
( spl263_400
<=> ! [X2,X0] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2)
| bot_bot_fun_a_bool != collect_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_400])]) ).
fof(f5093,plain,
! [X2,X0] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2)
| bot_bot_fun_a_bool != collect_a(X0) ),
inference(cnf_transformation,[],[f4058]) ).
fof(f4058,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ( hBOOL(hAPP_a_bool(X0,sK65(X0)))
& is_a(sK65(X0)) ) )
& ( ! [X2] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f4056,f4057]) ).
fof(f4057,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) )
=> ( hBOOL(hAPP_a_bool(X0,sK65(X0)))
& is_a(sK65(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4056,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) ) )
& ( ! [X2] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(rectify,[],[f4055]) ).
fof(f4055,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) ) )
& ( ! [X1] :
( ~ hBOOL(hAPP_a_bool(X0,X1))
| ~ is_a(X1) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(nnf_transformation,[],[f2747]) ).
fof(f2747,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
<=> ! [X1] :
( ~ hBOOL(hAPP_a_bool(X0,X1))
| ~ is_a(X1) ) ),
inference(ennf_transformation,[],[f1580]) ).
fof(f1580,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
<=> ! [X1] :
( is_a(X1)
=> ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
inference(rectify,[],[f630]) ).
fof(f630,axiom,
! [X12] :
( bot_bot_fun_a_bool = collect_a(X12)
<=> ! [X29] :
( is_a(X29)
=> ~ hBOOL(hAPP_a_bool(X12,X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9840,plain,
spl263_399,
inference(avatar_split_clause,[],[f5038,f9838]) ).
fof(f9838,plain,
( spl263_399
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK50(X0)))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_399])]) ).
fof(f5038,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK50(X0)))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f4018]) ).
fof(f9836,plain,
spl263_398,
inference(avatar_split_clause,[],[f5030,f9834]) ).
fof(f9834,plain,
( spl263_398
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK48(X0)),sK49(X0)))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_398])]) ).
fof(f5030,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK48(X0)),sK49(X0)))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f4012]) ).
fof(f9832,plain,
spl263_397,
inference(avatar_split_clause,[],[f5011,f9830]) ).
fof(f9830,plain,
( spl263_397
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(X0)))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_397])]) ).
fof(f5011,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(X0)))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f3999]) ).
fof(f9828,plain,
spl263_396,
inference(avatar_split_clause,[],[f5003,f9826]) ).
fof(f9826,plain,
( spl263_396
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK42(X0)),sK43(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_396])]) ).
fof(f5003,plain,
! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK42(X0)),sK43(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f9824,plain,
spl263_395,
inference(avatar_split_clause,[],[f4967,f9822]) ).
fof(f9822,plain,
( spl263_395
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_395])]) ).
fof(f4967,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))),
inference(cnf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))),
inference(rectify,[],[f1097]) ).
fof(f1097,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9820,plain,
spl263_394,
inference(avatar_split_clause,[],[f4966,f9818]) ).
fof(f9818,plain,
( spl263_394
<=> ! [X0] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_394])]) ).
fof(f9721,plain,
spl263_393,
inference(avatar_split_clause,[],[f7645,f9719]) ).
fof(f9719,plain,
( spl263_393
<=> ! [X0,X1] :
( one_one_nat = X1
| zero_zero_nat = X1
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_393])]) ).
fof(f7645,plain,
! [X0,X1] :
( one_one_nat = X1
| zero_zero_nat = X1
| ~ sP19(X0,X1) ),
inference(forward_demodulation,[],[f6027,f4848]) ).
fof(f6027,plain,
! [X0,X1] :
( zero_zero_nat = X1
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f4404]) ).
fof(f4404,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X0
| zero_zero_nat != X1 )
& ( zero_zero_nat != X0
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0
& zero_zero_nat = X1 )
| ( zero_zero_nat = X0
& hAPP_nat_nat(suc,zero_zero_nat) = X1 )
| ~ sP19(X0,X1) ) ),
inference(rectify,[],[f4403]) ).
fof(f4403,plain,
! [X1,X0] :
( ( sP19(X1,X0)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1
| zero_zero_nat != X0 )
& ( zero_zero_nat != X1
| hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 )
| ~ sP19(X1,X0) ) ),
inference(flattening,[],[f4402]) ).
fof(f4402,plain,
! [X1,X0] :
( ( sP19(X1,X0)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1
| zero_zero_nat != X0 )
& ( zero_zero_nat != X1
| hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 )
| ~ sP19(X1,X0) ) ),
inference(nnf_transformation,[],[f3944]) ).
fof(f9717,plain,
spl263_392,
inference(avatar_split_clause,[],[f7644,f9715]) ).
fof(f9715,plain,
( spl263_392
<=> ! [X0,X1] :
( one_one_nat = X1
| one_one_nat = X0
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_392])]) ).
fof(f7644,plain,
! [X0,X1] :
( one_one_nat = X1
| one_one_nat = X0
| ~ sP19(X0,X1) ),
inference(forward_demodulation,[],[f7643,f4848]) ).
fof(f7643,plain,
! [X0,X1] :
( one_one_nat = X0
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP19(X0,X1) ),
inference(forward_demodulation,[],[f6029,f4848]) ).
fof(f6029,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = X0
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f4404]) ).
fof(f9713,plain,
spl263_391,
inference(avatar_split_clause,[],[f7642,f9711]) ).
fof(f9711,plain,
( spl263_391
<=> ! [X0,X1] :
( one_one_nat = X0
| zero_zero_nat = X0
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_391])]) ).
fof(f7642,plain,
! [X0,X1] :
( one_one_nat = X0
| zero_zero_nat = X0
| ~ sP19(X0,X1) ),
inference(forward_demodulation,[],[f6030,f4848]) ).
fof(f6030,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = X0
| zero_zero_nat = X0
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f4404]) ).
fof(f9709,plain,
spl263_390,
inference(avatar_split_clause,[],[f7637,f9707]) ).
fof(f9707,plain,
( spl263_390
<=> ! [X0,X1] :
( one_one_nat = X1
| zero_zero_nat = X1
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_390])]) ).
fof(f7637,plain,
! [X0,X1] :
( one_one_nat = X1
| zero_zero_nat = X1
| ~ sP18(X0,X1) ),
inference(forward_demodulation,[],[f6019,f4848]) ).
fof(f6019,plain,
! [X0,X1] :
( zero_zero_nat = X1
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f4400]) ).
fof(f4400,plain,
! [X0,X1] :
( ( sP18(X0,X1)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X0
| zero_zero_nat != X1 )
& ( zero_zero_nat != X0
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0
& zero_zero_nat = X1 )
| ( zero_zero_nat = X0
& hAPP_nat_nat(suc,zero_zero_nat) = X1 )
| ~ sP18(X0,X1) ) ),
inference(rectify,[],[f4399]) ).
fof(f4399,plain,
! [X1,X0] :
( ( sP18(X1,X0)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1
| zero_zero_nat != X0 )
& ( zero_zero_nat != X1
| hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 )
| ~ sP18(X1,X0) ) ),
inference(flattening,[],[f4398]) ).
fof(f4398,plain,
! [X1,X0] :
( ( sP18(X1,X0)
| ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1
| zero_zero_nat != X0 )
& ( zero_zero_nat != X1
| hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) )
& ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1
& zero_zero_nat = X0 )
| ( zero_zero_nat = X1
& hAPP_nat_nat(suc,zero_zero_nat) = X0 )
| ~ sP18(X1,X0) ) ),
inference(nnf_transformation,[],[f3942]) ).
fof(f9705,plain,
spl263_389,
inference(avatar_split_clause,[],[f7636,f9703]) ).
fof(f9703,plain,
( spl263_389
<=> ! [X0,X1] :
( one_one_nat = X1
| one_one_nat = X0
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_389])]) ).
fof(f7636,plain,
! [X0,X1] :
( one_one_nat = X1
| one_one_nat = X0
| ~ sP18(X0,X1) ),
inference(forward_demodulation,[],[f7635,f4848]) ).
fof(f7635,plain,
! [X0,X1] :
( one_one_nat = X0
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP18(X0,X1) ),
inference(forward_demodulation,[],[f6021,f4848]) ).
fof(f6021,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = X0
| hAPP_nat_nat(suc,zero_zero_nat) = X1
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f4400]) ).
fof(f9701,plain,
spl263_388,
inference(avatar_split_clause,[],[f7634,f9699]) ).
fof(f9699,plain,
( spl263_388
<=> ! [X0,X1] :
( one_one_nat = X0
| zero_zero_nat = X0
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_388])]) ).
fof(f7634,plain,
! [X0,X1] :
( one_one_nat = X0
| zero_zero_nat = X0
| ~ sP18(X0,X1) ),
inference(forward_demodulation,[],[f6022,f4848]) ).
fof(f6022,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,zero_zero_nat) = X0
| zero_zero_nat = X0
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f4400]) ).
fof(f9697,plain,
spl263_387,
inference(avatar_split_clause,[],[f7432,f9695]) ).
fof(f9695,plain,
( spl263_387
<=> ! [X0] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_387])]) ).
fof(f7432,plain,
! [X0] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
| zero_zero_nat = X0 ),
inference(forward_demodulation,[],[f5171,f4848]) ).
fof(f5171,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat))) ),
inference(cnf_transformation,[],[f4127]) ).
fof(f4127,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)))
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
inference(nnf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)))
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f1054]) ).
fof(f1054,axiom,
! [X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),hAPP_nat_nat(suc,zero_zero_nat)))
<=> zero_zero_nat = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9693,plain,
spl263_386,
inference(avatar_split_clause,[],[f7397,f9691]) ).
fof(f9688,plain,
spl263_385,
inference(avatar_split_clause,[],[f7396,f9686]) ).
fof(f9684,plain,
spl263_384,
inference(avatar_split_clause,[],[f7050,f9682]) ).
fof(f9682,plain,
( spl263_384
<=> ! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_384])]) ).
fof(f7050,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
inference(definition_unfolding,[],[f5077,f4829,f4829]) ).
fof(f4829,plain,
bot_bot_nat = zero_zero_nat,
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5077,plain,
! [X0] :
( bot_bot_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat)) ),
inference(cnf_transformation,[],[f2745]) ).
fof(f2745,plain,
! [X0] :
( bot_bot_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat)) ),
inference(ennf_transformation,[],[f1572]) ).
fof(f1572,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat))
=> bot_bot_nat = X0 ),
inference(rectify,[],[f727]) ).
fof(f727,axiom,
! [X73] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X73),bot_bot_nat))
=> bot_bot_nat = X73 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9680,plain,
spl263_383,
inference(avatar_split_clause,[],[f6471,f9678]) ).
fof(f6471,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f4569]) ).
fof(f9676,plain,
spl263_382,
inference(avatar_split_clause,[],[f6434,f9674]) ).
fof(f9674,plain,
( spl263_382
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,sK210(X0,X1)))
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_382])]) ).
fof(f6434,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(X0,sK210(X0,X1)))
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f4549]) ).
fof(f9672,plain,
spl263_381,
inference(avatar_split_clause,[],[f6431,f9670]) ).
fof(f9670,plain,
( spl263_381
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK210(X0,X1)))
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_381])]) ).
fof(f6431,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK210(X0,X1)))
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f4549]) ).
fof(f9668,plain,
spl263_380,
inference(avatar_split_clause,[],[f6396,f9666]) ).
fof(f9666,plain,
( spl263_380
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,sK201(X0,X1)))
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_380])]) ).
fof(f6396,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(X0,sK201(X0,X1)))
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f4531]) ).
fof(f9664,plain,
spl263_379,
inference(avatar_split_clause,[],[f6393,f9662]) ).
fof(f9662,plain,
( spl263_379
<=> ! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK201(X0,X1)))
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_379])]) ).
fof(f6393,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK201(X0,X1)))
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f4531]) ).
fof(f9660,plain,
spl263_378,
inference(avatar_split_clause,[],[f6385,f9658]) ).
fof(f9658,plain,
( spl263_378
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK199(X0,X1)))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_378])]) ).
fof(f6385,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK199(X0,X1)))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f9656,plain,
spl263_377,
inference(avatar_split_clause,[],[f6382,f9654]) ).
fof(f9654,plain,
( spl263_377
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK199(X0,X1)))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_377])]) ).
fof(f6382,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK199(X0,X1)))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f9652,plain,
spl263_376,
inference(avatar_split_clause,[],[f6369,f9650]) ).
fof(f9650,plain,
( spl263_376
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK197(X0,X1)))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_376])]) ).
fof(f6369,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK197(X0,X1)))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f9648,plain,
spl263_375,
inference(avatar_split_clause,[],[f6366,f9646]) ).
fof(f9646,plain,
( spl263_375
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK197(X0,X1)))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_375])]) ).
fof(f6366,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK197(X0,X1)))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f9644,plain,
spl263_374,
inference(avatar_split_clause,[],[f6028,f9642]) ).
fof(f9642,plain,
( spl263_374
<=> ! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_374])]) ).
fof(f6028,plain,
! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f4404]) ).
fof(f9640,plain,
spl263_373,
inference(avatar_split_clause,[],[f6020,f9638]) ).
fof(f9638,plain,
( spl263_373
<=> ! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_373])]) ).
fof(f6020,plain,
! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat = X0
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f4400]) ).
fof(f9636,plain,
spl263_372,
inference(avatar_split_clause,[],[f5342,f9634]) ).
fof(f9634,plain,
( spl263_372
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_372])]) ).
fof(f5342,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1727]) ).
fof(f1727,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(rectify,[],[f1327]) ).
fof(f1327,axiom,
! [X17,X18] :
( X17 = X18
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9632,plain,
spl263_371,
inference(avatar_split_clause,[],[f5341,f9630]) ).
fof(f9630,plain,
( spl263_371
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_371])]) ).
fof(f5341,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ),
inference(cnf_transformation,[],[f1726]) ).
fof(f1726,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ),
inference(rectify,[],[f1325]) ).
fof(f1325,axiom,
! [X17,X18] :
( X17 = X18
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9628,plain,
spl263_370,
inference(avatar_split_clause,[],[f5340,f9626]) ).
fof(f9626,plain,
( spl263_370
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_370])]) ).
fof(f5340,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(cnf_transformation,[],[f1725]) ).
fof(f1725,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(rectify,[],[f1345]) ).
fof(f1345,axiom,
! [X17,X18] :
( X17 = X18
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9624,plain,
spl263_369,
inference(avatar_split_clause,[],[f5339,f9622]) ).
fof(f9622,plain,
( spl263_369
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_369])]) ).
fof(f5339,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ),
inference(cnf_transformation,[],[f1724]) ).
fof(f1724,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ),
inference(rectify,[],[f1343]) ).
fof(f1343,axiom,
! [X17,X18] :
( X17 = X18
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X17),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9620,plain,
spl263_368,
inference(avatar_split_clause,[],[f5098,f9618]) ).
fof(f9618,plain,
( spl263_368
<=> ! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| hBOOL(hAPP_a_bool(X0,sK66(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_368])]) ).
fof(f5098,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| hBOOL(hAPP_a_bool(X0,sK66(X0))) ),
inference(cnf_transformation,[],[f4062]) ).
fof(f4062,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ( hBOOL(hAPP_a_bool(X0,sK66(X0)))
& is_a(sK66(X0)) ) )
& ( ! [X2] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f4060,f4061]) ).
fof(f4061,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) )
=> ( hBOOL(hAPP_a_bool(X0,sK66(X0)))
& is_a(sK66(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f4060,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) ) )
& ( ! [X2] :
( ~ hBOOL(hAPP_a_bool(X0,X2))
| ~ is_a(X2) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(rectify,[],[f4059]) ).
fof(f4059,plain,
! [X0] :
( ( bot_bot_fun_a_bool = collect_a(X0)
| ? [X1] :
( hBOOL(hAPP_a_bool(X0,X1))
& is_a(X1) ) )
& ( ! [X1] :
( ~ hBOOL(hAPP_a_bool(X0,X1))
| ~ is_a(X1) )
| bot_bot_fun_a_bool != collect_a(X0) ) ),
inference(nnf_transformation,[],[f2748]) ).
fof(f2748,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
<=> ! [X1] :
( ~ hBOOL(hAPP_a_bool(X0,X1))
| ~ is_a(X1) ) ),
inference(ennf_transformation,[],[f1581]) ).
fof(f1581,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
<=> ! [X1] :
( is_a(X1)
=> ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
inference(rectify,[],[f617]) ).
fof(f617,axiom,
! [X12] :
( bot_bot_fun_a_bool = collect_a(X12)
<=> ! [X29] :
( is_a(X29)
=> ~ hBOOL(hAPP_a_bool(X12,X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9616,plain,
spl263_367,
inference(avatar_split_clause,[],[f5095,f9614]) ).
fof(f5095,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| hBOOL(hAPP_a_bool(X0,sK65(X0))) ),
inference(cnf_transformation,[],[f4058]) ).
fof(f9612,plain,
spl263_366,
inference(avatar_split_clause,[],[f5066,f9610]) ).
fof(f9610,plain,
( spl263_366
<=> ! [X0] :
( bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_366])]) ).
fof(f5066,plain,
! [X0] :
( bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ),
inference(cnf_transformation,[],[f2735]) ).
fof(f2735,plain,
! [X0] :
( bot_bot_fun_nat_bool = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ),
inference(ennf_transformation,[],[f1562]) ).
fof(f1562,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool))
=> bot_bot_fun_nat_bool = X0 ),
inference(rectify,[],[f725]) ).
fof(f725,axiom,
! [X7] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),bot_bot_fun_nat_bool))
=> bot_bot_fun_nat_bool = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9607,plain,
spl263_365,
inference(avatar_split_clause,[],[f5065,f9605]) ).
fof(f9605,plain,
( spl263_365
<=> ! [X0] :
( bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_365])]) ).
fof(f5065,plain,
! [X0] :
( bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ),
inference(cnf_transformation,[],[f2734]) ).
fof(f2734,plain,
! [X0] :
( bot_bot_fun_int_bool = X0
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ),
inference(ennf_transformation,[],[f1561]) ).
fof(f1561,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool))
=> bot_bot_fun_int_bool = X0 ),
inference(rectify,[],[f726]) ).
fof(f726,axiom,
! [X7] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),bot_bot_fun_int_bool))
=> bot_bot_fun_int_bool = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9603,plain,
spl263_364,
inference(avatar_split_clause,[],[f5054,f9601]) ).
fof(f9601,plain,
( spl263_364
<=> ! [X0] :
( hAPP_nat_nat(suc,sK55(X0)) = X0
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_364])]) ).
fof(f5054,plain,
! [X0] :
( hAPP_nat_nat(suc,sK55(X0)) = X0
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f4032]) ).
fof(f4032,plain,
! [X0] :
( hAPP_nat_nat(suc,sK55(X0)) = X0
| zero_zero_nat = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f2723,f4031]) ).
fof(f4031,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
=> hAPP_nat_nat(suc,sK55(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2723,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
| zero_zero_nat = X0 ),
inference(ennf_transformation,[],[f1550]) ).
fof(f1550,plain,
! [X0] :
( zero_zero_nat != X0
=> ? [X1] : hAPP_nat_nat(suc,X1) = X0 ),
inference(rectify,[],[f1082]) ).
fof(f1082,axiom,
! [X13] :
( zero_zero_nat != X13
=> ? [X34] : hAPP_nat_nat(suc,X34) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9599,plain,
spl263_363,
inference(avatar_split_clause,[],[f5053,f9597]) ).
fof(f9597,plain,
( spl263_363
<=> ! [X0] :
( hAPP_nat_nat(suc,sK54(X0)) = X0
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_363])]) ).
fof(f5053,plain,
! [X0] :
( hAPP_nat_nat(suc,sK54(X0)) = X0
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f4030]) ).
fof(f4030,plain,
! [X0] :
( hAPP_nat_nat(suc,sK54(X0)) = X0
| zero_zero_nat = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f2722,f4029]) ).
fof(f4029,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
=> hAPP_nat_nat(suc,sK54(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f2722,plain,
! [X0] :
( ? [X1] : hAPP_nat_nat(suc,X1) = X0
| zero_zero_nat = X0 ),
inference(ennf_transformation,[],[f1549]) ).
fof(f1549,plain,
! [X0] :
( zero_zero_nat != X0
=> ~ ! [X1] : hAPP_nat_nat(suc,X1) != X0 ),
inference(rectify,[],[f1080]) ).
fof(f1080,axiom,
! [X18] :
( zero_zero_nat != X18
=> ~ ! [X131] : hAPP_nat_nat(suc,X131) != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9595,plain,
spl263_362,
inference(avatar_split_clause,[],[f5052,f9593]) ).
fof(f9593,plain,
( spl263_362
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_362])]) ).
fof(f5052,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f2721]) ).
fof(f2721,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ),
inference(ennf_transformation,[],[f1548]) ).
fof(f1548,plain,
! [X0] :
( zero_zero_nat != X0
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(rectify,[],[f1042]) ).
fof(f1042,axiom,
! [X13] :
( zero_zero_nat != X13
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9591,plain,
spl263_361,
inference(avatar_split_clause,[],[f5023,f9589]) ).
fof(f9589,plain,
( spl263_361
<=> ! [X0] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_361])]) ).
fof(f5023,plain,
! [X0] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f2712]) ).
fof(f2712,plain,
! [X0] :
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0] :
( is_fun_a_bool(X0)
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0 ),
inference(rectify,[],[f623]) ).
fof(f623,axiom,
! [X4] :
( is_fun_a_bool(X4)
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),bot_bot_fun_a_bool) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9587,plain,
spl263_360,
inference(avatar_split_clause,[],[f4963,f9585]) ).
fof(f9585,plain,
( spl263_360
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_360])]) ).
fof(f4963,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0,
inference(cnf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0,
inference(rectify,[],[f853]) ).
fof(f853,axiom,
! [X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X13)),one_one_nat) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9583,plain,
( spl263_359
| ~ spl263_358 ),
inference(avatar_split_clause,[],[f9579,f9576,f9581]) ).
fof(f9581,plain,
( spl263_359
<=> ! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_359])]) ).
fof(f9576,plain,
( spl263_358
<=> ! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_358])]) ).
fof(f9579,plain,
( ! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0
| ~ spl263_358 ),
inference(forward_demodulation,[],[f9577,f7397]) ).
fof(f9577,plain,
( ! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0
| ~ spl263_358 ),
inference(avatar_component_clause,[],[f9576]) ).
fof(f9578,plain,
spl263_358,
inference(avatar_split_clause,[],[f4961,f9576]) ).
fof(f4961,plain,
! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0,
inference(cnf_transformation,[],[f1507]) ).
fof(f1507,plain,
! [X0] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0,
inference(rectify,[],[f804]) ).
fof(f804,axiom,
! [X10] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X10),bot_bot_fun_nat_bool)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9574,plain,
( spl263_357
| ~ spl263_356 ),
inference(avatar_split_clause,[],[f9570,f9567,f9572]) ).
fof(f9572,plain,
( spl263_357
<=> ! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_i1948725293t_bool(fequal_int,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_357])]) ).
fof(f9567,plain,
( spl263_356
<=> ! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_356])]) ).
fof(f9570,plain,
( ! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_i1948725293t_bool(fequal_int,X0)) = X0
| ~ spl263_356 ),
inference(forward_demodulation,[],[f9568,f7396]) ).
fof(f9568,plain,
( ! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0
| ~ spl263_356 ),
inference(avatar_component_clause,[],[f9567]) ).
fof(f9569,plain,
spl263_356,
inference(avatar_split_clause,[],[f4960,f9567]) ).
fof(f4960,plain,
! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0,
inference(cnf_transformation,[],[f1506]) ).
fof(f1506,plain,
! [X0] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0,
inference(rectify,[],[f805]) ).
fof(f805,axiom,
! [X10] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X10),bot_bot_fun_int_bool)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9565,plain,
spl263_355,
inference(avatar_split_clause,[],[f4959,f9563]) ).
fof(f9563,plain,
( spl263_355
<=> ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_355])]) ).
fof(f9561,plain,
spl263_354,
inference(avatar_split_clause,[],[f4958,f9559]) ).
fof(f9559,plain,
( spl263_354
<=> ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_354])]) ).
fof(f9557,plain,
spl263_353,
inference(avatar_split_clause,[],[f4957,f9555]) ).
fof(f9553,plain,
spl263_352,
inference(avatar_split_clause,[],[f4956,f9551]) ).
fof(f9551,plain,
( spl263_352
<=> ! [X0] : hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_352])]) ).
fof(f4956,plain,
! [X0] : hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0] : hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f1220]) ).
fof(f1220,axiom,
! [X4] : hAPP_f22106695ol_nat(finite_card_nat,X4) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9542,plain,
( spl263_351
| ~ spl263_336 ),
inference(avatar_split_clause,[],[f9315,f9312,f9540]) ).
fof(f9540,plain,
( spl263_351
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_351])]) ).
fof(f9312,plain,
( spl263_336
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_336])]) ).
fof(f9315,plain,
( ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),pls))
| ~ spl263_336 ),
inference(forward_demodulation,[],[f9313,f6111]) ).
fof(f9313,plain,
( ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls))
| ~ spl263_336 ),
inference(avatar_component_clause,[],[f9312]) ).
fof(f9538,plain,
( spl263_350
| ~ spl263_328 ),
inference(avatar_split_clause,[],[f9534,f9280,f9536]) ).
fof(f9536,plain,
( spl263_350
<=> ! [X0] : sP17(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_350])]) ).
fof(f9280,plain,
( spl263_328
<=> ! [X0,X1] :
( sP17(X0,X1)
| number_number_of_nat(X0) != number_number_of_nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_328])]) ).
fof(f9534,plain,
( ! [X0] : sP17(X0,X0)
| ~ spl263_328 ),
inference(equality_resolution,[],[f9281]) ).
fof(f9281,plain,
( ! [X0,X1] :
( number_number_of_nat(X0) != number_number_of_nat(X1)
| sP17(X0,X1) )
| ~ spl263_328 ),
inference(avatar_component_clause,[],[f9280]) ).
fof(f9440,plain,
( spl263_349
| ~ spl263_32
| ~ spl263_89 ),
inference(avatar_split_clause,[],[f8369,f8210,f7940,f9437]) ).
fof(f7940,plain,
( spl263_32
<=> ! [X0] : collect_int(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_32])]) ).
fof(f8210,plain,
( spl263_89
<=> bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_89])]) ).
fof(f8369,plain,
( bot_bot_fun_int_bool = cOMBK_bool_int(fFalse)
| ~ spl263_32
| ~ spl263_89 ),
inference(superposition,[],[f8212,f7941]) ).
fof(f7941,plain,
( ! [X0] : collect_int(X0) = X0
| ~ spl263_32 ),
inference(avatar_component_clause,[],[f7940]) ).
fof(f8212,plain,
( bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse))
| ~ spl263_89 ),
inference(avatar_component_clause,[],[f8210]) ).
fof(f9404,plain,
( ~ spl263_83
| spl263_348
| ~ spl263_24
| ~ spl263_300 ),
inference(avatar_split_clause,[],[f9393,f9168,f7901,f9401,f8156]) ).
fof(f8156,plain,
( spl263_83
<=> sP3(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_83])]) ).
fof(f9401,plain,
( spl263_348
<=> sP2(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_348])]) ).
fof(f7901,plain,
( spl263_24
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_24])]) ).
fof(f9168,plain,
( spl263_300
<=> ! [X0] :
( sP2(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_300])]) ).
fof(f9393,plain,
( sP2(u)
| ~ sP3(u)
| ~ spl263_24
| ~ spl263_300 ),
inference(resolution,[],[f9169,f7903]) ).
fof(f7903,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl263_24 ),
inference(avatar_component_clause,[],[f7901]) ).
fof(f9169,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| sP2(X0)
| ~ sP3(X0) )
| ~ spl263_300 ),
inference(avatar_component_clause,[],[f9168]) ).
fof(f9360,plain,
spl263_347,
inference(avatar_split_clause,[],[f7425,f9358]) ).
fof(f9358,plain,
( spl263_347
<=> ! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_nat_bool(X0,sK70(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_347])]) ).
fof(f7425,plain,
! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_nat_bool(X0,sK70(X0))) ),
inference(forward_demodulation,[],[f5106,f4876]) ).
fof(f5106,plain,
! [X0] :
( bot_bot_fun_nat_bool = collect_nat(X0)
| hBOOL(hAPP_nat_bool(X0,sK70(X0))) ),
inference(cnf_transformation,[],[f4078]) ).
fof(f4078,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| hBOOL(hAPP_nat_bool(X0,sK70(X0))) )
& ( ! [X2] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f4076,f4077]) ).
fof(f4077,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
=> hBOOL(hAPP_nat_bool(X0,sK70(X0))) ),
introduced(choice_axiom,[]) ).
fof(f4076,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| ? [X1] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X2] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(rectify,[],[f4075]) ).
fof(f4075,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| ? [X1] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(nnf_transformation,[],[f1585]) ).
fof(f1585,plain,
! [X0] :
( bot_bot_fun_nat_bool = collect_nat(X0)
<=> ! [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(rectify,[],[f629]) ).
fof(f629,axiom,
! [X12] :
( collect_nat(X12) = bot_bot_fun_nat_bool
<=> ! [X29] : ~ hBOOL(hAPP_nat_bool(X12,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9356,plain,
spl263_346,
inference(avatar_split_clause,[],[f7423,f9354]) ).
fof(f9354,plain,
( spl263_346
<=> ! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_nat_bool(X0,sK69(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_346])]) ).
fof(f7423,plain,
! [X0] :
( bot_bot_fun_nat_bool = X0
| hBOOL(hAPP_nat_bool(X0,sK69(X0))) ),
inference(forward_demodulation,[],[f5104,f4876]) ).
fof(f5104,plain,
! [X0] :
( bot_bot_fun_nat_bool = collect_nat(X0)
| hBOOL(hAPP_nat_bool(X0,sK69(X0))) ),
inference(cnf_transformation,[],[f4074]) ).
fof(f4074,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| hBOOL(hAPP_nat_bool(X0,sK69(X0))) )
& ( ! [X2] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f4072,f4073]) ).
fof(f4073,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
=> hBOOL(hAPP_nat_bool(X0,sK69(X0))) ),
introduced(choice_axiom,[]) ).
fof(f4072,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| ? [X1] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X2] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(rectify,[],[f4071]) ).
fof(f4071,plain,
! [X0] :
( ( bot_bot_fun_nat_bool = collect_nat(X0)
| ? [X1] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1))
| bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(nnf_transformation,[],[f1584]) ).
fof(f1584,plain,
! [X0] :
( bot_bot_fun_nat_bool = collect_nat(X0)
<=> ! [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(rectify,[],[f616]) ).
fof(f616,axiom,
! [X12] :
( collect_nat(X12) = bot_bot_fun_nat_bool
<=> ! [X29] : ~ hBOOL(hAPP_nat_bool(X12,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9352,plain,
spl263_345,
inference(avatar_split_clause,[],[f7421,f9350]) ).
fof(f9350,plain,
( spl263_345
<=> ! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_int_bool(X0,sK68(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_345])]) ).
fof(f7421,plain,
! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_int_bool(X0,sK68(X0))) ),
inference(forward_demodulation,[],[f5102,f4874]) ).
fof(f5102,plain,
! [X0] :
( bot_bot_fun_int_bool = collect_int(X0)
| hBOOL(hAPP_int_bool(X0,sK68(X0))) ),
inference(cnf_transformation,[],[f4070]) ).
fof(f4070,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| hBOOL(hAPP_int_bool(X0,sK68(X0))) )
& ( ! [X2] : ~ hBOOL(hAPP_int_bool(X0,X2))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f4068,f4069]) ).
fof(f4069,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_int_bool(X0,X1))
=> hBOOL(hAPP_int_bool(X0,sK68(X0))) ),
introduced(choice_axiom,[]) ).
fof(f4068,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| ? [X1] : hBOOL(hAPP_int_bool(X0,X1)) )
& ( ! [X2] : ~ hBOOL(hAPP_int_bool(X0,X2))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(rectify,[],[f4067]) ).
fof(f4067,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| ? [X1] : hBOOL(hAPP_int_bool(X0,X1)) )
& ( ! [X1] : ~ hBOOL(hAPP_int_bool(X0,X1))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(nnf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0] :
( bot_bot_fun_int_bool = collect_int(X0)
<=> ! [X1] : ~ hBOOL(hAPP_int_bool(X0,X1)) ),
inference(rectify,[],[f628]) ).
fof(f628,axiom,
! [X12] :
( collect_int(X12) = bot_bot_fun_int_bool
<=> ! [X29] : ~ hBOOL(hAPP_int_bool(X12,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9348,plain,
spl263_344,
inference(avatar_split_clause,[],[f7419,f9346]) ).
fof(f9346,plain,
( spl263_344
<=> ! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_int_bool(X0,sK67(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_344])]) ).
fof(f7419,plain,
! [X0] :
( bot_bot_fun_int_bool = X0
| hBOOL(hAPP_int_bool(X0,sK67(X0))) ),
inference(forward_demodulation,[],[f5100,f4874]) ).
fof(f5100,plain,
! [X0] :
( bot_bot_fun_int_bool = collect_int(X0)
| hBOOL(hAPP_int_bool(X0,sK67(X0))) ),
inference(cnf_transformation,[],[f4066]) ).
fof(f4066,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| hBOOL(hAPP_int_bool(X0,sK67(X0))) )
& ( ! [X2] : ~ hBOOL(hAPP_int_bool(X0,X2))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f4064,f4065]) ).
fof(f4065,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_int_bool(X0,X1))
=> hBOOL(hAPP_int_bool(X0,sK67(X0))) ),
introduced(choice_axiom,[]) ).
fof(f4064,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| ? [X1] : hBOOL(hAPP_int_bool(X0,X1)) )
& ( ! [X2] : ~ hBOOL(hAPP_int_bool(X0,X2))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(rectify,[],[f4063]) ).
fof(f4063,plain,
! [X0] :
( ( bot_bot_fun_int_bool = collect_int(X0)
| ? [X1] : hBOOL(hAPP_int_bool(X0,X1)) )
& ( ! [X1] : ~ hBOOL(hAPP_int_bool(X0,X1))
| bot_bot_fun_int_bool != collect_int(X0) ) ),
inference(nnf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0] :
( bot_bot_fun_int_bool = collect_int(X0)
<=> ! [X1] : ~ hBOOL(hAPP_int_bool(X0,X1)) ),
inference(rectify,[],[f615]) ).
fof(f615,axiom,
! [X12] :
( collect_int(X12) = bot_bot_fun_int_bool
<=> ! [X29] : ~ hBOOL(hAPP_int_bool(X12,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9344,plain,
spl263_343,
inference(avatar_split_clause,[],[f7417,f9342]) ).
fof(f9342,plain,
( spl263_343
<=> ! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| zero_zero_nat = number_number_of_nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_343])]) ).
fof(f7417,plain,
! [X0] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
| zero_zero_nat = number_number_of_nat(X0) ),
inference(forward_demodulation,[],[f5063,f4875]) ).
fof(f5063,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f2732]) ).
fof(f2732,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(ennf_transformation,[],[f1559]) ).
fof(f1559,plain,
! [X0] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> zero_zero_nat = number_number_of_nat(X0) ),
inference(rectify,[],[f1260]) ).
fof(f1260,axiom,
! [X132] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
=> zero_zero_nat = number_number_of_nat(X132) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9340,plain,
( spl263_342
| ~ spl263_34
| ~ spl263_88 ),
inference(avatar_split_clause,[],[f8367,f8205,f7948,f9337]) ).
fof(f7948,plain,
( spl263_34
<=> ! [X0] : collect_nat(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_34])]) ).
fof(f8205,plain,
( spl263_88
<=> bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_88])]) ).
fof(f8367,plain,
( bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse)
| ~ spl263_34
| ~ spl263_88 ),
inference(superposition,[],[f8207,f7949]) ).
fof(f7949,plain,
( ! [X0] : collect_nat(X0) = X0
| ~ spl263_34 ),
inference(avatar_component_clause,[],[f7948]) ).
fof(f8207,plain,
( bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse))
| ~ spl263_88 ),
inference(avatar_component_clause,[],[f8205]) ).
fof(f9335,plain,
spl263_341,
inference(avatar_split_clause,[],[f7401,f9333]) ).
fof(f9333,plain,
( spl263_341
<=> ! [X0] : hAPP_n1699378549t_bool(fequal_nat,X0) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_341])]) ).
fof(f9331,plain,
spl263_340,
inference(avatar_split_clause,[],[f7399,f9329]) ).
fof(f9329,plain,
( spl263_340
<=> ! [X0] : hAPP_i1948725293t_bool(fequal_int,X0) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_340])]) ).
fof(f9327,plain,
spl263_339,
inference(avatar_split_clause,[],[f7395,f9325]) ).
fof(f9325,plain,
( spl263_339
<=> ! [X0] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_339])]) ).
fof(f7395,plain,
! [X0] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)) = X0,
inference(forward_demodulation,[],[f4962,f4876]) ).
fof(f4962,plain,
! [X0] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) = X0,
inference(cnf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) = X0,
inference(rectify,[],[f1003]) ).
fof(f1003,axiom,
! [X16] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X16))) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9323,plain,
spl263_338,
inference(avatar_split_clause,[],[f7056,f9321]) ).
fof(f9321,plain,
( spl263_338
<=> ! [X0] :
( zero_zero_nat = X0
| pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_338])]) ).
fof(f7056,plain,
! [X0] :
( zero_zero_nat = X0
| pls != hAPP_nat_int(semiri1621563631at_int,X0) ),
inference(definition_unfolding,[],[f5137,f4830]) ).
fof(f5137,plain,
! [X0] :
( zero_zero_nat = X0
| zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ),
inference(cnf_transformation,[],[f4107]) ).
fof(f4107,plain,
! [X0] :
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0)
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(nnf_transformation,[],[f1598]) ).
fof(f1598,plain,
! [X0] :
( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0)
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f1207]) ).
fof(f1207,axiom,
! [X16] :
( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X16)
<=> zero_zero_nat = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9319,plain,
spl263_337,
inference(avatar_split_clause,[],[f7034,f9317]) ).
fof(f9317,plain,
( spl263_337
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_337])]) ).
fof(f7034,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(definition_unfolding,[],[f4952,f4830]) ).
fof(f4952,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(cnf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(rectify,[],[f1203]) ).
fof(f1203,axiom,
! [X13] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9314,plain,
spl263_336,
inference(avatar_split_clause,[],[f7033,f9312]) ).
fof(f7033,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f4946,f4830]) ).
fof(f4946,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(rectify,[],[f1204]) ).
fof(f1204,axiom,
! [X21] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X21)),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9310,plain,
spl263_335,
inference(avatar_split_clause,[],[f6728,f9308]) ).
fof(f9308,plain,
( spl263_335
<=> ! [X2,X0,X1] :
( sP28(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_335])]) ).
fof(f6728,plain,
! [X2,X0,X1] :
( sP28(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f4644]) ).
fof(f9306,plain,
spl263_334,
inference(avatar_split_clause,[],[f6727,f9304]) ).
fof(f9304,plain,
( spl263_334
<=> ! [X2,X0,X1] :
( sP28(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_334])]) ).
fof(f6727,plain,
! [X2,X0,X1] :
( sP28(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f4644]) ).
fof(f9302,plain,
spl263_333,
inference(avatar_split_clause,[],[f6721,f9300]) ).
fof(f9300,plain,
( spl263_333
<=> ! [X2,X0,X1] :
( sP27(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_333])]) ).
fof(f6721,plain,
! [X2,X0,X1] :
( sP27(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f4639]) ).
fof(f9298,plain,
spl263_332,
inference(avatar_split_clause,[],[f6720,f9296]) ).
fof(f9296,plain,
( spl263_332
<=> ! [X2,X0,X1] :
( sP27(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_332])]) ).
fof(f6720,plain,
! [X2,X0,X1] :
( sP27(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f4639]) ).
fof(f9294,plain,
( spl263_331
| ~ spl263_37
| ~ spl263_76 ),
inference(avatar_split_clause,[],[f8193,f8116,f7960,f9292]) ).
fof(f9292,plain,
( spl263_331
<=> ! [X0,X1] : sP5(hAPP_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_331])]) ).
fof(f8116,plain,
( spl263_76
<=> ! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_76])]) ).
fof(f8193,plain,
( ! [X0,X1] : sP5(hAPP_nat_fun_a_bool(X0,X1))
| ~ spl263_37
| ~ spl263_76 ),
inference(resolution,[],[f8117,f7961]) ).
fof(f8117,plain,
( ! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1))
| ~ spl263_76 ),
inference(avatar_component_clause,[],[f8116]) ).
fof(f9290,plain,
spl263_330,
inference(avatar_split_clause,[],[f5902,f9288]) ).
fof(f9288,plain,
( spl263_330
<=> ! [X0,X1] :
( bot_bot_fun_nat_bool = X1
| bot_bot_fun_int_bool != image_nat_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_330])]) ).
fof(f5902,plain,
! [X0,X1] :
( bot_bot_fun_nat_bool = X1
| bot_bot_fun_int_bool != image_nat_int(X0,X1) ),
inference(cnf_transformation,[],[f4311]) ).
fof(f4311,plain,
! [X0,X1] :
( ( bot_bot_fun_int_bool = image_nat_int(X0,X1)
| bot_bot_fun_nat_bool != X1 )
& ( bot_bot_fun_nat_bool = X1
| bot_bot_fun_int_bool != image_nat_int(X0,X1) ) ),
inference(nnf_transformation,[],[f2083]) ).
fof(f2083,plain,
! [X0,X1] :
( bot_bot_fun_int_bool = image_nat_int(X0,X1)
<=> bot_bot_fun_nat_bool = X1 ),
inference(rectify,[],[f719]) ).
fof(f719,axiom,
! [X8,X4] :
( image_nat_int(X8,X4) = bot_bot_fun_int_bool
<=> bot_bot_fun_nat_bool = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9286,plain,
spl263_329,
inference(avatar_split_clause,[],[f5901,f9284]) ).
fof(f9284,plain,
( spl263_329
<=> ! [X0,X1] :
( number_number_of_nat(X0) = number_number_of_nat(X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_329])]) ).
fof(f5901,plain,
! [X0,X1] :
( number_number_of_nat(X0) = number_number_of_nat(X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f4310]) ).
fof(f4310,plain,
! [X0,X1] :
( ( number_number_of_nat(X0) = number_number_of_nat(X1)
| ~ sP17(X0,X1) )
& ( sP17(X0,X1)
| number_number_of_nat(X0) != number_number_of_nat(X1) ) ),
inference(nnf_transformation,[],[f3941]) ).
fof(f3941,plain,
! [X0,X1] :
( number_number_of_nat(X0) = number_number_of_nat(X1)
<=> sP17(X0,X1) ),
inference(definition_folding,[],[f3279,f3940,f3939]) ).
fof(f3279,plain,
! [X0,X1] :
( number_number_of_nat(X0) = number_number_of_nat(X1)
<=> ( ( ( ( X0 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
& ( zero_zero_int = number_number_of_int(X0)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ) ),
inference(ennf_transformation,[],[f2082]) ).
fof(f2082,plain,
! [X0,X1] :
( number_number_of_nat(X0) = number_number_of_nat(X1)
<=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
=> X0 = X1 )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
=> zero_zero_int = number_number_of_int(X0) ) ) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ) ) ),
inference(rectify,[],[f1261]) ).
fof(f1261,axiom,
! [X153,X154] :
( number_number_of_nat(X153) = number_number_of_nat(X154)
<=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X153)))
=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> X153 = X154 )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> zero_zero_int = number_number_of_int(X153) ) ) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X153)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X154)),zero_zero_int)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9282,plain,
spl263_328,
inference(avatar_split_clause,[],[f5900,f9280]) ).
fof(f5900,plain,
! [X0,X1] :
( sP17(X0,X1)
| number_number_of_nat(X0) != number_number_of_nat(X1) ),
inference(cnf_transformation,[],[f4310]) ).
fof(f9278,plain,
spl263_327,
inference(avatar_split_clause,[],[f5811,f9276]) ).
fof(f9276,plain,
( spl263_327
<=> ! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_327])]) ).
fof(f5811,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f3241]) ).
fof(f3241,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f3240]) ).
fof(f3240,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( ( is_a(X1)
& is_fun_a_bool(X0) )
=> is_bool(hAPP_a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9274,plain,
spl263_326,
inference(avatar_split_clause,[],[f5808,f9272]) ).
fof(f9272,plain,
( spl263_326
<=> ! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_326])]) ).
fof(f5808,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f3235]) ).
fof(f3235,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f3234]) ).
fof(f3234,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] :
( ( is_pname(X1)
& is_fun_pname_bool(X0) )
=> is_bool(hAPP_pname_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9270,plain,
spl263_325,
inference(avatar_split_clause,[],[f5369,f9268]) ).
fof(f5369,plain,
! [X0,X1] :
( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2785]) ).
fof(f2785,plain,
! [X0,X1] :
( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1] :
( is_bool(X0)
=> hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ),
inference(rectify,[],[f1336]) ).
fof(f1336,axiom,
! [X158,X159] :
( is_bool(X158)
=> hAPP_nat_bool(cOMBK_bool_nat(X158),X159) = X158 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9266,plain,
spl263_324,
inference(avatar_split_clause,[],[f5368,f9264]) ).
fof(f5368,plain,
! [X0,X1] :
( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2784]) ).
fof(f2784,plain,
! [X0,X1] :
( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0,X1] :
( is_bool(X0)
=> hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 ),
inference(rectify,[],[f1335]) ).
fof(f1335,axiom,
! [X158,X159] :
( is_bool(X158)
=> hAPP_int_bool(cOMBK_bool_int(X158),X159) = X158 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9262,plain,
spl263_323,
inference(avatar_split_clause,[],[f5367,f9260]) ).
fof(f9260,plain,
( spl263_323
<=> ! [X0,X1] :
( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_323])]) ).
fof(f5367,plain,
! [X0,X1] :
( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2783]) ).
fof(f2783,plain,
! [X0,X1] :
( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1734]) ).
fof(f1734,plain,
! [X0,X1] :
( is_bool(X0)
=> hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0 ),
inference(rectify,[],[f1331]) ).
fof(f1331,axiom,
! [X158,X159] :
( is_bool(X158)
=> hAPP_a_bool(cOMBK_bool_a(X158),X159) = X158 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9258,plain,
spl263_322,
inference(avatar_split_clause,[],[f5351,f9256]) ).
fof(f9256,plain,
( spl263_322
<=> ! [X0,X1] :
( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_322])]) ).
fof(f5351,plain,
! [X0,X1] :
( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f2767]) ).
fof(f2767,plain,
! [X0,X1] :
( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f1733]) ).
fof(f1733,plain,
! [X0,X1] :
( is_a(X0)
=> hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0 ),
inference(rectify,[],[f1332]) ).
fof(f1332,axiom,
! [X158,X159] :
( is_a(X158)
=> hAPP_pname_a(cOMBK_a_pname(X158),X159) = X158 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9254,plain,
spl263_321,
inference(avatar_split_clause,[],[f5338,f9252]) ).
fof(f9252,plain,
( spl263_321
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_321])]) ).
fof(f5338,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f1723]) ).
fof(f1723,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f1309]) ).
fof(f1309,axiom,
! [X158,X159] :
( hBOOL(X158)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X158),X159)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9250,plain,
( spl263_320
| ~ spl263_38
| ~ spl263_76 ),
inference(avatar_split_clause,[],[f8192,f8116,f7964,f9248]) ).
fof(f9248,plain,
( spl263_320
<=> ! [X0,X1] : sP7(hAPP_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_320])]) ).
fof(f8192,plain,
( ! [X0,X1] : sP7(hAPP_nat_fun_a_bool(X0,X1))
| ~ spl263_38
| ~ spl263_76 ),
inference(resolution,[],[f8117,f7965]) ).
fof(f9246,plain,
spl263_319,
inference(avatar_split_clause,[],[f5337,f9244]) ).
fof(f9244,plain,
( spl263_319
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_319])]) ).
fof(f5337,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f1310]) ).
fof(f1310,axiom,
! [X158,X159] :
( hBOOL(X159)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X158),X159)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9242,plain,
spl263_318,
inference(avatar_split_clause,[],[f5326,f9240]) ).
fof(f9240,plain,
( spl263_318
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_318])]) ).
fof(f5326,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f1711]) ).
fof(f1711,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f1316]) ).
fof(f1316,axiom,
! [X159,X158] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X158),X159))
| hBOOL(X158) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9238,plain,
spl263_317,
inference(avatar_split_clause,[],[f5325,f9236]) ).
fof(f9236,plain,
( spl263_317
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_317])]) ).
fof(f5325,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1710]) ).
fof(f1710,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f1311]) ).
fof(f1311,axiom,
! [X159,X158] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X158),X159))
| ~ hBOOL(X158) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9234,plain,
spl263_316,
inference(avatar_split_clause,[],[f5324,f9232]) ).
fof(f9232,plain,
( spl263_316
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_316])]) ).
fof(f5324,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1709]) ).
fof(f1709,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f1312]) ).
fof(f1312,axiom,
! [X158,X159] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X158),X159))
| ~ hBOOL(X159) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9230,plain,
spl263_315,
inference(avatar_split_clause,[],[f5323,f9228]) ).
fof(f9228,plain,
( spl263_315
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_315])]) ).
fof(f5323,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f1708]) ).
fof(f1708,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f1317]) ).
fof(f1317,axiom,
! [X158,X159] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X158),X159))
| ~ hBOOL(X159) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9226,plain,
spl263_314,
inference(avatar_split_clause,[],[f5236,f9224]) ).
fof(f9224,plain,
( spl263_314
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_314])]) ).
fof(f5236,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1,
inference(cnf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1,
inference(rectify,[],[f1322]) ).
fof(f1322,axiom,
! [X17,X18] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X17),X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9222,plain,
spl263_313,
inference(avatar_split_clause,[],[f5235,f9220]) ).
fof(f9220,plain,
( spl263_313
<=> ! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_313])]) ).
fof(f5235,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0,
inference(cnf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0,
inference(rectify,[],[f1321]) ).
fof(f1321,axiom,
! [X17,X18] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X17),X18) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9218,plain,
spl263_312,
inference(avatar_split_clause,[],[f5050,f9216]) ).
fof(f9216,plain,
( spl263_312
<=> ! [X0] :
( is_a(sK53(X0))
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_312])]) ).
fof(f5050,plain,
! [X0] :
( is_a(sK53(X0))
| bot_bot_fun_a_bool = X0
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4028]) ).
fof(f9214,plain,
spl263_311,
inference(avatar_split_clause,[],[f5046,f9212]) ).
fof(f9212,plain,
( spl263_311
<=> ! [X0] :
( bot_bot_fun_a_bool = X0
| is_a(sK52(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_311])]) ).
fof(f5046,plain,
! [X0] :
( bot_bot_fun_a_bool = X0
| is_a(sK52(X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f4024]) ).
fof(f9210,plain,
spl263_310,
inference(avatar_split_clause,[],[f5036,f9208]) ).
fof(f9208,plain,
( spl263_310
<=> ! [X0] :
( is_a(sK51(X0))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_310])]) ).
fof(f5036,plain,
! [X0] :
( is_a(sK51(X0))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f4018]) ).
fof(f9206,plain,
( spl263_309
| ~ spl263_37
| ~ spl263_75 ),
inference(avatar_split_clause,[],[f8191,f8112,f7960,f9204]) ).
fof(f9204,plain,
( spl263_309
<=> ! [X0,X1] : sP5(image_int_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_309])]) ).
fof(f8112,plain,
( spl263_75
<=> ! [X0,X1] : is_fun_a_bool(image_int_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_75])]) ).
fof(f8191,plain,
( ! [X0,X1] : sP5(image_int_a(X0,X1))
| ~ spl263_37
| ~ spl263_75 ),
inference(resolution,[],[f8113,f7961]) ).
fof(f8113,plain,
( ! [X0,X1] : is_fun_a_bool(image_int_a(X0,X1))
| ~ spl263_75 ),
inference(avatar_component_clause,[],[f8112]) ).
fof(f9202,plain,
spl263_308,
inference(avatar_split_clause,[],[f5035,f9200]) ).
fof(f9200,plain,
( spl263_308
<=> ! [X0] :
( is_fun_a_bool(sK50(X0))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_308])]) ).
fof(f5035,plain,
! [X0] :
( is_fun_a_bool(sK50(X0))
| bot_bot_fun_a_bool = X0
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f4018]) ).
fof(f9198,plain,
spl263_307,
inference(avatar_split_clause,[],[f5034,f9196]) ).
fof(f9196,plain,
( spl263_307
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ sP6(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_307])]) ).
fof(f5034,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ sP6(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f4013]) ).
fof(f4013,plain,
! [X0] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ sP6(X0) )
& ( sP6(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f3921]) ).
fof(f3921,plain,
! [X0] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f9194,plain,
spl263_306,
inference(avatar_split_clause,[],[f5033,f9192]) ).
fof(f9192,plain,
( spl263_306
<=> ! [X0] :
( sP6(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_306])]) ).
fof(f5033,plain,
! [X0] :
( sP6(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f4013]) ).
fof(f9190,plain,
spl263_305,
inference(avatar_split_clause,[],[f5019,f9188]) ).
fof(f9188,plain,
( spl263_305
<=> ! [X0] :
( is_pname(sK47(X0))
| bot_bo844097828e_bool = X0
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_305])]) ).
fof(f5019,plain,
! [X0] :
( is_pname(sK47(X0))
| bot_bo844097828e_bool = X0
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f4007]) ).
fof(f9186,plain,
spl263_304,
inference(avatar_split_clause,[],[f5015,f9184]) ).
fof(f9184,plain,
( spl263_304
<=> ! [X0] :
( bot_bo844097828e_bool = X0
| is_pname(sK46(X0))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_304])]) ).
fof(f5015,plain,
! [X0] :
( bot_bo844097828e_bool = X0
| is_pname(sK46(X0))
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f4003]) ).
fof(f9182,plain,
spl263_303,
inference(avatar_split_clause,[],[f5009,f9180]) ).
fof(f9180,plain,
( spl263_303
<=> ! [X0] :
( is_pname(sK45(X0))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_303])]) ).
fof(f5009,plain,
! [X0] :
( is_pname(sK45(X0))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f3999]) ).
fof(f9178,plain,
spl263_302,
inference(avatar_split_clause,[],[f5008,f9176]) ).
fof(f9176,plain,
( spl263_302
<=> ! [X0] :
( is_fun_pname_bool(sK44(X0))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_302])]) ).
fof(f5008,plain,
! [X0] :
( is_fun_pname_bool(sK44(X0))
| bot_bo844097828e_bool = X0
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f3999]) ).
fof(f9174,plain,
spl263_301,
inference(avatar_split_clause,[],[f5007,f9172]) ).
fof(f9172,plain,
( spl263_301
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ sP2(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_301])]) ).
fof(f5007,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ sP2(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3994]) ).
fof(f3994,plain,
! [X0] :
( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ sP2(X0) )
& ( sP2(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f3915]) ).
fof(f3915,plain,
! [X0] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
<=> sP2(X0) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f9170,plain,
spl263_300,
inference(avatar_split_clause,[],[f5006,f9168]) ).
fof(f5006,plain,
! [X0] :
( sP2(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3994]) ).
fof(f9166,plain,
spl263_299,
inference(avatar_split_clause,[],[f4995,f9164]) ).
fof(f9164,plain,
( spl263_299
<=> ! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_299])]) ).
fof(f4995,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2702]) ).
fof(f2702,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(flattening,[],[f2701]) ).
fof(f2701,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1534]) ).
fof(f1534,plain,
! [X0] :
( is_bool(X0)
=> ( fFalse = X0
| fTrue = X0 ) ),
inference(rectify,[],[f1323]) ).
fof(f1323,axiom,
! [X158] :
( is_bool(X158)
=> ( fFalse = X158
| fTrue = X158 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9162,plain,
spl263_298,
inference(avatar_split_clause,[],[f4955,f9160]) ).
fof(f9160,plain,
( spl263_298
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_298])]) ).
fof(f4955,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))),
inference(cnf_transformation,[],[f1501]) ).
fof(f1501,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))),
inference(rectify,[],[f962]) ).
fof(f962,axiom,
! [X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),hAPP_nat_nat(suc,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9158,plain,
spl263_297,
inference(avatar_split_clause,[],[f4954,f9156]) ).
fof(f9156,plain,
( spl263_297
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_297])]) ).
fof(f4954,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))),
inference(cnf_transformation,[],[f1500]) ).
fof(f1500,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))),
inference(rectify,[],[f1030]) ).
fof(f1030,axiom,
! [X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9154,plain,
spl263_296,
inference(avatar_split_clause,[],[f4949,f9152]) ).
fof(f4949,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1495]) ).
fof(f1495,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f1259]) ).
fof(f1259,axiom,
! [X14] : hAPP_nat_int(semiri1621563631at_int,X14) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9149,plain,
spl263_295,
inference(avatar_split_clause,[],[f4947,f9147]) ).
fof(f9147,plain,
( spl263_295
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_295])]) ).
fof(f4947,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(cnf_transformation,[],[f1493]) ).
fof(f1493,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X13] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X13)),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9145,plain,
spl263_294,
inference(avatar_split_clause,[],[f4820,f9143]) ).
fof(f9143,plain,
( spl263_294
<=> ! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_294])]) ).
fof(f4820,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f2692]) ).
fof(f2692,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(flattening,[],[f2691]) ).
fof(f2691,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0,X1] :
( ( is_fun_a_bool(X1)
& is_fun949378684l_bool(X0) )
=> is_bool(hAPP_fun_a_bool_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9141,plain,
spl263_293,
inference(avatar_split_clause,[],[f4819,f9139]) ).
fof(f9139,plain,
( spl263_293
<=> ! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_293])]) ).
fof(f4819,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f2690]) ).
fof(f2690,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(flattening,[],[f2689]) ).
fof(f2689,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0,X1] :
( ( is_fun_pname_bool(X1)
& is_fun1661590463l_bool(X0) )
=> is_bool(hAPP_f1664156314l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9137,plain,
( spl263_292
| spl263_26
| ~ spl263_283 ),
inference(avatar_split_clause,[],[f9120,f9081,f7910,f9134]) ).
fof(f9134,plain,
( spl263_292
<=> sP16(one_one_int,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_292])]) ).
fof(f7910,plain,
( spl263_26
<=> hBOOL(hAPP_int_bool(nat_neg,one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_26])]) ).
fof(f9081,plain,
( spl263_283
<=> ! [X1] :
( hBOOL(hAPP_int_bool(nat_neg,X1))
| sP16(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_283])]) ).
fof(f9120,plain,
( sP16(one_one_int,one_one_int)
| spl263_26
| ~ spl263_283 ),
inference(resolution,[],[f9082,f7912]) ).
fof(f7912,plain,
( ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int))
| spl263_26 ),
inference(avatar_component_clause,[],[f7910]) ).
fof(f9082,plain,
( ! [X1] :
( hBOOL(hAPP_int_bool(nat_neg,X1))
| sP16(X1,X1) )
| ~ spl263_283 ),
inference(avatar_component_clause,[],[f9081]) ).
fof(f9132,plain,
spl263_291,
inference(avatar_split_clause,[],[f4809,f9129]) ).
fof(f4809,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1410]) ).
fof(f1410,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9127,plain,
~ spl263_290,
inference(avatar_split_clause,[],[f4808,f9124]) ).
fof(f4808,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(cnf_transformation,[],[f1414]) ).
fof(f1414,axiom,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9115,plain,
( spl263_289
| ~ spl263_38
| ~ spl263_75 ),
inference(avatar_split_clause,[],[f8190,f8112,f7964,f9113]) ).
fof(f9113,plain,
( spl263_289
<=> ! [X0,X1] : sP7(image_int_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_289])]) ).
fof(f8190,plain,
( ! [X0,X1] : sP7(image_int_a(X0,X1))
| ~ spl263_38
| ~ spl263_75 ),
inference(resolution,[],[f8113,f7965]) ).
fof(f9109,plain,
( spl263_288
| ~ spl263_37
| ~ spl263_74 ),
inference(avatar_split_clause,[],[f8189,f8108,f7960,f9107]) ).
fof(f9107,plain,
( spl263_288
<=> ! [X0,X1] : sP5(image_fun_int_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_288])]) ).
fof(f8108,plain,
( spl263_74
<=> ! [X0,X1] : is_fun_a_bool(image_fun_int_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_74])]) ).
fof(f8189,plain,
( ! [X0,X1] : sP5(image_fun_int_bool_a(X0,X1))
| ~ spl263_37
| ~ spl263_74 ),
inference(resolution,[],[f8109,f7961]) ).
fof(f8109,plain,
( ! [X0,X1] : is_fun_a_bool(image_fun_int_bool_a(X0,X1))
| ~ spl263_74 ),
inference(avatar_component_clause,[],[f8108]) ).
fof(f9105,plain,
( spl263_287
| ~ spl263_38
| ~ spl263_74 ),
inference(avatar_split_clause,[],[f8188,f8108,f7964,f9103]) ).
fof(f9103,plain,
( spl263_287
<=> ! [X0,X1] : sP7(image_fun_int_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_287])]) ).
fof(f8188,plain,
( ! [X0,X1] : sP7(image_fun_int_bool_a(X0,X1))
| ~ spl263_38
| ~ spl263_74 ),
inference(resolution,[],[f8109,f7965]) ).
fof(f9097,plain,
( spl263_286
| ~ spl263_37
| ~ spl263_73 ),
inference(avatar_split_clause,[],[f8187,f8104,f7960,f9095]) ).
fof(f9095,plain,
( spl263_286
<=> ! [X0,X1] : sP5(image_nat_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_286])]) ).
fof(f8104,plain,
( spl263_73
<=> ! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_73])]) ).
fof(f8187,plain,
( ! [X0,X1] : sP5(image_nat_a(X0,X1))
| ~ spl263_37
| ~ spl263_73 ),
inference(resolution,[],[f8105,f7961]) ).
fof(f8105,plain,
( ! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1))
| ~ spl263_73 ),
inference(avatar_component_clause,[],[f8104]) ).
fof(f9093,plain,
( spl263_285
| ~ spl263_38
| ~ spl263_73 ),
inference(avatar_split_clause,[],[f8186,f8104,f7964,f9091]) ).
fof(f9091,plain,
( spl263_285
<=> ! [X0,X1] : sP7(image_nat_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_285])]) ).
fof(f8186,plain,
( ! [X0,X1] : sP7(image_nat_a(X0,X1))
| ~ spl263_38
| ~ spl263_73 ),
inference(resolution,[],[f8105,f7965]) ).
fof(f9087,plain,
( spl263_284
| ~ spl263_37
| ~ spl263_72 ),
inference(avatar_split_clause,[],[f8185,f8100,f7960,f9085]) ).
fof(f9085,plain,
( spl263_284
<=> ! [X0,X1] : sP5(image_fun_nat_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_284])]) ).
fof(f8100,plain,
( spl263_72
<=> ! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_72])]) ).
fof(f8185,plain,
( ! [X0,X1] : sP5(image_fun_nat_bool_a(X0,X1))
| ~ spl263_37
| ~ spl263_72 ),
inference(resolution,[],[f8101,f7961]) ).
fof(f8101,plain,
( ! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1))
| ~ spl263_72 ),
inference(avatar_component_clause,[],[f8100]) ).
fof(f9083,plain,
spl263_283,
inference(avatar_split_clause,[],[f7589,f9081]) ).
fof(f7589,plain,
! [X1] :
( hBOOL(hAPP_int_bool(nat_neg,X1))
| sP16(X1,X1) ),
inference(forward_demodulation,[],[f7256,f4875]) ).
fof(f7256,plain,
! [X1] :
( sP16(X1,X1)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(equality_resolution,[],[f5898]) ).
fof(f5898,plain,
! [X0,X1] :
( sP16(X0,X1)
| X0 != X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f4309]) ).
fof(f9079,plain,
spl263_282,
inference(avatar_split_clause,[],[f7424,f9077]) ).
fof(f7424,plain,
! [X2,X0] :
( bot_bot_fun_nat_bool != X0
| ~ hBOOL(hAPP_nat_bool(X0,X2)) ),
inference(forward_demodulation,[],[f5103,f4876]) ).
fof(f5103,plain,
! [X2,X0] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
| bot_bot_fun_nat_bool != collect_nat(X0) ),
inference(cnf_transformation,[],[f4074]) ).
fof(f9075,plain,
spl263_281,
inference(avatar_split_clause,[],[f7420,f9073]) ).
fof(f7420,plain,
! [X2,X0] :
( bot_bot_fun_int_bool != X0
| ~ hBOOL(hAPP_int_bool(X0,X2)) ),
inference(forward_demodulation,[],[f5099,f4874]) ).
fof(f5099,plain,
! [X2,X0] :
( ~ hBOOL(hAPP_int_bool(X0,X2))
| bot_bot_fun_int_bool != collect_int(X0) ),
inference(cnf_transformation,[],[f4066]) ).
fof(f9071,plain,
spl263_280,
inference(avatar_split_clause,[],[f7394,f9069]) ).
fof(f9069,plain,
( spl263_280
<=> ! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_280])]) ).
fof(f7394,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
inference(forward_demodulation,[],[f4951,f4876]) ).
fof(f4951,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
inference(cnf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X15] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X15)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9067,plain,
spl263_279,
inference(avatar_split_clause,[],[f7393,f9065]) ).
fof(f9065,plain,
( spl263_279
<=> ! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_279])]) ).
fof(f7393,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))),
inference(forward_demodulation,[],[f4950,f4876]) ).
fof(f4950,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)))),
inference(cnf_transformation,[],[f1496]) ).
fof(f1496,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)))),
inference(rectify,[],[f964]) ).
fof(f964,axiom,
! [X15] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X15)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9063,plain,
spl263_278,
inference(avatar_split_clause,[],[f7177,f9060]) ).
fof(f9060,plain,
( spl263_278
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_278])]) ).
fof(f7177,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)),
inference(equality_resolution,[],[f7067]) ).
fof(f7067,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| pls != X0 ),
inference(definition_unfolding,[],[f5162,f4830]) ).
fof(f5162,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| zero_zero_int != X0 ),
inference(cnf_transformation,[],[f4122]) ).
fof(f9058,plain,
spl263_277,
inference(avatar_split_clause,[],[f6381,f9056]) ).
fof(f9056,plain,
( spl263_277
<=> ! [X0,X1] :
( is_fun_a_bool(sK199(X0,X1))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_277])]) ).
fof(f6381,plain,
! [X0,X1] :
( is_fun_a_bool(sK199(X0,X1))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f9054,plain,
spl263_276,
inference(avatar_split_clause,[],[f6380,f9052]) ).
fof(f9052,plain,
( spl263_276
<=> ! [X0,X1] :
( is_a(sK198(X0,X1))
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_276])]) ).
fof(f6380,plain,
! [X0,X1] :
( is_a(sK198(X0,X1))
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f4527]) ).
fof(f9050,plain,
spl263_275,
inference(avatar_split_clause,[],[f6365,f9048]) ).
fof(f9048,plain,
( spl263_275
<=> ! [X0,X1] :
( is_fun_pname_bool(sK197(X0,X1))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_275])]) ).
fof(f6365,plain,
! [X0,X1] :
( is_fun_pname_bool(sK197(X0,X1))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f9046,plain,
spl263_274,
inference(avatar_split_clause,[],[f6364,f9044]) ).
fof(f9044,plain,
( spl263_274
<=> ! [X0,X1] :
( is_pname(sK196(X0,X1))
| ~ sP20(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_274])]) ).
fof(f6364,plain,
! [X0,X1] :
( is_pname(sK196(X0,X1))
| ~ sP20(X0,X1) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f9042,plain,
( spl263_273
| ~ spl263_38
| ~ spl263_72 ),
inference(avatar_split_clause,[],[f8184,f8100,f7964,f9040]) ).
fof(f9040,plain,
( spl263_273
<=> ! [X0,X1] : sP7(image_fun_nat_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_273])]) ).
fof(f8184,plain,
( ! [X0,X1] : sP7(image_fun_nat_bool_a(X0,X1))
| ~ spl263_38
| ~ spl263_72 ),
inference(resolution,[],[f8101,f7965]) ).
fof(f9038,plain,
spl263_272,
inference(avatar_split_clause,[],[f5669,f9036]) ).
fof(f9036,plain,
( spl263_272
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(X0,sK126(X0)))
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_272])]) ).
fof(f5669,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(X0,sK126(X0)))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f4230]) ).
fof(f9034,plain,
spl263_271,
inference(avatar_split_clause,[],[f5666,f9032]) ).
fof(f9032,plain,
( spl263_271
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK126(X0)))
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_271])]) ).
fof(f5666,plain,
! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK126(X0)))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f4230]) ).
fof(f9030,plain,
spl263_270,
inference(avatar_split_clause,[],[f5626,f9028]) ).
fof(f9028,plain,
( spl263_270
<=> ! [X0] :
( hBOOL(hAPP_f448129468l_bool(X0,sK119(X0)))
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_270])]) ).
fof(f5626,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(X0,sK119(X0)))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f4219]) ).
fof(f9026,plain,
spl263_269,
inference(avatar_split_clause,[],[f5623,f9024]) ).
fof(f9024,plain,
( spl263_269
<=> ! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK119(X0)))
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_269])]) ).
fof(f5623,plain,
! [X0] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK119(X0)))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f4219]) ).
fof(f9022,plain,
spl263_268,
inference(avatar_split_clause,[],[f5596,f9020]) ).
fof(f9020,plain,
( spl263_268
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK117(X0)))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_268])]) ).
fof(f5596,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK117(X0)))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f9018,plain,
spl263_267,
inference(avatar_split_clause,[],[f5594,f9016]) ).
fof(f9016,plain,
( spl263_267
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK117(X0)))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_267])]) ).
fof(f5594,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK117(X0)))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f9014,plain,
spl263_266,
inference(avatar_split_clause,[],[f5589,f9012]) ).
fof(f9012,plain,
( spl263_266
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK115(X0)))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_266])]) ).
fof(f5589,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK115(X0)))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f9010,plain,
spl263_265,
inference(avatar_split_clause,[],[f5587,f9008]) ).
fof(f9008,plain,
( spl263_265
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK115(X0)))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_265])]) ).
fof(f5587,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK115(X0)))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f9006,plain,
spl263_264,
inference(avatar_split_clause,[],[f5556,f9004]) ).
fof(f9004,plain,
( spl263_264
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK113(X0)))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_264])]) ).
fof(f5556,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK113(X0)))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f9002,plain,
spl263_263,
inference(avatar_split_clause,[],[f5554,f9000]) ).
fof(f9000,plain,
( spl263_263
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK113(X0)))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_263])]) ).
fof(f5554,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK113(X0)))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f8998,plain,
( spl263_262
| ~ spl263_37
| ~ spl263_71 ),
inference(avatar_split_clause,[],[f8183,f8096,f7960,f8996]) ).
fof(f8996,plain,
( spl263_262
<=> ! [X0,X1] : sP5(hAPP_int_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_262])]) ).
fof(f8096,plain,
( spl263_71
<=> ! [X0,X1] : is_fun_a_bool(hAPP_int_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_71])]) ).
fof(f8183,plain,
( ! [X0,X1] : sP5(hAPP_int_fun_a_bool(X0,X1))
| ~ spl263_37
| ~ spl263_71 ),
inference(resolution,[],[f8097,f7961]) ).
fof(f8097,plain,
( ! [X0,X1] : is_fun_a_bool(hAPP_int_fun_a_bool(X0,X1))
| ~ spl263_71 ),
inference(avatar_component_clause,[],[f8096]) ).
fof(f8994,plain,
spl263_261,
inference(avatar_split_clause,[],[f5549,f8992]) ).
fof(f8992,plain,
( spl263_261
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK111(X0)))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_261])]) ).
fof(f5549,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK111(X0)))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f8990,plain,
spl263_260,
inference(avatar_split_clause,[],[f5547,f8988]) ).
fof(f8988,plain,
( spl263_260
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK111(X0)))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_260])]) ).
fof(f5547,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK111(X0)))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f8986,plain,
spl263_259,
inference(avatar_split_clause,[],[f5408,f8984]) ).
fof(f8984,plain,
( spl263_259
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK94(X0)))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_259])]) ).
fof(f5408,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(X0,sK94(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f8982,plain,
spl263_258,
inference(avatar_split_clause,[],[f5405,f8980]) ).
fof(f8980,plain,
( spl263_258
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK94(X0)))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_258])]) ).
fof(f5405,plain,
! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK94(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f8978,plain,
spl263_257,
inference(avatar_split_clause,[],[f5385,f8976]) ).
fof(f8976,plain,
( spl263_257
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK91(X0)))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_257])]) ).
fof(f5385,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(X0,sK91(X0)))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f8974,plain,
spl263_256,
inference(avatar_split_clause,[],[f5382,f8972]) ).
fof(f8972,plain,
( spl263_256
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK91(X0)))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_256])]) ).
fof(f5382,plain,
! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK91(X0)))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f8970,plain,
spl263_255,
inference(avatar_split_clause,[],[f5233,f8968]) ).
fof(f5233,plain,
! [X0,X1] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1),
inference(cnf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1),
inference(rectify,[],[f711]) ).
fof(f711,axiom,
! [X7,X4] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X7),X4) != bot_bot_fun_nat_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8966,plain,
spl263_254,
inference(avatar_split_clause,[],[f5231,f8964]) ).
fof(f5231,plain,
! [X0,X1] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1),
inference(cnf_transformation,[],[f1627]) ).
fof(f1627,plain,
! [X0,X1] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1),
inference(rectify,[],[f715]) ).
fof(f715,axiom,
! [X7,X4] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X7),X4) != bot_bot_fun_int_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8962,plain,
spl263_253,
inference(avatar_split_clause,[],[f5229,f8960]) ).
fof(f8960,plain,
( spl263_253
<=> ! [X0,X1] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_253])]) ).
fof(f5229,plain,
! [X0,X1] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),
inference(cnf_transformation,[],[f1625]) ).
fof(f1625,plain,
! [X0,X1] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),
inference(rectify,[],[f713]) ).
fof(f713,axiom,
! [X7,X4] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X7),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8958,plain,
spl263_252,
inference(avatar_split_clause,[],[f5097,f8956]) ).
fof(f8956,plain,
( spl263_252
<=> ! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| is_a(sK66(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_252])]) ).
fof(f5097,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| is_a(sK66(X0)) ),
inference(cnf_transformation,[],[f4062]) ).
fof(f8954,plain,
( spl263_251
| ~ spl263_38
| ~ spl263_71 ),
inference(avatar_split_clause,[],[f8182,f8096,f7964,f8952]) ).
fof(f8952,plain,
( spl263_251
<=> ! [X0,X1] : sP7(hAPP_int_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_251])]) ).
fof(f8182,plain,
( ! [X0,X1] : sP7(hAPP_int_fun_a_bool(X0,X1))
| ~ spl263_38
| ~ spl263_71 ),
inference(resolution,[],[f8097,f7965]) ).
fof(f8950,plain,
spl263_250,
inference(avatar_split_clause,[],[f5094,f8948]) ).
fof(f8948,plain,
( spl263_250
<=> ! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| is_a(sK65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_250])]) ).
fof(f5094,plain,
! [X0] :
( bot_bot_fun_a_bool = collect_a(X0)
| is_a(sK65(X0)) ),
inference(cnf_transformation,[],[f4058]) ).
fof(f8946,plain,
spl263_249,
inference(avatar_split_clause,[],[f5025,f8944]) ).
fof(f5025,plain,
! [X0] :
( sP4(X0)
| bot_bot_fun_a_bool = X0
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f4008]) ).
fof(f4008,plain,
! [X0] :
( ( ( bot_bot_fun_a_bool != X0
| ~ sP4(X0) )
& ( sP4(X0)
| bot_bot_fun_a_bool = X0 ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f3918]) ).
fof(f3918,plain,
! [X0] :
( ( bot_bot_fun_a_bool != X0
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f8942,plain,
spl263_248,
inference(avatar_split_clause,[],[f4998,f8940]) ).
fof(f4998,plain,
! [X0] :
( sP0(X0)
| bot_bo844097828e_bool = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f3989]) ).
fof(f3989,plain,
! [X0] :
( ( ( bot_bo844097828e_bool != X0
| ~ sP0(X0) )
& ( sP0(X0)
| bot_bo844097828e_bool = X0 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f3912]) ).
fof(f3912,plain,
! [X0] :
( ( bot_bo844097828e_bool != X0
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8938,plain,
spl263_247,
inference(avatar_split_clause,[],[f4945,f8936]) ).
fof(f8936,plain,
( spl263_247
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_247])]) ).
fof(f4945,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0,
inference(cnf_transformation,[],[f1491]) ).
fof(f1491,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0,
inference(rectify,[],[f1040]) ).
fof(f1040,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),zero_zero_nat) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8934,plain,
spl263_246,
inference(avatar_split_clause,[],[f4944,f8932]) ).
fof(f4944,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0,
inference(cnf_transformation,[],[f1490]) ).
fof(f1490,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0,
inference(rectify,[],[f1035]) ).
fof(f1035,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),zero_zero_nat) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8930,plain,
spl263_245,
inference(avatar_split_clause,[],[f4943,f8928]) ).
fof(f8928,plain,
( spl263_245
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_245])]) ).
fof(f4943,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0,
inference(cnf_transformation,[],[f1489]) ).
fof(f1489,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0,
inference(rectify,[],[f1101]) ).
fof(f1101,axiom,
! [X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),one_one_nat) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8926,plain,
spl263_244,
inference(avatar_split_clause,[],[f4942,f8924]) ).
fof(f8924,plain,
( spl263_244
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_244])]) ).
fof(f4942,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0,
inference(cnf_transformation,[],[f1488]) ).
fof(f1488,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0,
inference(rectify,[],[f1041]) ).
fof(f1041,axiom,
! [X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8922,plain,
spl263_243,
inference(avatar_split_clause,[],[f4941,f8920]) ).
fof(f8920,plain,
( spl263_243
<=> ! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_243])]) ).
fof(f4941,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0,
inference(cnf_transformation,[],[f1487]) ).
fof(f1487,plain,
! [X0] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0,
inference(rectify,[],[f1103]) ).
fof(f1103,axiom,
! [X13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8918,plain,
spl263_242,
inference(avatar_split_clause,[],[f4939,f8916]) ).
fof(f4939,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0,
inference(cnf_transformation,[],[f1485]) ).
fof(f1485,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0,
inference(rectify,[],[f1293]) ).
fof(f1293,axiom,
! [X21] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),pls) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8914,plain,
spl263_241,
inference(avatar_split_clause,[],[f4938,f8912]) ).
fof(f8912,plain,
( spl263_241
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_241])]) ).
fof(f4938,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0,
inference(cnf_transformation,[],[f1484]) ).
fof(f1484,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0,
inference(rectify,[],[f1127]) ).
fof(f1127,axiom,
! [X97] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X97),one_one_int) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8910,plain,
spl263_240,
inference(avatar_split_clause,[],[f4937,f8908]) ).
fof(f8908,plain,
( spl263_240
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_240])]) ).
fof(f4937,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0,
inference(cnf_transformation,[],[f1483]) ).
fof(f1483,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0,
inference(rectify,[],[f1291]) ).
fof(f1291,axiom,
! [X21] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X21),pls) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8906,plain,
spl263_239,
inference(avatar_split_clause,[],[f4935,f8904]) ).
fof(f4935,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0,
inference(cnf_transformation,[],[f1481]) ).
fof(f1481,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0,
inference(rectify,[],[f1292]) ).
fof(f1292,axiom,
! [X21] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8902,plain,
spl263_238,
inference(avatar_split_clause,[],[f4934,f8900]) ).
fof(f8900,plain,
( spl263_238
<=> ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_238])]) ).
fof(f4934,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0,
inference(cnf_transformation,[],[f1480]) ).
fof(f1480,plain,
! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0,
inference(rectify,[],[f1126]) ).
fof(f1126,axiom,
! [X97] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X97) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8898,plain,
spl263_237,
inference(avatar_split_clause,[],[f4933,f8896]) ).
fof(f8896,plain,
( spl263_237
<=> ! [X0] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_237])]) ).
fof(f4933,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0,
inference(cnf_transformation,[],[f1479]) ).
fof(f1479,plain,
! [X0] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0,
inference(rectify,[],[f621]) ).
fof(f621,axiom,
! [X4] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),bot_bot_fun_nat_bool) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8894,plain,
spl263_236,
inference(avatar_split_clause,[],[f4932,f8892]) ).
fof(f8892,plain,
( spl263_236
<=> ! [X0] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_236])]) ).
fof(f4932,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0,
inference(cnf_transformation,[],[f1478]) ).
fof(f1478,plain,
! [X0] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0,
inference(rectify,[],[f622]) ).
fof(f622,axiom,
! [X4] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),bot_bot_fun_int_bool) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8890,plain,
spl263_235,
inference(avatar_split_clause,[],[f4931,f8888]) ).
fof(f8888,plain,
( spl263_235
<=> ! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_235])]) ).
fof(f4931,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0),
inference(cnf_transformation,[],[f1477]) ).
fof(f1477,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0),
inference(rectify,[],[f1034]) ).
fof(f1034,axiom,
! [X14] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8886,plain,
spl263_234,
inference(avatar_split_clause,[],[f4930,f8884]) ).
fof(f8884,plain,
( spl263_234
<=> ! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_234])]) ).
fof(f4930,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat),
inference(cnf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat),
inference(rectify,[],[f1086]) ).
fof(f1086,axiom,
! [X14] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8882,plain,
spl263_233,
inference(avatar_split_clause,[],[f4929,f8880]) ).
fof(f8880,plain,
( spl263_233
<=> ! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_233])]) ).
fof(f4929,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0),
inference(cnf_transformation,[],[f1475]) ).
fof(f1475,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0),
inference(rectify,[],[f1036]) ).
fof(f1036,axiom,
! [X13] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8878,plain,
spl263_232,
inference(avatar_split_clause,[],[f4928,f8876]) ).
fof(f8876,plain,
( spl263_232
<=> ! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_232])]) ).
fof(f4928,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0),
inference(cnf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0),
inference(rectify,[],[f1085]) ).
fof(f1085,axiom,
! [X13] : zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8874,plain,
spl263_231,
inference(avatar_split_clause,[],[f4927,f8872]) ).
fof(f8872,plain,
( spl263_231
<=> ! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_231])]) ).
fof(f4927,plain,
! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0),
inference(cnf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0),
inference(rectify,[],[f620]) ).
fof(f620,axiom,
! [X4] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8870,plain,
( spl263_230
| ~ spl263_214 ),
inference(avatar_split_clause,[],[f8831,f8763,f8867]) ).
fof(f8867,plain,
( spl263_230
<=> sP16(pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_230])]) ).
fof(f8763,plain,
( spl263_214
<=> ! [X1] :
( pls != X1
| sP16(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_214])]) ).
fof(f8831,plain,
( sP16(pls,pls)
| ~ spl263_214 ),
inference(equality_resolution,[],[f8764]) ).
fof(f8764,plain,
( ! [X1] :
( pls != X1
| sP16(X1,X1) )
| ~ spl263_214 ),
inference(avatar_component_clause,[],[f8763]) ).
fof(f8865,plain,
spl263_229,
inference(avatar_split_clause,[],[f4926,f8863]) ).
fof(f8863,plain,
( spl263_229
<=> ! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_229])]) ).
fof(f4926,plain,
! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0),
inference(cnf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0),
inference(rectify,[],[f633]) ).
fof(f633,axiom,
! [X4] : bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8861,plain,
spl263_228,
inference(avatar_split_clause,[],[f4925,f8859]) ).
fof(f8859,plain,
( spl263_228
<=> ! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_228])]) ).
fof(f4925,plain,
! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0),
inference(cnf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0),
inference(rectify,[],[f619]) ).
fof(f619,axiom,
! [X4] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8857,plain,
spl263_227,
inference(avatar_split_clause,[],[f4924,f8855]) ).
fof(f8855,plain,
( spl263_227
<=> ! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_227])]) ).
fof(f4924,plain,
! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0),
inference(cnf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0),
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X4] : bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8853,plain,
spl263_226,
inference(avatar_split_clause,[],[f4923,f8851]) ).
fof(f8851,plain,
( spl263_226
<=> ! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_226])]) ).
fof(f4923,plain,
! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0),
inference(cnf_transformation,[],[f1469]) ).
fof(f1469,plain,
! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0),
inference(rectify,[],[f618]) ).
fof(f618,axiom,
! [X4] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8849,plain,
spl263_225,
inference(avatar_split_clause,[],[f4922,f8847]) ).
fof(f8847,plain,
( spl263_225
<=> ! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_225])]) ).
fof(f4922,plain,
! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0),
inference(cnf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0),
inference(rectify,[],[f631]) ).
fof(f631,axiom,
! [X4] : bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8845,plain,
spl263_224,
inference(avatar_split_clause,[],[f4921,f8843]) ).
fof(f8843,plain,
( spl263_224
<=> ! [X0] : pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_224])]) ).
fof(f4921,plain,
! [X0] : pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0),
inference(cnf_transformation,[],[f1467]) ).
fof(f1467,plain,
! [X0] : pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0),
inference(rectify,[],[f1294]) ).
fof(f1294,axiom,
! [X134] : pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X134),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8841,plain,
spl263_223,
inference(avatar_split_clause,[],[f4866,f8838]) ).
fof(f8838,plain,
( spl263_223
<=> is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_223])]) ).
fof(f4866,plain,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8836,plain,
spl263_222,
inference(avatar_split_clause,[],[f4865,f8833]) ).
fof(f8833,plain,
( spl263_222
<=> is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_222])]) ).
fof(f4865,plain,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8830,plain,
( spl263_221
| ~ spl263_35
| ~ spl263_70 ),
inference(avatar_split_clause,[],[f8181,f8092,f7952,f8828]) ).
fof(f8828,plain,
( spl263_221
<=> ! [X0,X1] : sP1(hAPP_n1025906991e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_221])]) ).
fof(f8092,plain,
( spl263_70
<=> ! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_70])]) ).
fof(f8181,plain,
( ! [X0,X1] : sP1(hAPP_n1025906991e_bool(X0,X1))
| ~ spl263_35
| ~ spl263_70 ),
inference(resolution,[],[f8093,f7953]) ).
fof(f8093,plain,
( ! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1))
| ~ spl263_70 ),
inference(avatar_component_clause,[],[f8092]) ).
fof(f8826,plain,
( spl263_220
| ~ spl263_36
| ~ spl263_70 ),
inference(avatar_split_clause,[],[f8180,f8092,f7956,f8824]) ).
fof(f8824,plain,
( spl263_220
<=> ! [X0,X1] : sP3(hAPP_n1025906991e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_220])]) ).
fof(f8180,plain,
( ! [X0,X1] : sP3(hAPP_n1025906991e_bool(X0,X1))
| ~ spl263_36
| ~ spl263_70 ),
inference(resolution,[],[f8093,f7957]) ).
fof(f8814,plain,
( spl263_219
| ~ spl263_35
| ~ spl263_69 ),
inference(avatar_split_clause,[],[f8174,f8088,f7952,f8812]) ).
fof(f8812,plain,
( spl263_219
<=> ! [X0,X1] : sP1(image_nat_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_219])]) ).
fof(f8088,plain,
( spl263_69
<=> ! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_69])]) ).
fof(f8174,plain,
( ! [X0,X1] : sP1(image_nat_pname(X0,X1))
| ~ spl263_35
| ~ spl263_69 ),
inference(resolution,[],[f8089,f7953]) ).
fof(f8089,plain,
( ! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1))
| ~ spl263_69 ),
inference(avatar_component_clause,[],[f8088]) ).
fof(f8802,plain,
( spl263_218
| ~ spl263_36
| ~ spl263_69 ),
inference(avatar_split_clause,[],[f8173,f8088,f7956,f8800]) ).
fof(f8800,plain,
( spl263_218
<=> ! [X0,X1] : sP3(image_nat_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_218])]) ).
fof(f8173,plain,
( ! [X0,X1] : sP3(image_nat_pname(X0,X1))
| ~ spl263_36
| ~ spl263_69 ),
inference(resolution,[],[f8089,f7957]) ).
fof(f8788,plain,
( spl263_217
| ~ spl263_35
| ~ spl263_68 ),
inference(avatar_split_clause,[],[f8172,f8084,f7952,f8786]) ).
fof(f8786,plain,
( spl263_217
<=> ! [X0,X1] : sP1(image_1921560913_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_217])]) ).
fof(f8084,plain,
( spl263_68
<=> ! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_68])]) ).
fof(f8172,plain,
( ! [X0,X1] : sP1(image_1921560913_pname(X0,X1))
| ~ spl263_35
| ~ spl263_68 ),
inference(resolution,[],[f8085,f7953]) ).
fof(f8085,plain,
( ! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1))
| ~ spl263_68 ),
inference(avatar_component_clause,[],[f8084]) ).
fof(f8775,plain,
( spl263_216
| ~ spl263_36
| ~ spl263_68 ),
inference(avatar_split_clause,[],[f8171,f8084,f7956,f8773]) ).
fof(f8773,plain,
( spl263_216
<=> ! [X0,X1] : sP3(image_1921560913_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_216])]) ).
fof(f8171,plain,
( ! [X0,X1] : sP3(image_1921560913_pname(X0,X1))
| ~ spl263_36
| ~ spl263_68 ),
inference(resolution,[],[f8085,f7957]) ).
fof(f8771,plain,
( spl263_215
| ~ spl263_35
| ~ spl263_67 ),
inference(avatar_split_clause,[],[f8170,f8080,f7952,f8769]) ).
fof(f8769,plain,
( spl263_215
<=> ! [X0,X1] : sP1(image_62782965_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_215])]) ).
fof(f8080,plain,
( spl263_67
<=> ! [X0,X1] : is_fun_pname_bool(image_62782965_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_67])]) ).
fof(f8170,plain,
( ! [X0,X1] : sP1(image_62782965_pname(X0,X1))
| ~ spl263_35
| ~ spl263_67 ),
inference(resolution,[],[f8081,f7953]) ).
fof(f8081,plain,
( ! [X0,X1] : is_fun_pname_bool(image_62782965_pname(X0,X1))
| ~ spl263_67 ),
inference(avatar_component_clause,[],[f8080]) ).
fof(f8765,plain,
spl263_214,
inference(avatar_split_clause,[],[f7588,f8763]) ).
fof(f7588,plain,
! [X1] :
( pls != X1
| sP16(X1,X1) ),
inference(forward_demodulation,[],[f7255,f4875]) ).
fof(f7255,plain,
! [X1] :
( sP16(X1,X1)
| pls != number_number_of_int(X1) ),
inference(equality_resolution,[],[f7099]) ).
fof(f7099,plain,
! [X0,X1] :
( sP16(X0,X1)
| X0 != X1
| pls != number_number_of_int(X1) ),
inference(definition_unfolding,[],[f5899,f4830]) ).
fof(f5899,plain,
! [X0,X1] :
( sP16(X0,X1)
| X0 != X1
| zero_zero_int != number_number_of_int(X1) ),
inference(cnf_transformation,[],[f4309]) ).
fof(f8761,plain,
spl263_213,
inference(avatar_split_clause,[],[f7259,f8759]) ).
fof(f8759,plain,
( spl263_213
<=> ! [X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_213])]) ).
fof(f7259,plain,
! [X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_resolution,[],[f5934]) ).
fof(f5934,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f4336]) ).
fof(f8757,plain,
spl263_212,
inference(avatar_split_clause,[],[f7194,f8755]) ).
fof(f7194,plain,
! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(equality_resolution,[],[f5334]) ).
fof(f5334,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1719]) ).
fof(f1719,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1328]) ).
fof(f1328,axiom,
! [X17,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8753,plain,
spl263_211,
inference(avatar_split_clause,[],[f7193,f8751]) ).
fof(f8751,plain,
( spl263_211
<=> ! [X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_211])]) ).
fof(f7193,plain,
! [X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)),
inference(equality_resolution,[],[f5333]) ).
fof(f5333,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1718]) ).
fof(f1718,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1326]) ).
fof(f1326,axiom,
! [X17,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8749,plain,
( spl263_210
| ~ spl263_36
| ~ spl263_67 ),
inference(avatar_split_clause,[],[f8169,f8080,f7956,f8747]) ).
fof(f8747,plain,
( spl263_210
<=> ! [X0,X1] : sP3(image_62782965_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_210])]) ).
fof(f8169,plain,
( ! [X0,X1] : sP3(image_62782965_pname(X0,X1))
| ~ spl263_36
| ~ spl263_67 ),
inference(resolution,[],[f8081,f7957]) ).
fof(f8745,plain,
spl263_209,
inference(avatar_split_clause,[],[f7192,f8743]) ).
fof(f8743,plain,
( spl263_209
<=> ! [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_209])]) ).
fof(f7192,plain,
! [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
inference(equality_resolution,[],[f5332]) ).
fof(f5332,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1717]) ).
fof(f1717,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1346]) ).
fof(f1346,axiom,
! [X17,X18] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8741,plain,
spl263_208,
inference(avatar_split_clause,[],[f7191,f8739]) ).
fof(f8739,plain,
( spl263_208
<=> ! [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_208])]) ).
fof(f7191,plain,
! [X1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X1)),
inference(equality_resolution,[],[f5331]) ).
fof(f5331,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1716]) ).
fof(f1716,plain,
! [X0,X1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1344]) ).
fof(f1344,axiom,
! [X17,X18] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8737,plain,
spl263_207,
inference(avatar_split_clause,[],[f7190,f8735]) ).
fof(f8735,plain,
( spl263_207
<=> ! [X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_207])]) ).
fof(f7190,plain,
! [X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
inference(equality_resolution,[],[f5330]) ).
fof(f5330,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1715]) ).
fof(f1715,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1338]) ).
fof(f1338,axiom,
! [X17,X18] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8733,plain,
spl263_206,
inference(avatar_split_clause,[],[f7189,f8731]) ).
fof(f8731,plain,
( spl263_206
<=> ! [X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_206])]) ).
fof(f7189,plain,
! [X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
inference(equality_resolution,[],[f5329]) ).
fof(f5329,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1714]) ).
fof(f1714,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1348]) ).
fof(f1348,axiom,
! [X17,X18] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8729,plain,
spl263_205,
inference(avatar_split_clause,[],[f7188,f8727]) ).
fof(f8727,plain,
( spl263_205
<=> ! [X1] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_205])]) ).
fof(f7188,plain,
! [X1] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
inference(equality_resolution,[],[f5328]) ).
fof(f5328,plain,
! [X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1713]) ).
fof(f1713,plain,
! [X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1320]) ).
fof(f1320,axiom,
! [X17,X18] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8725,plain,
spl263_204,
inference(avatar_split_clause,[],[f7187,f8723]) ).
fof(f8723,plain,
( spl263_204
<=> ! [X1] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_204])]) ).
fof(f7187,plain,
! [X1] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
inference(equality_resolution,[],[f5327]) ).
fof(f5327,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f1712]) ).
fof(f1712,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f1330]) ).
fof(f1330,axiom,
! [X17,X18] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X17),X18))
| X17 != X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8721,plain,
spl263_203,
inference(avatar_split_clause,[],[f7030,f8719]) ).
fof(f7030,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(definition_unfolding,[],[f4908,f4829]) ).
fof(f4908,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X0)),
inference(cnf_transformation,[],[f1454]) ).
fof(f1454,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X0)),
inference(rectify,[],[f735]) ).
fof(f735,axiom,
! [X74] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X74)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8717,plain,
spl263_202,
inference(avatar_split_clause,[],[f7022,f8714]) ).
fof(f8714,plain,
( spl263_202
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_202])]) ).
fof(f7022,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
inference(definition_unfolding,[],[f4861,f4830]) ).
fof(f4861,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8712,plain,
spl263_201,
inference(avatar_split_clause,[],[f7021,f8709]) ).
fof(f8709,plain,
( spl263_201
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_201])]) ).
fof(f7021,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
inference(definition_unfolding,[],[f4859,f4830]) ).
fof(f4859,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8707,plain,
spl263_200,
inference(avatar_split_clause,[],[f5667,f8705]) ).
fof(f8705,plain,
( spl263_200
<=> ! [X0] :
( bot_bot_fun_nat_bool != sK126(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_200])]) ).
fof(f5667,plain,
! [X0] :
( bot_bot_fun_nat_bool != sK126(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f4230]) ).
fof(f8703,plain,
( spl263_199
| ~ spl263_35
| ~ spl263_66 ),
inference(avatar_split_clause,[],[f8168,f8076,f7952,f8701]) ).
fof(f8701,plain,
( spl263_199
<=> ! [X0,X1] : sP1(image_int_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_199])]) ).
fof(f8076,plain,
( spl263_66
<=> ! [X0,X1] : is_fun_pname_bool(image_int_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_66])]) ).
fof(f8168,plain,
( ! [X0,X1] : sP1(image_int_pname(X0,X1))
| ~ spl263_35
| ~ spl263_66 ),
inference(resolution,[],[f8077,f7953]) ).
fof(f8077,plain,
( ! [X0,X1] : is_fun_pname_bool(image_int_pname(X0,X1))
| ~ spl263_66 ),
inference(avatar_component_clause,[],[f8076]) ).
fof(f8699,plain,
spl263_198,
inference(avatar_split_clause,[],[f5624,f8697]) ).
fof(f8697,plain,
( spl263_198
<=> ! [X0] :
( bot_bot_fun_int_bool != sK119(X0)
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_198])]) ).
fof(f5624,plain,
! [X0] :
( bot_bot_fun_int_bool != sK119(X0)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f4219]) ).
fof(f8695,plain,
spl263_197,
inference(avatar_split_clause,[],[f5406,f8693]) ).
fof(f8693,plain,
( spl263_197
<=> ! [X0] :
( bot_bot_fun_a_bool != sK94(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_197])]) ).
fof(f5406,plain,
! [X0] :
( bot_bot_fun_a_bool != sK94(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f8691,plain,
spl263_196,
inference(avatar_split_clause,[],[f5402,f8689]) ).
fof(f8689,plain,
( spl263_196
<=> ! [X0,X1] :
( is_fun_a_bool(cOMBS_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_196])]) ).
fof(f5402,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBS_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2811]) ).
fof(f2811,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBS_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(cOMBS_a_bool_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8687,plain,
spl263_195,
inference(avatar_split_clause,[],[f5401,f8685]) ).
fof(f8685,plain,
( spl263_195
<=> ! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_195])]) ).
fof(f5401,plain,
! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2810]) ).
fof(f2810,plain,
! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(image_a_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8683,plain,
spl263_194,
inference(avatar_split_clause,[],[f5400,f8681]) ).
fof(f5400,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2809]) ).
fof(f2809,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(cOMBB_bool_bool_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8679,plain,
spl263_193,
inference(avatar_split_clause,[],[f5399,f8677]) ).
fof(f5399,plain,
! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2808]) ).
fof(f2808,plain,
! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun_pname_bool(image_a_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8675,plain,
spl263_192,
inference(avatar_split_clause,[],[f5398,f8673]) ).
fof(f8673,plain,
( spl263_192
<=> ! [X0,X1] :
( is_fun949378684l_bool(image_a_fun_a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_192])]) ).
fof(f5398,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_a_fun_a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2807]) ).
fof(f2807,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_a_fun_a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(image_a_fun_a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8671,plain,
spl263_191,
inference(avatar_split_clause,[],[f5397,f8669]) ).
fof(f8669,plain,
( spl263_191
<=> ! [X0,X1] :
( is_fun1661590463l_bool(image_819518260e_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_191])]) ).
fof(f5397,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_819518260e_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2806]) ).
fof(f2806,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_819518260e_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun1661590463l_bool(image_819518260e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8667,plain,
spl263_190,
inference(avatar_split_clause,[],[f5396,f8665]) ).
fof(f8665,plain,
( spl263_190
<=> ! [X0,X1] :
( is_a(hAPP_fun_a_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_190])]) ).
fof(f5396,plain,
! [X0,X1] :
( is_a(hAPP_fun_a_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2805]) ).
fof(f2805,plain,
! [X0,X1] :
( is_a(hAPP_fun_a_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_a(hAPP_fun_a_bool_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8663,plain,
spl263_189,
inference(avatar_split_clause,[],[f5383,f8661]) ).
fof(f8661,plain,
( spl263_189
<=> ! [X0] :
( bot_bo844097828e_bool != sK91(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_189])]) ).
fof(f5383,plain,
! [X0] :
( bot_bo844097828e_bool != sK91(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f8659,plain,
( spl263_188
| ~ spl263_36
| ~ spl263_66 ),
inference(avatar_split_clause,[],[f8167,f8076,f7956,f8657]) ).
fof(f8657,plain,
( spl263_188
<=> ! [X0,X1] : sP3(image_int_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_188])]) ).
fof(f8167,plain,
( ! [X0,X1] : sP3(image_int_pname(X0,X1))
| ~ spl263_36
| ~ spl263_66 ),
inference(resolution,[],[f8077,f7957]) ).
fof(f8655,plain,
spl263_187,
inference(avatar_split_clause,[],[f5377,f8653]) ).
fof(f5377,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2793]) ).
fof(f2793,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8651,plain,
spl263_186,
inference(avatar_split_clause,[],[f5376,f8649]) ).
fof(f5376,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2792]) ).
fof(f2792,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8647,plain,
spl263_185,
inference(avatar_split_clause,[],[f5375,f8645]) ).
fof(f5375,plain,
! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2791]) ).
fof(f2791,plain,
! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(image_pname_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8643,plain,
spl263_184,
inference(avatar_split_clause,[],[f5374,f8641]) ).
fof(f5374,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2790]) ).
fof(f2790,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(cOMBB_647938656_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8639,plain,
spl263_183,
inference(avatar_split_clause,[],[f5373,f8637]) ).
fof(f8637,plain,
( spl263_183
<=> ! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_183])]) ).
fof(f5373,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2789]) ).
fof(f2789,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun949378684l_bool(image_112932426a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8635,plain,
spl263_182,
inference(avatar_split_clause,[],[f5372,f8633]) ).
fof(f8633,plain,
( spl263_182
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_182])]) ).
fof(f5372,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2788]) ).
fof(f2788,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8631,plain,
spl263_181,
inference(avatar_split_clause,[],[f5371,f8629]) ).
fof(f8629,plain,
( spl263_181
<=> ! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_181])]) ).
fof(f5371,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2787]) ).
fof(f2787,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun1661590463l_bool(image_47868345e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8627,plain,
spl263_180,
inference(avatar_split_clause,[],[f5370,f8625]) ).
fof(f8625,plain,
( spl263_180
<=> ! [X0,X1] :
( is_pname(hAPP_f1297739591_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_180])]) ).
fof(f5370,plain,
! [X0,X1] :
( is_pname(hAPP_f1297739591_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2786]) ).
fof(f2786,plain,
! [X0,X1] :
( is_pname(hAPP_f1297739591_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_pname(hAPP_f1297739591_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8623,plain,
spl263_179,
inference(avatar_split_clause,[],[f5366,f8621]) ).
fof(f8621,plain,
( spl263_179
<=> ! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_179])]) ).
fof(f5366,plain,
! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ),
inference(cnf_transformation,[],[f2782]) ).
fof(f2782,plain,
! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( is_bool(X1)
=> is_bool(hAPP_bool_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8619,plain,
spl263_178,
inference(avatar_split_clause,[],[f5365,f8617]) ).
fof(f5365,plain,
! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f2781]) ).
fof(f2781,plain,
! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun_a_bool(image_fun_a_bool_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8615,plain,
( spl263_177
| ~ spl263_35
| ~ spl263_65 ),
inference(avatar_split_clause,[],[f8166,f8072,f7952,f8613]) ).
fof(f8613,plain,
( spl263_177
<=> ! [X0,X1] : sP1(hAPP_i7355787e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_177])]) ).
fof(f8072,plain,
( spl263_65
<=> ! [X0,X1] : is_fun_pname_bool(hAPP_i7355787e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_65])]) ).
fof(f8166,plain,
( ! [X0,X1] : sP1(hAPP_i7355787e_bool(X0,X1))
| ~ spl263_35
| ~ spl263_65 ),
inference(resolution,[],[f8073,f7953]) ).
fof(f8073,plain,
( ! [X0,X1] : is_fun_pname_bool(hAPP_i7355787e_bool(X0,X1))
| ~ spl263_65 ),
inference(avatar_component_clause,[],[f8072]) ).
fof(f8611,plain,
spl263_176,
inference(avatar_split_clause,[],[f5364,f8609]) ).
fof(f5364,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBB_1273333599bool_a(X0,X1))
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f2780]) ).
fof(f2780,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBB_1273333599bool_a(X0,X1))
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X0)
=> is_fun_a_bool(cOMBB_1273333599bool_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8607,plain,
spl263_175,
inference(avatar_split_clause,[],[f5363,f8605]) ).
fof(f5363,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f2779]) ).
fof(f2779,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun_pname_bool(image_1854862208_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8603,plain,
spl263_174,
inference(avatar_split_clause,[],[f5362,f8601]) ).
fof(f8601,plain,
( spl263_174
<=> ! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_174])]) ).
fof(f5362,plain,
! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f2778]) ).
fof(f2778,plain,
! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_bool(hAPP_f621171935l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8599,plain,
spl263_173,
inference(avatar_split_clause,[],[f5361,f8597]) ).
fof(f8597,plain,
( spl263_173
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_173])]) ).
fof(f5361,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f2777]) ).
fof(f2777,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8595,plain,
spl263_172,
inference(avatar_split_clause,[],[f5360,f8593]) ).
fof(f8593,plain,
( spl263_172
<=> ! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_172])]) ).
fof(f5360,plain,
! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f2776]) ).
fof(f2776,plain,
! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8591,plain,
spl263_171,
inference(avatar_split_clause,[],[f5359,f8589]) ).
fof(f5359,plain,
! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,plain,
! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun_a_bool(image_876012084bool_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8587,plain,
spl263_170,
inference(avatar_split_clause,[],[f5358,f8585]) ).
fof(f5358,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f2774]) ).
fof(f2774,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun_pname_bool(image_1283814551_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8583,plain,
spl263_169,
inference(avatar_split_clause,[],[f5357,f8581]) ).
fof(f8581,plain,
( spl263_169
<=> ! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_169])]) ).
fof(f5357,plain,
! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f2773]) ).
fof(f2773,plain,
! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_bool(hAPP_f1935102916l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8579,plain,
spl263_168,
inference(avatar_split_clause,[],[f5356,f8577]) ).
fof(f8577,plain,
( spl263_168
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_168])]) ).
fof(f5356,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f2772]) ).
fof(f2772,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8575,plain,
spl263_167,
inference(avatar_split_clause,[],[f5355,f8573]) ).
fof(f8573,plain,
( spl263_167
<=> ! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_167])]) ).
fof(f5355,plain,
! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f2771]) ).
fof(f2771,plain,
! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8571,plain,
( spl263_166
| ~ spl263_36
| ~ spl263_65 ),
inference(avatar_split_clause,[],[f8165,f8072,f7956,f8569]) ).
fof(f8569,plain,
( spl263_166
<=> ! [X0,X1] : sP3(hAPP_i7355787e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_166])]) ).
fof(f8165,plain,
( ! [X0,X1] : sP3(hAPP_i7355787e_bool(X0,X1))
| ~ spl263_36
| ~ spl263_65 ),
inference(resolution,[],[f8073,f7957]) ).
fof(f8567,plain,
spl263_165,
inference(avatar_split_clause,[],[f5354,f8565]) ).
fof(f5354,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f2770]) ).
fof(f2770,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8563,plain,
spl263_164,
inference(avatar_split_clause,[],[f5353,f8561]) ).
fof(f5353,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f2769]) ).
fof(f2769,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8559,plain,
spl263_163,
inference(avatar_split_clause,[],[f5352,f8557]) ).
fof(f8557,plain,
( spl263_163
<=> ! [X0,X1] :
( is_pname(hAPP_pname_pname(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_163])]) ).
fof(f5352,plain,
! [X0,X1] :
( is_pname(hAPP_pname_pname(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f2768]) ).
fof(f2768,plain,
! [X0,X1] :
( is_pname(hAPP_pname_pname(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_pname(hAPP_pname_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8555,plain,
spl263_162,
inference(avatar_split_clause,[],[f5350,f8553]) ).
fof(f5350,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f2766,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1] :
( is_a(X1)
=> is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8551,plain,
spl263_161,
inference(avatar_split_clause,[],[f5349,f8549]) ).
fof(f5349,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f2765]) ).
fof(f2765,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
( is_a(X1)
=> is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8547,plain,
spl263_160,
inference(avatar_split_clause,[],[f5348,f8545]) ).
fof(f8545,plain,
( spl263_160
<=> ! [X0,X1] :
( is_a(hAPP_a_a(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_160])]) ).
fof(f5348,plain,
! [X0,X1] :
( is_a(hAPP_a_a(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f2764]) ).
fof(f2764,plain,
! [X0,X1] :
( is_a(hAPP_a_a(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
( is_a(X1)
=> is_a(hAPP_a_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8543,plain,
spl263_159,
inference(avatar_split_clause,[],[f5228,f8541]) ).
fof(f8541,plain,
( spl263_159
<=> ! [X0,X1] : hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_159])]) ).
fof(f5228,plain,
! [X0,X1] : hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0,
inference(cnf_transformation,[],[f1624]) ).
fof(f1624,plain,
! [X0,X1] : hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0,
inference(rectify,[],[f1334]) ).
fof(f1334,axiom,
! [X158,X159] : hAPP_nat_int(cOMBK_int_nat(X158),X159) = X158,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8539,plain,
( ~ spl263_154
| ~ spl263_156 ),
inference(avatar_contradiction_clause,[],[f8538]) ).
fof(f8538,plain,
( $false
| ~ spl263_154
| ~ spl263_156 ),
inference(resolution,[],[f8520,f8528]) ).
fof(f8528,plain,
( ! [X0] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
| ~ spl263_156 ),
inference(avatar_component_clause,[],[f8527]) ).
fof(f8527,plain,
( spl263_156
<=> ! [X0] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_156])]) ).
fof(f8537,plain,
( ~ spl263_155
| spl263_158 ),
inference(avatar_split_clause,[],[f5134,f8535,f8522]) ).
fof(f8522,plain,
( spl263_155
<=> hBOOL(bot_bot_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_155])]) ).
fof(f5134,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f4105]) ).
fof(f4105,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ) ),
inference(nnf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f642]) ).
fof(f642,axiom,
! [X10] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X10))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8533,plain,
( ~ spl263_155
| spl263_157 ),
inference(avatar_split_clause,[],[f5130,f8531,f8522]) ).
fof(f5130,plain,
! [X0] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f4103]) ).
fof(f4103,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0)) ) ),
inference(nnf_transformation,[],[f1594]) ).
fof(f1594,plain,
! [X0] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f643]) ).
fof(f643,axiom,
! [X10] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X10))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8529,plain,
( ~ spl263_155
| spl263_156 ),
inference(avatar_split_clause,[],[f5108,f8527,f8522]) ).
fof(f5108,plain,
! [X0] :
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f4079]) ).
fof(f4079,plain,
! [X0] :
( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ) ),
inference(nnf_transformation,[],[f1586]) ).
fof(f1586,plain,
! [X0] :
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f650]) ).
fof(f650,axiom,
! [X29] :
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X29))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8525,plain,
( spl263_154
| spl263_155 ),
inference(avatar_split_clause,[],[f5107,f8522,f8519]) ).
fof(f5107,plain,
! [X0] :
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
inference(cnf_transformation,[],[f4079]) ).
fof(f8517,plain,
spl263_153,
inference(avatar_split_clause,[],[f4990,f8515]) ).
fof(f8515,plain,
( spl263_153
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_153])]) ).
fof(f4990,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(cnf_transformation,[],[f1532]) ).
fof(f1532,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(rectify,[],[f1306]) ).
fof(f1306,axiom,
! [X158] :
( ~ hBOOL(X158)
| ~ hBOOL(hAPP_bool_bool(fNot,X158)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8513,plain,
spl263_152,
inference(avatar_split_clause,[],[f4989,f8511]) ).
fof(f8511,plain,
( spl263_152
<=> ! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_152])]) ).
fof(f4989,plain,
! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f1531]) ).
fof(f1531,plain,
! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f1307]) ).
fof(f1307,axiom,
! [X158] :
( hBOOL(hAPP_bool_bool(fNot,X158))
| hBOOL(X158) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8509,plain,
spl263_151,
inference(avatar_split_clause,[],[f4919,f8507]) ).
fof(f4919,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f1465]) ).
fof(f1465,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f237]) ).
fof(f237,axiom,
! [X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8505,plain,
spl263_150,
inference(avatar_split_clause,[],[f4917,f8503]) ).
fof(f8503,plain,
( spl263_150
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_150])]) ).
fof(f4917,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(cnf_transformation,[],[f1463]) ).
fof(f1463,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(rectify,[],[f410]) ).
fof(f410,axiom,
! [X35] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X35),X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8501,plain,
spl263_149,
inference(avatar_split_clause,[],[f4915,f8499]) ).
fof(f8499,plain,
( spl263_149
<=> ! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_149])]) ).
fof(f4915,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(cnf_transformation,[],[f1461]) ).
fof(f1461,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(rectify,[],[f509]) ).
fof(f509,axiom,
! [X4] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8497,plain,
spl263_148,
inference(avatar_split_clause,[],[f4913,f8495]) ).
fof(f8495,plain,
( spl263_148
<=> ! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_148])]) ).
fof(f4913,plain,
! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)),
inference(cnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X10] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8493,plain,
spl263_147,
inference(avatar_split_clause,[],[f4911,f8491]) ).
fof(f4911,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(cnf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(rectify,[],[f510]) ).
fof(f510,axiom,
! [X4] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8489,plain,
spl263_146,
inference(avatar_split_clause,[],[f4906,f8487]) ).
fof(f4906,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)),
inference(cnf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)),
inference(rectify,[],[f733]) ).
fof(f733,axiom,
! [X7] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8485,plain,
spl263_145,
inference(avatar_split_clause,[],[f4904,f8483]) ).
fof(f4904,plain,
! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)),
inference(cnf_transformation,[],[f1450]) ).
fof(f1450,plain,
! [X0] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)),
inference(rectify,[],[f609]) ).
fof(f609,axiom,
! [X4] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8481,plain,
spl263_144,
inference(avatar_split_clause,[],[f4902,f8479]) ).
fof(f4902,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)),
inference(cnf_transformation,[],[f1448]) ).
fof(f1448,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)),
inference(rectify,[],[f736]) ).
fof(f736,axiom,
! [X7] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8477,plain,
spl263_143,
inference(avatar_split_clause,[],[f4900,f8475]) ).
fof(f8475,plain,
( spl263_143
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_143])]) ).
fof(f4900,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(cnf_transformation,[],[f1446]) ).
fof(f1446,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(rectify,[],[f968]) ).
fof(f968,axiom,
! [X13] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8473,plain,
spl263_142,
inference(avatar_split_clause,[],[f4897,f8471]) ).
fof(f4897,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(cnf_transformation,[],[f1443]) ).
fof(f1443,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(rectify,[],[f1044]) ).
fof(f1044,axiom,
! [X13] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X13),zero_zero_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8469,plain,
spl263_141,
inference(avatar_split_clause,[],[f4896,f8467]) ).
fof(f4896,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))),
inference(cnf_transformation,[],[f1442]) ).
fof(f1442,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))),
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X13] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8465,plain,
( ~ spl263_140
| ~ spl263_87
| ~ spl263_93 ),
inference(avatar_split_clause,[],[f8375,f8230,f8200,f8462]) ).
fof(f8462,plain,
( spl263_140
<=> one_one_nat = zero_zero_nat ),
introduced(avatar_definition,[new_symbols(naming,[spl263_140])]) ).
fof(f8230,plain,
( spl263_93
<=> ! [X0] : zero_zero_nat != hAPP_nat_nat(suc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_93])]) ).
fof(f8375,plain,
( one_one_nat != zero_zero_nat
| ~ spl263_87
| ~ spl263_93 ),
inference(superposition,[],[f8231,f8202]) ).
fof(f8231,plain,
( ! [X0] : zero_zero_nat != hAPP_nat_nat(suc,X0)
| ~ spl263_93 ),
inference(avatar_component_clause,[],[f8230]) ).
fof(f8460,plain,
spl263_139,
inference(avatar_split_clause,[],[f4894,f8458]) ).
fof(f4894,plain,
! [X0] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)),
inference(cnf_transformation,[],[f1440]) ).
fof(f1440,plain,
! [X0] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)),
inference(rectify,[],[f625]) ).
fof(f625,axiom,
! [X31] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8456,plain,
spl263_138,
inference(avatar_split_clause,[],[f4892,f8454]) ).
fof(f4892,plain,
! [X0] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)),
inference(cnf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)),
inference(rectify,[],[f624]) ).
fof(f624,axiom,
! [X31] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),bot_bot_fun_int_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8452,plain,
spl263_137,
inference(avatar_split_clause,[],[f4890,f8450]) ).
fof(f4890,plain,
! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)),
inference(cnf_transformation,[],[f1436]) ).
fof(f1436,plain,
! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)),
inference(rectify,[],[f599]) ).
fof(f599,axiom,
! [X7] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),bot_bot_fun_a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8448,plain,
spl263_136,
inference(avatar_split_clause,[],[f4888,f8446]) ).
fof(f4888,plain,
! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)),
inference(cnf_transformation,[],[f1434]) ).
fof(f1434,plain,
! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)),
inference(rectify,[],[f627]) ).
fof(f627,axiom,
! [X31] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),bot_bo844097828e_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8439,plain,
spl263_135,
inference(avatar_split_clause,[],[f4818,f8437]) ).
fof(f4818,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2688]) ).
fof(f2688,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8435,plain,
spl263_134,
inference(avatar_split_clause,[],[f4817,f8433]) ).
fof(f8433,plain,
( spl263_134
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_134])]) ).
fof(f4817,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f2687]) ).
fof(f2687,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8431,plain,
spl263_133,
inference(avatar_split_clause,[],[f4816,f8429]) ).
fof(f4816,plain,
! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f2686]) ).
fof(f2686,plain,
! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> is_fun_a_bool(image_pname_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8427,plain,
spl263_132,
inference(avatar_split_clause,[],[f4815,f8425]) ).
fof(f8425,plain,
( spl263_132
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_132])]) ).
fof(f4815,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f2685]) ).
fof(f2685,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8423,plain,
spl263_131,
inference(avatar_split_clause,[],[f4814,f8421]) ).
fof(f8421,plain,
( spl263_131
<=> ! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_131])]) ).
fof(f4814,plain,
! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f2684]) ).
fof(f2684,plain,
! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_a(hAPP_pname_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8419,plain,
spl263_130,
inference(avatar_split_clause,[],[f4813,f8417]) ).
fof(f8417,plain,
( spl263_130
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_130])]) ).
fof(f4813,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f2683]) ).
fof(f2683,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
( is_a(X1)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8415,plain,
spl263_129,
inference(avatar_split_clause,[],[f4807,f8412]) ).
fof(f4807,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1413]) ).
fof(f1413,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8404,plain,
( spl263_128
| ~ spl263_11
| ~ spl263_38 ),
inference(avatar_split_clause,[],[f8149,f7964,f7838,f8401]) ).
fof(f8401,plain,
( spl263_128
<=> sP7(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_128])]) ).
fof(f7838,plain,
( spl263_11
<=> is_fun_a_bool(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_11])]) ).
fof(f8149,plain,
( sP7(bot_bot_fun_a_bool)
| ~ spl263_11
| ~ spl263_38 ),
inference(resolution,[],[f7965,f7840]) ).
fof(f7840,plain,
( is_fun_a_bool(bot_bot_fun_a_bool)
| ~ spl263_11 ),
inference(avatar_component_clause,[],[f7838]) ).
fof(f8391,plain,
( spl263_80
| ~ spl263_11
| ~ spl263_37 ),
inference(avatar_split_clause,[],[f8147,f7960,f7838,f8134]) ).
fof(f8134,plain,
( spl263_80
<=> sP5(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_80])]) ).
fof(f8147,plain,
( sP5(bot_bot_fun_a_bool)
| ~ spl263_11
| ~ spl263_37 ),
inference(resolution,[],[f7961,f7840]) ).
fof(f8381,plain,
( spl263_127
| ~ spl263_10
| ~ spl263_36 ),
inference(avatar_split_clause,[],[f8145,f7956,f7833,f8378]) ).
fof(f8378,plain,
( spl263_127
<=> sP3(bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_127])]) ).
fof(f7833,plain,
( spl263_10
<=> is_fun_pname_bool(bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_10])]) ).
fof(f8145,plain,
( sP3(bot_bo844097828e_bool)
| ~ spl263_10
| ~ spl263_36 ),
inference(resolution,[],[f7957,f7835]) ).
fof(f7835,plain,
( is_fun_pname_bool(bot_bo844097828e_bool)
| ~ spl263_10 ),
inference(avatar_component_clause,[],[f7833]) ).
fof(f8366,plain,
( spl263_78
| ~ spl263_10
| ~ spl263_35 ),
inference(avatar_split_clause,[],[f8143,f7952,f7833,f8125]) ).
fof(f8125,plain,
( spl263_78
<=> sP1(bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_78])]) ).
fof(f8143,plain,
( sP1(bot_bo844097828e_bool)
| ~ spl263_10
| ~ spl263_35 ),
inference(resolution,[],[f7953,f7835]) ).
fof(f8365,plain,
spl263_126,
inference(avatar_split_clause,[],[f7367,f8363]) ).
fof(f8363,plain,
( spl263_126
<=> ! [X2,X3] : sP41(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_126])]) ).
fof(f7367,plain,
! [X2,X3] : sP41(X3,X2,X2,X3),
inference(equality_resolution,[],[f7366]) ).
fof(f7366,plain,
! [X2,X3,X0] :
( sP41(X0,X2,X2,X3)
| X0 != X3 ),
inference(equality_resolution,[],[f6990]) ).
fof(f6990,plain,
! [X2,X3,X0,X1] :
( sP41(X0,X1,X2,X3)
| X1 != X2
| X0 != X3 ),
inference(cnf_transformation,[],[f4793]) ).
fof(f8361,plain,
spl263_125,
inference(avatar_split_clause,[],[f7365,f8359]) ).
fof(f8359,plain,
( spl263_125
<=> ! [X1,X3] : sP41(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_125])]) ).
fof(f7365,plain,
! [X3,X1] : sP41(X1,X1,X3,X3),
inference(equality_resolution,[],[f7364]) ).
fof(f7364,plain,
! [X2,X3,X1] :
( sP41(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f6991]) ).
fof(f6991,plain,
! [X2,X3,X0,X1] :
( sP41(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f4793]) ).
fof(f8357,plain,
spl263_124,
inference(avatar_split_clause,[],[f7363,f8355]) ).
fof(f8355,plain,
( spl263_124
<=> ! [X2,X3] : sP40(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_124])]) ).
fof(f7363,plain,
! [X2,X3] : sP40(X3,X2,X2,X3),
inference(equality_resolution,[],[f7362]) ).
fof(f7362,plain,
! [X2,X3,X0] :
( sP40(X0,X2,X2,X3)
| X0 != X3 ),
inference(equality_resolution,[],[f6982]) ).
fof(f6982,plain,
! [X2,X3,X0,X1] :
( sP40(X0,X1,X2,X3)
| X1 != X2
| X0 != X3 ),
inference(cnf_transformation,[],[f4789]) ).
fof(f8353,plain,
spl263_123,
inference(avatar_split_clause,[],[f7361,f8351]) ).
fof(f8351,plain,
( spl263_123
<=> ! [X1,X3] : sP40(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_123])]) ).
fof(f7361,plain,
! [X3,X1] : sP40(X1,X1,X3,X3),
inference(equality_resolution,[],[f7360]) ).
fof(f7360,plain,
! [X2,X3,X1] :
( sP40(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f6983]) ).
fof(f6983,plain,
! [X2,X3,X0,X1] :
( sP40(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f4789]) ).
fof(f8349,plain,
spl263_122,
inference(avatar_split_clause,[],[f7359,f8347]) ).
fof(f8347,plain,
( spl263_122
<=> ! [X2,X3] : sP37(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_122])]) ).
fof(f7359,plain,
! [X2,X3] : sP37(X3,X2,X2,X3),
inference(equality_resolution,[],[f7358]) ).
fof(f7358,plain,
! [X2,X3,X0] :
( sP37(X0,X2,X2,X3)
| X0 != X3 ),
inference(equality_resolution,[],[f6969]) ).
fof(f6969,plain,
! [X2,X3,X0,X1] :
( sP37(X0,X1,X2,X3)
| X1 != X2
| X0 != X3 ),
inference(cnf_transformation,[],[f4779]) ).
fof(f8345,plain,
spl263_121,
inference(avatar_split_clause,[],[f7357,f8343]) ).
fof(f8343,plain,
( spl263_121
<=> ! [X1,X3] : sP37(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_121])]) ).
fof(f7357,plain,
! [X3,X1] : sP37(X1,X1,X3,X3),
inference(equality_resolution,[],[f7356]) ).
fof(f7356,plain,
! [X2,X3,X1] :
( sP37(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f6970]) ).
fof(f6970,plain,
! [X2,X3,X0,X1] :
( sP37(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f4779]) ).
fof(f8341,plain,
spl263_120,
inference(avatar_split_clause,[],[f7018,f8338]) ).
fof(f7018,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls,
inference(definition_unfolding,[],[f4849,f4830]) ).
fof(f4849,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f1223]) ).
fof(f1223,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8336,plain,
spl263_119,
inference(avatar_split_clause,[],[f5593,f8334]) ).
fof(f5593,plain,
! [X0] :
( is_fun_a_bool(sK117(X0))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f8332,plain,
spl263_118,
inference(avatar_split_clause,[],[f5592,f8330]) ).
fof(f8330,plain,
( spl263_118
<=> ! [X0] :
( is_a(sK116(X0))
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_118])]) ).
fof(f5592,plain,
! [X0] :
( is_a(sK116(X0))
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f4215]) ).
fof(f8328,plain,
spl263_117,
inference(avatar_split_clause,[],[f5586,f8326]) ).
fof(f5586,plain,
! [X0] :
( is_fun_a_bool(sK115(X0))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f8324,plain,
spl263_116,
inference(avatar_split_clause,[],[f5585,f8322]) ).
fof(f8322,plain,
( spl263_116
<=> ! [X0] :
( is_a(sK114(X0))
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_116])]) ).
fof(f5585,plain,
! [X0] :
( is_a(sK114(X0))
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f4211]) ).
fof(f8320,plain,
spl263_115,
inference(avatar_split_clause,[],[f5553,f8318]) ).
fof(f5553,plain,
! [X0] :
( is_fun_pname_bool(sK113(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f8316,plain,
spl263_114,
inference(avatar_split_clause,[],[f5552,f8314]) ).
fof(f8314,plain,
( spl263_114
<=> ! [X0] :
( is_pname(sK112(X0))
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_114])]) ).
fof(f5552,plain,
! [X0] :
( is_pname(sK112(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f4206]) ).
fof(f8312,plain,
spl263_113,
inference(avatar_split_clause,[],[f5546,f8310]) ).
fof(f5546,plain,
! [X0] :
( is_fun_pname_bool(sK111(X0))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f8308,plain,
spl263_112,
inference(avatar_split_clause,[],[f5545,f8306]) ).
fof(f8306,plain,
( spl263_112
<=> ! [X0] :
( is_pname(sK110(X0))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_112])]) ).
fof(f5545,plain,
! [X0] :
( is_pname(sK110(X0))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f4202]) ).
fof(f8304,plain,
spl263_111,
inference(avatar_split_clause,[],[f5404,f8302]) ).
fof(f5404,plain,
! [X0] :
( is_fun_a_bool(sK94(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f8300,plain,
spl263_110,
inference(avatar_split_clause,[],[f5403,f8298]) ).
fof(f8298,plain,
( spl263_110
<=> ! [X0] :
( is_a(sK93(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_110])]) ).
fof(f5403,plain,
! [X0] :
( is_a(sK93(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f4168]) ).
fof(f8296,plain,
spl263_109,
inference(avatar_split_clause,[],[f5381,f8294]) ).
fof(f5381,plain,
! [X0] :
( is_fun_pname_bool(sK91(X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f8292,plain,
spl263_108,
inference(avatar_split_clause,[],[f5380,f8290]) ).
fof(f8290,plain,
( spl263_108
<=> ! [X0] :
( is_pname(sK90(X0))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_108])]) ).
fof(f5380,plain,
! [X0] :
( is_pname(sK90(X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f4160]) ).
fof(f8288,plain,
spl263_107,
inference(avatar_split_clause,[],[f5028,f8286]) ).
fof(f5028,plain,
! [X0] :
( is_fun_a_bool(sK49(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f4012]) ).
fof(f8284,plain,
spl263_106,
inference(avatar_split_clause,[],[f5027,f8282]) ).
fof(f8282,plain,
( spl263_106
<=> ! [X0] :
( is_a(sK48(X0))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_106])]) ).
fof(f5027,plain,
! [X0] :
( is_a(sK48(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f4012]) ).
fof(f8280,plain,
spl263_105,
inference(avatar_split_clause,[],[f5022,f8278]) ).
fof(f5022,plain,
! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f2711]) ).
fof(f2711,plain,
! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( is_fun_a_bool(X0)
=> is_fun_a_bool(collect_a(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8276,plain,
spl263_104,
inference(avatar_split_clause,[],[f5021,f8274]) ).
fof(f8274,plain,
( spl263_104
<=> ! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_104])]) ).
fof(f5021,plain,
! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f2710]) ).
fof(f2710,plain,
! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,axiom,
! [X0] :
( is_fun_a_bool(X0)
=> is_fun949378684l_bool(p(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8272,plain,
spl263_103,
inference(avatar_split_clause,[],[f5001,f8270]) ).
fof(f5001,plain,
! [X0] :
( is_fun_pname_bool(sK43(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f8268,plain,
spl263_102,
inference(avatar_split_clause,[],[f5000,f8266]) ).
fof(f8266,plain,
( spl263_102
<=> ! [X0] :
( is_pname(sK42(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_102])]) ).
fof(f5000,plain,
! [X0] :
( is_pname(sK42(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f8264,plain,
spl263_101,
inference(avatar_split_clause,[],[f4997,f8262]) ).
fof(f4997,plain,
! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f2705]) ).
fof(f2705,plain,
! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( is_fun_pname_bool(X0)
=> is_fun_pname_bool(collect_pname(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8260,plain,
spl263_100,
inference(avatar_split_clause,[],[f4994,f8258]) ).
fof(f4994,plain,
! [X0] :
( is_fun_a_bool(cOMBK_bool_a(X0))
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2700]) ).
fof(f2700,plain,
! [X0] :
( is_fun_a_bool(cOMBK_bool_a(X0))
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( is_bool(X0)
=> is_fun_a_bool(cOMBK_bool_a(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8256,plain,
spl263_99,
inference(avatar_split_clause,[],[f4993,f8254]) ).
fof(f8254,plain,
( spl263_99
<=> ! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_99])]) ).
fof(f4993,plain,
! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f2699]) ).
fof(f2699,plain,
! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( is_fun949378684l_bool(X0)
=> is_fun949378684l_bool(collect_fun_a_bool(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8252,plain,
spl263_98,
inference(avatar_split_clause,[],[f4992,f8250]) ).
fof(f8250,plain,
( spl263_98
<=> ! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_98])]) ).
fof(f4992,plain,
! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f2698]) ).
fof(f2698,plain,
! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( is_fun1661590463l_bool(X0)
=> is_fun1661590463l_bool(collec1974731493e_bool(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8248,plain,
spl263_97,
inference(avatar_split_clause,[],[f4887,f8246]) ).
fof(f8246,plain,
( spl263_97
<=> ! [X0] : hAPP_nat_nat(cOMBI_nat,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_97])]) ).
fof(f4887,plain,
! [X0] : hAPP_nat_nat(cOMBI_nat,X0) = X0,
inference(cnf_transformation,[],[f1433]) ).
fof(f1433,plain,
! [X0] : hAPP_nat_nat(cOMBI_nat,X0) = X0,
inference(rectify,[],[f1324]) ).
fof(f1324,axiom,
! [X158] : hAPP_nat_nat(cOMBI_nat,X158) = X158,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8244,plain,
spl263_96,
inference(avatar_split_clause,[],[f4886,f8242]) ).
fof(f8242,plain,
( spl263_96
<=> ! [X0] : bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_96])]) ).
fof(f4886,plain,
! [X0] : bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool),
inference(cnf_transformation,[],[f1432]) ).
fof(f1432,plain,
! [X0] : bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool),
inference(rectify,[],[f722]) ).
fof(f722,axiom,
! [X8] : bot_bot_fun_a_bool = image_pname_a(X8,bot_bo844097828e_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8240,plain,
spl263_95,
inference(avatar_split_clause,[],[f4885,f8238]) ).
fof(f8238,plain,
( spl263_95
<=> ! [X0] : bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_95])]) ).
fof(f4885,plain,
! [X0] : bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool),
inference(cnf_transformation,[],[f1431]) ).
fof(f1431,plain,
! [X0] : bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool),
inference(rectify,[],[f721]) ).
fof(f721,axiom,
! [X8] : bot_bot_fun_int_bool = image_nat_int(X8,bot_bot_fun_nat_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8236,plain,
spl263_94,
inference(avatar_split_clause,[],[f4879,f8234]) ).
fof(f8234,plain,
( spl263_94
<=> ! [X0] : hAPP_nat_nat(suc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_94])]) ).
fof(f4879,plain,
! [X0] : hAPP_nat_nat(suc,X0) != X0,
inference(cnf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0] : hAPP_nat_nat(suc,X0) != X0,
inference(rectify,[],[f231]) ).
fof(f231,axiom,
! [X13] : hAPP_nat_nat(suc,X13) != X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8232,plain,
spl263_93,
inference(avatar_split_clause,[],[f4877,f8230]) ).
fof(f4877,plain,
! [X0] : zero_zero_nat != hAPP_nat_nat(suc,X0),
inference(cnf_transformation,[],[f1423]) ).
fof(f1423,plain,
! [X0] : zero_zero_nat != hAPP_nat_nat(suc,X0),
inference(rectify,[],[f1051]) ).
fof(f1051,axiom,
! [X128] : zero_zero_nat != hAPP_nat_nat(suc,X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8228,plain,
spl263_92,
inference(avatar_split_clause,[],[f4857,f8225]) ).
fof(f4857,plain,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8223,plain,
spl263_91,
inference(avatar_split_clause,[],[f4856,f8220]) ).
fof(f4856,plain,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8218,plain,
spl263_90,
inference(avatar_split_clause,[],[f4854,f8215]) ).
fof(f8215,plain,
( spl263_90
<=> bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_90])]) ).
fof(f4854,plain,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
inference(cnf_transformation,[],[f647]) ).
fof(f647,axiom,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8213,plain,
spl263_89,
inference(avatar_split_clause,[],[f4852,f8210]) ).
fof(f4852,plain,
bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
inference(cnf_transformation,[],[f645]) ).
fof(f645,axiom,
bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8208,plain,
spl263_88,
inference(avatar_split_clause,[],[f4851,f8205]) ).
fof(f4851,plain,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
inference(cnf_transformation,[],[f646]) ).
fof(f646,axiom,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8203,plain,
spl263_87,
inference(avatar_split_clause,[],[f4848,f8200]) ).
fof(f8198,plain,
spl263_86,
inference(avatar_split_clause,[],[f4844,f8195]) ).
fof(f4844,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8179,plain,
( spl263_85
| ~ spl263_4
| ~ spl263_38 ),
inference(avatar_split_clause,[],[f8148,f7964,f7803,f8176]) ).
fof(f8176,plain,
( spl263_85
<=> sP7(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_85])]) ).
fof(f7803,plain,
( spl263_4
<=> is_fun_a_bool(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_4])]) ).
fof(f8148,plain,
( sP7(g)
| ~ spl263_4
| ~ spl263_38 ),
inference(resolution,[],[f7965,f7805]) ).
fof(f7805,plain,
( is_fun_a_bool(g)
| ~ spl263_4 ),
inference(avatar_component_clause,[],[f7803]) ).
fof(f8164,plain,
( spl263_84
| ~ spl263_4
| ~ spl263_37 ),
inference(avatar_split_clause,[],[f8146,f7960,f7803,f8161]) ).
fof(f8146,plain,
( sP5(g)
| ~ spl263_4
| ~ spl263_37 ),
inference(resolution,[],[f7961,f7805]) ).
fof(f8159,plain,
( spl263_83
| ~ spl263_3
| ~ spl263_36 ),
inference(avatar_split_clause,[],[f8144,f7956,f7798,f8156]) ).
fof(f7798,plain,
( spl263_3
<=> is_fun_pname_bool(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_3])]) ).
fof(f8144,plain,
( sP3(u)
| ~ spl263_3
| ~ spl263_36 ),
inference(resolution,[],[f7957,f7800]) ).
fof(f7800,plain,
( is_fun_pname_bool(u)
| ~ spl263_3 ),
inference(avatar_component_clause,[],[f7798]) ).
fof(f8154,plain,
( spl263_82
| ~ spl263_3
| ~ spl263_35 ),
inference(avatar_split_clause,[],[f8142,f7952,f7798,f8151]) ).
fof(f8142,plain,
( sP1(u)
| ~ spl263_3
| ~ spl263_35 ),
inference(resolution,[],[f7953,f7800]) ).
fof(f8141,plain,
( ~ spl263_80
| ~ spl263_81 ),
inference(avatar_split_clause,[],[f7150,f8138,f8134]) ).
fof(f8138,plain,
( spl263_81
<=> sP4(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_81])]) ).
fof(f7150,plain,
( ~ sP4(bot_bot_fun_a_bool)
| ~ sP5(bot_bot_fun_a_bool) ),
inference(equality_resolution,[],[f5026]) ).
fof(f5026,plain,
! [X0] :
( bot_bot_fun_a_bool != X0
| ~ sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f4008]) ).
fof(f8132,plain,
( ~ spl263_78
| ~ spl263_79 ),
inference(avatar_split_clause,[],[f7144,f8129,f8125]) ).
fof(f8129,plain,
( spl263_79
<=> sP0(bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_79])]) ).
fof(f7144,plain,
( ~ sP0(bot_bo844097828e_bool)
| ~ sP1(bot_bo844097828e_bool) ),
inference(equality_resolution,[],[f4999]) ).
fof(f4999,plain,
! [X0] :
( bot_bo844097828e_bool != X0
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f3989]) ).
fof(f8123,plain,
~ spl263_77,
inference(avatar_split_clause,[],[f7013,f8120]) ).
fof(f8120,plain,
( spl263_77
<=> hBOOL(hAPP_int_bool(nat_neg,pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_77])]) ).
fof(f7013,plain,
~ hBOOL(hAPP_int_bool(nat_neg,pls)),
inference(definition_unfolding,[],[f4834,f4830]) ).
fof(f4834,plain,
~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
inference(cnf_transformation,[],[f1256]) ).
fof(f1256,axiom,
~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8118,plain,
spl263_76,
inference(avatar_split_clause,[],[f5227,f8116]) ).
fof(f5227,plain,
! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8114,plain,
spl263_75,
inference(avatar_split_clause,[],[f5226,f8112]) ).
fof(f5226,plain,
! [X0,X1] : is_fun_a_bool(image_int_a(X0,X1)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] : is_fun_a_bool(image_int_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8110,plain,
spl263_74,
inference(avatar_split_clause,[],[f5225,f8108]) ).
fof(f5225,plain,
! [X0,X1] : is_fun_a_bool(image_fun_int_bool_a(X0,X1)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] : is_fun_a_bool(image_fun_int_bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8106,plain,
spl263_73,
inference(avatar_split_clause,[],[f5224,f8104]) ).
fof(f5224,plain,
! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8102,plain,
spl263_72,
inference(avatar_split_clause,[],[f5223,f8100]) ).
fof(f5223,plain,
! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8098,plain,
spl263_71,
inference(avatar_split_clause,[],[f5222,f8096]) ).
fof(f5222,plain,
! [X0,X1] : is_fun_a_bool(hAPP_int_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0,X1] : is_fun_a_bool(hAPP_int_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8094,plain,
spl263_70,
inference(avatar_split_clause,[],[f5221,f8092]) ).
fof(f5221,plain,
! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8090,plain,
spl263_69,
inference(avatar_split_clause,[],[f5220,f8088]) ).
fof(f5220,plain,
! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8086,plain,
spl263_68,
inference(avatar_split_clause,[],[f5219,f8084]) ).
fof(f5219,plain,
! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8082,plain,
spl263_67,
inference(avatar_split_clause,[],[f5218,f8080]) ).
fof(f5218,plain,
! [X0,X1] : is_fun_pname_bool(image_62782965_pname(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] : is_fun_pname_bool(image_62782965_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8078,plain,
spl263_66,
inference(avatar_split_clause,[],[f5217,f8076]) ).
fof(f5217,plain,
! [X0,X1] : is_fun_pname_bool(image_int_pname(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] : is_fun_pname_bool(image_int_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8074,plain,
spl263_65,
inference(avatar_split_clause,[],[f5216,f8072]) ).
fof(f5216,plain,
! [X0,X1] : is_fun_pname_bool(hAPP_i7355787e_bool(X0,X1)),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1] : is_fun_pname_bool(hAPP_i7355787e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8070,plain,
spl263_64,
inference(avatar_split_clause,[],[f5215,f8068]) ).
fof(f8068,plain,
( spl263_64
<=> ! [X0,X1] : is_bool(hAPP_int_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_64])]) ).
fof(f5215,plain,
! [X0,X1] : is_bool(hAPP_int_bool(X0,X1)),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] : is_bool(hAPP_int_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8066,plain,
spl263_63,
inference(avatar_split_clause,[],[f5214,f8064]) ).
fof(f8064,plain,
( spl263_63
<=> ! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_63])]) ).
fof(f5214,plain,
! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)),
inference(cnf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8062,plain,
spl263_62,
inference(avatar_split_clause,[],[f5213,f8060]) ).
fof(f8060,plain,
( spl263_62
<=> ! [X0,X1] : is_bool(hAPP_f448129468l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_62])]) ).
fof(f5213,plain,
! [X0,X1] : is_bool(hAPP_f448129468l_bool(X0,X1)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0,X1] : is_bool(hAPP_f448129468l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8058,plain,
spl263_61,
inference(avatar_split_clause,[],[f5212,f8056]) ).
fof(f8056,plain,
( spl263_61
<=> ! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_61])]) ).
fof(f5212,plain,
! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)),
inference(cnf_transformation,[],[f96]) ).
fof(f96,axiom,
! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8054,plain,
spl263_60,
inference(avatar_split_clause,[],[f5211,f8052]) ).
fof(f8052,plain,
( spl263_60
<=> ! [X0,X1] : is_bool(hAPP_f215623910l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_60])]) ).
fof(f5211,plain,
! [X0,X1] : is_bool(hAPP_f215623910l_bool(X0,X1)),
inference(cnf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0,X1] : is_bool(hAPP_f215623910l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8050,plain,
spl263_59,
inference(avatar_split_clause,[],[f5210,f8048]) ).
fof(f8048,plain,
( spl263_59
<=> ! [X0,X1] : is_bool(finite_folding_one_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_59])]) ).
fof(f5210,plain,
! [X0,X1] : is_bool(finite_folding_one_a(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : is_bool(finite_folding_one_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8046,plain,
spl263_58,
inference(avatar_split_clause,[],[f5209,f8044]) ).
fof(f8044,plain,
( spl263_58
<=> ! [X0,X1] : is_bool(finite1626084323ne_int(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_58])]) ).
fof(f5209,plain,
! [X0,X1] : is_bool(finite1626084323ne_int(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : is_bool(finite1626084323ne_int(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8042,plain,
spl263_57,
inference(avatar_split_clause,[],[f5208,f8040]) ).
fof(f8040,plain,
( spl263_57
<=> ! [X0,X1] : is_bool(finite988810631ne_nat(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_57])]) ).
fof(f5208,plain,
! [X0,X1] : is_bool(finite988810631ne_nat(X0,X1)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] : is_bool(finite988810631ne_nat(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8038,plain,
spl263_56,
inference(avatar_split_clause,[],[f5207,f8036]) ).
fof(f8036,plain,
( spl263_56
<=> ! [X0,X1] : is_bool(finite1282449217_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_56])]) ).
fof(f5207,plain,
! [X0,X1] : is_bool(finite1282449217_pname(X0,X1)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] : is_bool(finite1282449217_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8034,plain,
spl263_55,
inference(avatar_split_clause,[],[f5206,f8032]) ).
fof(f8032,plain,
( spl263_55
<=> ! [X0,X1] : is_bool(finite89670078_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_55])]) ).
fof(f5206,plain,
! [X0,X1] : is_bool(finite89670078_pname(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] : is_bool(finite89670078_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8030,plain,
spl263_54,
inference(avatar_split_clause,[],[f5205,f8028]) ).
fof(f8028,plain,
( spl263_54
<=> ! [X0,X1] : is_bool(finite1819937229idem_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_54])]) ).
fof(f5205,plain,
! [X0,X1] : is_bool(finite1819937229idem_a(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] : is_bool(finite1819937229idem_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8026,plain,
spl263_53,
inference(avatar_split_clause,[],[f5204,f8024]) ).
fof(f8024,plain,
( spl263_53
<=> ! [X0,X1] : is_bool(finite1432773856em_int(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_53])]) ).
fof(f5204,plain,
! [X0,X1] : is_bool(finite1432773856em_int(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : is_bool(finite1432773856em_int(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8022,plain,
spl263_52,
inference(avatar_split_clause,[],[f5203,f8020]) ).
fof(f8020,plain,
( spl263_52
<=> ! [X0,X1] : is_bool(finite795500164em_nat(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_52])]) ).
fof(f5203,plain,
! [X0,X1] : is_bool(finite795500164em_nat(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] : is_bool(finite795500164em_nat(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8018,plain,
spl263_51,
inference(avatar_split_clause,[],[f5202,f8016]) ).
fof(f8016,plain,
( spl263_51
<=> ! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_51])]) ).
fof(f5202,plain,
! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)),
inference(cnf_transformation,[],[f97]) ).
fof(f97,axiom,
! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8014,plain,
spl263_50,
inference(avatar_split_clause,[],[f5201,f8012]) ).
fof(f8012,plain,
( spl263_50
<=> ! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_50])]) ).
fof(f5201,plain,
! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)),
inference(cnf_transformation,[],[f100]) ).
fof(f100,axiom,
! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8010,plain,
spl263_49,
inference(avatar_split_clause,[],[f5200,f8008]) ).
fof(f8008,plain,
( spl263_49
<=> ! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_49])]) ).
fof(f5200,plain,
! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)),
inference(cnf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8006,plain,
spl263_48,
inference(avatar_split_clause,[],[f5199,f8004]) ).
fof(f8004,plain,
( spl263_48
<=> ! [X0,X1] : is_bool(hAPP_f1593524852l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_48])]) ).
fof(f5199,plain,
! [X0,X1] : is_bool(hAPP_f1593524852l_bool(X0,X1)),
inference(cnf_transformation,[],[f99]) ).
fof(f99,axiom,
! [X0,X1] : is_bool(hAPP_f1593524852l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8002,plain,
spl263_47,
inference(avatar_split_clause,[],[f5198,f8000]) ).
fof(f8000,plain,
( spl263_47
<=> ! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_47])]) ).
fof(f5198,plain,
! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7998,plain,
spl263_46,
inference(avatar_split_clause,[],[f5197,f7996]) ).
fof(f7996,plain,
( spl263_46
<=> ! [X0,X1] : is_fun949378684l_bool(image_int_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_46])]) ).
fof(f5197,plain,
! [X0,X1] : is_fun949378684l_bool(image_int_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] : is_fun949378684l_bool(image_int_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7994,plain,
spl263_45,
inference(avatar_split_clause,[],[f5196,f7992]) ).
fof(f7992,plain,
( spl263_45
<=> ! [X0,X1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_45])]) ).
fof(f5196,plain,
! [X0,X1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X0,X1)),
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0,X1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7990,plain,
spl263_44,
inference(avatar_split_clause,[],[f5195,f7988]) ).
fof(f7988,plain,
( spl263_44
<=> ! [X0,X1] : is_fun949378684l_bool(hAPP_i888906320l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_44])]) ).
fof(f5195,plain,
! [X0,X1] : is_fun949378684l_bool(hAPP_i888906320l_bool(X0,X1)),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0,X1] : is_fun949378684l_bool(hAPP_i888906320l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7986,plain,
spl263_43,
inference(avatar_split_clause,[],[f5194,f7984]) ).
fof(f7984,plain,
( spl263_43
<=> ! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_43])]) ).
fof(f5194,plain,
! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7982,plain,
spl263_42,
inference(avatar_split_clause,[],[f5193,f7980]) ).
fof(f7980,plain,
( spl263_42
<=> ! [X0,X1] : is_fun1661590463l_bool(image_637364955e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_42])]) ).
fof(f5193,plain,
! [X0,X1] : is_fun1661590463l_bool(image_637364955e_bool(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] : is_fun1661590463l_bool(image_637364955e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7978,plain,
spl263_41,
inference(avatar_split_clause,[],[f5192,f7976]) ).
fof(f7976,plain,
( spl263_41
<=> ! [X0,X1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_41])]) ).
fof(f5192,plain,
! [X0,X1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X0,X1)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7974,plain,
spl263_40,
inference(avatar_split_clause,[],[f5191,f7972]) ).
fof(f7972,plain,
( spl263_40
<=> ! [X0,X1] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_40])]) ).
fof(f5191,plain,
! [X0,X1] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(X0,X1)),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0,X1] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7970,plain,
spl263_39,
inference(avatar_split_clause,[],[f5190,f7968]) ).
fof(f7968,plain,
( spl263_39
<=> ! [X0,X1] : is_a(hAPP_int_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_39])]) ).
fof(f5190,plain,
! [X0,X1] : is_a(hAPP_int_a(X0,X1)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] : is_a(hAPP_int_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7966,plain,
spl263_38,
inference(avatar_split_clause,[],[f5041,f7964]) ).
fof(f5041,plain,
! [X0] :
( sP7(X0)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f3922]) ).
fof(f3922,plain,
! [X0] :
( sP7(X0)
| ~ is_fun_a_bool(X0) ),
inference(definition_folding,[],[f2716,f3921,f3920]) ).
fof(f2716,plain,
! [X0] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0
& is_a(X2)
& is_fun_a_bool(X1) )
| bot_bot_fun_a_bool = X0 ) )
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0] :
( is_fun_a_bool(X0)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0
& is_a(X2)
& is_fun_a_bool(X1) )
| bot_bot_fun_a_bool = X0 ) ) ),
inference(rectify,[],[f798]) ).
fof(f798,axiom,
! [X7] :
( is_fun_a_bool(X7)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
<=> ( ? [X80,X77] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X80))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X77),X80) = X7
& is_a(X77)
& is_fun_a_bool(X80) )
| bot_bot_fun_a_bool = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7962,plain,
spl263_37,
inference(avatar_split_clause,[],[f5032,f7960]) ).
fof(f5032,plain,
! [X0] :
( sP5(X0)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f3919]) ).
fof(f3919,plain,
! [X0] :
( sP5(X0)
| ~ is_fun_a_bool(X0) ),
inference(definition_folding,[],[f2715,f3918,f3917]) ).
fof(f2715,plain,
! [X0] :
( ( bot_bot_fun_a_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0
& is_fun_a_bool(X2)
& is_a(X1) ) )
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f1542]) ).
fof(f1542,plain,
! [X0] :
( is_fun_a_bool(X0)
=> ( bot_bot_fun_a_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0
& is_fun_a_bool(X2)
& is_a(X1) ) ) ),
inference(rectify,[],[f806]) ).
fof(f806,axiom,
! [X4] :
( is_fun_a_bool(X4)
=> ( bot_bot_fun_a_bool != X4
<=> ? [X29,X82] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X82))
& hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),X82) = X4
& is_fun_a_bool(X82)
& is_a(X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7958,plain,
spl263_36,
inference(avatar_split_clause,[],[f5014,f7956]) ).
fof(f5014,plain,
! [X0] :
( sP3(X0)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f3916]) ).
fof(f3916,plain,
! [X0] :
( sP3(X0)
| ~ is_fun_pname_bool(X0) ),
inference(definition_folding,[],[f2707,f3915,f3914]) ).
fof(f2707,plain,
! [X0] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0
& is_pname(X2)
& is_fun_pname_bool(X1) )
| bot_bo844097828e_bool = X0 ) )
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0] :
( is_fun_pname_bool(X0)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
<=> ( ? [X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0
& is_pname(X2)
& is_fun_pname_bool(X1) )
| bot_bo844097828e_bool = X0 ) ) ),
inference(rectify,[],[f801]) ).
fof(f801,axiom,
! [X7] :
( is_fun_pname_bool(X7)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
<=> ( ? [X80,X77] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X80))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X77),X80) = X7
& is_pname(X77)
& is_fun_pname_bool(X80) )
| bot_bo844097828e_bool = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7954,plain,
spl263_35,
inference(avatar_split_clause,[],[f5005,f7952]) ).
fof(f5005,plain,
! [X0] :
( sP1(X0)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f3913]) ).
fof(f3913,plain,
! [X0] :
( sP1(X0)
| ~ is_fun_pname_bool(X0) ),
inference(definition_folding,[],[f2706,f3912,f3911]) ).
fof(f2706,plain,
! [X0] :
( ( bot_bo844097828e_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0
& is_fun_pname_bool(X2)
& is_pname(X1) ) )
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0] :
( is_fun_pname_bool(X0)
=> ( bot_bo844097828e_bool != X0
<=> ? [X1,X2] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0
& is_fun_pname_bool(X2)
& is_pname(X1) ) ) ),
inference(rectify,[],[f809]) ).
fof(f809,axiom,
! [X4] :
( is_fun_pname_bool(X4)
=> ( bot_bo844097828e_bool != X4
<=> ? [X29,X82] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X82))
& hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X29),X82) = X4
& is_fun_pname_bool(X82)
& is_pname(X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7950,plain,
spl263_34,
inference(avatar_split_clause,[],[f4876,f7948]) ).
fof(f7946,plain,
spl263_33,
inference(avatar_split_clause,[],[f4875,f7944]) ).
fof(f7944,plain,
( spl263_33
<=> ! [X0] : number_number_of_int(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl263_33])]) ).
fof(f7942,plain,
spl263_32,
inference(avatar_split_clause,[],[f4874,f7940]) ).
fof(f7938,plain,
spl263_31,
inference(avatar_split_clause,[],[f4841,f7935]) ).
fof(f7935,plain,
( spl263_31
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_31])]) ).
fof(f4841,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
inference(cnf_transformation,[],[f605]) ).
fof(f605,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7933,plain,
spl263_30,
inference(avatar_split_clause,[],[f4840,f7930]) ).
fof(f7930,plain,
( spl263_30
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_30])]) ).
fof(f4840,plain,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
inference(cnf_transformation,[],[f604]) ).
fof(f604,axiom,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7928,plain,
spl263_29,
inference(avatar_split_clause,[],[f4839,f7925]) ).
fof(f7925,plain,
( spl263_29
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_29])]) ).
fof(f4839,plain,
hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
inference(cnf_transformation,[],[f607]) ).
fof(f607,axiom,
hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7923,plain,
spl263_28,
inference(avatar_split_clause,[],[f4838,f7920]) ).
fof(f7920,plain,
( spl263_28
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_28])]) ).
fof(f4838,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
inference(cnf_transformation,[],[f606]) ).
fof(f606,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7918,plain,
spl263_27,
inference(avatar_split_clause,[],[f4836,f7915]) ).
fof(f7915,plain,
( spl263_27
<=> zero_zero_nat = number_number_of_nat(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_27])]) ).
fof(f4836,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(cnf_transformation,[],[f1285]) ).
fof(f1285,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7913,plain,
~ spl263_26,
inference(avatar_split_clause,[],[f4833,f7910]) ).
fof(f4833,plain,
~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
inference(cnf_transformation,[],[f1255]) ).
fof(f1255,axiom,
~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7908,plain,
spl263_25,
inference(avatar_split_clause,[],[f4812,f7906]) ).
fof(f4812,plain,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7904,plain,
spl263_24,
inference(avatar_split_clause,[],[f4806,f7901]) ).
fof(f4806,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(cnf_transformation,[],[f1409]) ).
fof(f1409,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7899,plain,
~ spl263_23,
inference(avatar_split_clause,[],[f4801,f7896]) ).
fof(f4801,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1417]) ).
fof(f1417,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(flattening,[],[f1416]) ).
fof(f1416,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[],[f1415]) ).
fof(f1415,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7894,plain,
spl263_22,
inference(avatar_split_clause,[],[f7641,f7891]) ).
fof(f7891,plain,
( spl263_22
<=> sP19(zero_zero_nat,one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_22])]) ).
fof(f7641,plain,
sP19(zero_zero_nat,one_one_nat),
inference(forward_demodulation,[],[f7290,f4848]) ).
fof(f7290,plain,
sP19(zero_zero_nat,hAPP_nat_nat(suc,zero_zero_nat)),
inference(equality_resolution,[],[f7289]) ).
fof(f7289,plain,
! [X1] :
( sP19(zero_zero_nat,X1)
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ),
inference(equality_resolution,[],[f6031]) ).
fof(f6031,plain,
! [X0,X1] :
( sP19(X0,X1)
| zero_zero_nat != X0
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ),
inference(cnf_transformation,[],[f4404]) ).
fof(f7889,plain,
spl263_21,
inference(avatar_split_clause,[],[f7640,f7886]) ).
fof(f7886,plain,
( spl263_21
<=> sP19(one_one_nat,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_21])]) ).
fof(f7640,plain,
sP19(one_one_nat,zero_zero_nat),
inference(forward_demodulation,[],[f7288,f4848]) ).
fof(f7288,plain,
sP19(hAPP_nat_nat(suc,zero_zero_nat),zero_zero_nat),
inference(equality_resolution,[],[f7287]) ).
fof(f7287,plain,
! [X1] :
( sP19(hAPP_nat_nat(suc,zero_zero_nat),X1)
| zero_zero_nat != X1 ),
inference(equality_resolution,[],[f6032]) ).
fof(f6032,plain,
! [X0,X1] :
( sP19(X0,X1)
| hAPP_nat_nat(suc,zero_zero_nat) != X0
| zero_zero_nat != X1 ),
inference(cnf_transformation,[],[f4404]) ).
fof(f7884,plain,
spl263_20,
inference(avatar_split_clause,[],[f7633,f7881]) ).
fof(f7881,plain,
( spl263_20
<=> sP18(zero_zero_nat,one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_20])]) ).
fof(f7633,plain,
sP18(zero_zero_nat,one_one_nat),
inference(forward_demodulation,[],[f7286,f4848]) ).
fof(f7286,plain,
sP18(zero_zero_nat,hAPP_nat_nat(suc,zero_zero_nat)),
inference(equality_resolution,[],[f7285]) ).
fof(f7285,plain,
! [X1] :
( sP18(zero_zero_nat,X1)
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ),
inference(equality_resolution,[],[f6023]) ).
fof(f6023,plain,
! [X0,X1] :
( sP18(X0,X1)
| zero_zero_nat != X0
| hAPP_nat_nat(suc,zero_zero_nat) != X1 ),
inference(cnf_transformation,[],[f4400]) ).
fof(f7879,plain,
spl263_19,
inference(avatar_split_clause,[],[f7632,f7876]) ).
fof(f7876,plain,
( spl263_19
<=> sP18(one_one_nat,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_19])]) ).
fof(f7632,plain,
sP18(one_one_nat,zero_zero_nat),
inference(forward_demodulation,[],[f7284,f4848]) ).
fof(f7284,plain,
sP18(hAPP_nat_nat(suc,zero_zero_nat),zero_zero_nat),
inference(equality_resolution,[],[f7283]) ).
fof(f7283,plain,
! [X1] :
( sP18(hAPP_nat_nat(suc,zero_zero_nat),X1)
| zero_zero_nat != X1 ),
inference(equality_resolution,[],[f6024]) ).
fof(f6024,plain,
! [X0,X1] :
( sP18(X0,X1)
| hAPP_nat_nat(suc,zero_zero_nat) != X0
| zero_zero_nat != X1 ),
inference(cnf_transformation,[],[f4400]) ).
fof(f7874,plain,
~ spl263_18,
inference(avatar_split_clause,[],[f7012,f7871]) ).
fof(f7871,plain,
( spl263_18
<=> one_one_int = pls ),
introduced(avatar_definition,[new_symbols(naming,[spl263_18])]) ).
fof(f7012,plain,
one_one_int != pls,
inference(definition_unfolding,[],[f4828,f4830]) ).
fof(f4828,plain,
one_one_int != zero_zero_int,
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7869,plain,
spl263_17,
inference(avatar_split_clause,[],[f4871,f7867]) ).
fof(f7867,plain,
( spl263_17
<=> ! [X0] : is_bool(wt(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_17])]) ).
fof(f4871,plain,
! [X0] : is_bool(wt(X0)),
inference(cnf_transformation,[],[f106]) ).
fof(f106,axiom,
! [X0] : is_bool(wt(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7865,plain,
spl263_16,
inference(avatar_split_clause,[],[f4870,f7863]) ).
fof(f7863,plain,
( spl263_16
<=> ! [X0] : is_a(mgt(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_16])]) ).
fof(f4870,plain,
! [X0] : is_a(mgt(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f104,axiom,
! [X0] : is_a(mgt(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7861,plain,
spl263_15,
inference(avatar_split_clause,[],[f4832,f7858]) ).
fof(f7858,plain,
( spl263_15
<=> is_pname(undefined_pname(pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_15])]) ).
fof(f4832,plain,
is_pname(undefined_pname(pname)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
is_pname(undefined_pname(pname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7856,plain,
spl263_14,
inference(avatar_split_clause,[],[f4831,f7853]) ).
fof(f7853,plain,
( spl263_14
<=> is_a(undefined_a(x_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_14])]) ).
fof(f4831,plain,
is_a(undefined_a(x_a)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
is_a(undefined_a(x_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7851,plain,
spl263_13,
inference(avatar_split_clause,[],[f7153,f7848]) ).
fof(f7848,plain,
( spl263_13
<=> sP6(bot_bot_fun_a_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_13])]) ).
fof(f7153,plain,
sP6(bot_bot_fun_a_bool),
inference(equality_resolution,[],[f5039]) ).
fof(f5039,plain,
! [X0] :
( sP6(X0)
| bot_bot_fun_a_bool != X0 ),
inference(cnf_transformation,[],[f4018]) ).
fof(f7846,plain,
spl263_12,
inference(avatar_split_clause,[],[f7147,f7843]) ).
fof(f7843,plain,
( spl263_12
<=> sP2(bot_bo844097828e_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_12])]) ).
fof(f7147,plain,
sP2(bot_bo844097828e_bool),
inference(equality_resolution,[],[f5012]) ).
fof(f5012,plain,
! [X0] :
( sP2(X0)
| bot_bo844097828e_bool != X0 ),
inference(cnf_transformation,[],[f3999]) ).
fof(f7841,plain,
spl263_11,
inference(avatar_split_clause,[],[f4827,f7838]) ).
fof(f4827,plain,
is_fun_a_bool(bot_bot_fun_a_bool),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
is_fun_a_bool(bot_bot_fun_a_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7836,plain,
spl263_10,
inference(avatar_split_clause,[],[f4826,f7833]) ).
fof(f4826,plain,
is_fun_pname_bool(bot_bo844097828e_bool),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
is_fun_pname_bool(bot_bo844097828e_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7831,plain,
spl263_9,
inference(avatar_split_clause,[],[f4825,f7828]) ).
fof(f4825,plain,
is_bool(fFalse),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
is_bool(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7826,plain,
spl263_8,
inference(avatar_split_clause,[],[f4824,f7823]) ).
fof(f7823,plain,
( spl263_8
<=> is_bool(bot_bot_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_8])]) ).
fof(f4824,plain,
is_bool(bot_bot_bool),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
is_bool(bot_bot_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7821,plain,
spl263_7,
inference(avatar_split_clause,[],[f4823,f7818]) ).
fof(f7818,plain,
( spl263_7
<=> is_bool(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_7])]) ).
fof(f4823,plain,
is_bool(fTrue),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
is_bool(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7816,plain,
spl263_6,
inference(avatar_split_clause,[],[f4822,f7813]) ).
fof(f7813,plain,
( spl263_6
<=> is_fun949378684l_bool(finite_finite_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_6])]) ).
fof(f4822,plain,
is_fun949378684l_bool(finite_finite_a),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
is_fun949378684l_bool(finite_finite_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7811,plain,
~ spl263_5,
inference(avatar_split_clause,[],[f4821,f7808]) ).
fof(f4821,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f1314]) ).
fof(f1314,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7806,plain,
spl263_4,
inference(avatar_split_clause,[],[f4805,f7803]) ).
fof(f4805,plain,
is_fun_a_bool(g),
inference(cnf_transformation,[],[f101]) ).
fof(f101,axiom,
is_fun_a_bool(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7801,plain,
spl263_3,
inference(avatar_split_clause,[],[f4804,f7798]) ).
fof(f4804,plain,
is_fun_pname_bool(u),
inference(cnf_transformation,[],[f103]) ).
fof(f103,axiom,
is_fun_pname_bool(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7796,plain,
spl263_2,
inference(avatar_split_clause,[],[f4803,f7793]) ).
fof(f7793,plain,
( spl263_2
<=> is_fun1661590463l_bool(finite_finite_pname) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_2])]) ).
fof(f4803,plain,
is_fun1661590463l_bool(finite_finite_pname),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
is_fun1661590463l_bool(finite_finite_pname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7791,plain,
spl263_1,
inference(avatar_split_clause,[],[f4802,f7788]) ).
fof(f7788,plain,
( spl263_1
<=> is_pname(pn) ),
introduced(avatar_definition,[new_symbols(naming,[spl263_1])]) ).
fof(f4802,plain,
is_pname(pn),
inference(cnf_transformation,[],[f105]) ).
fof(f105,axiom,
is_pname(pn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW473+3 : TPTP v8.2.0. Released v5.3.0.
% 0.04/0.13 % Command : run_vampire %s %d SAT
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 04:44:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.22/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.22/0.36 Running first-order model finding
% 0.22/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27443)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27441)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27444)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27439)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:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27438)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.22/0.51 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (27440)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.22/0.53 % (27432)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.53 % (27442)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.94/0.56 % (27444)Instruction limit reached!
% 0.94/0.56 % (27444)------------------------------
% 0.94/0.56 % (27444)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.94/0.56 % (27444)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.94/0.56 % (27444)Termination reason: Time limit
% 0.94/0.56 % (27444)Termination phase: Blocked clause elimination
% 0.94/0.56
% 0.94/0.56 % (27444)Memory used [KB]: 4705
% 0.94/0.56 % (27444)Time elapsed: 0.056 s
% 0.94/0.56 % (27444)Instructions burned: 116 (million)
% 0.94/0.57 % (27442)Instruction limit reached!
% 0.94/0.57 % (27442)------------------------------
% 0.94/0.57 % (27442)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.94/0.57 % (27442)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.94/0.57 % (27442)Termination reason: Time limit
% 0.94/0.57 % (27442)Termination phase: Saturation
% 0.94/0.57
% 0.94/0.57 % (27442)Memory used [KB]: 4343
% 0.94/0.57 % (27442)Time elapsed: 0.040 s
% 0.94/0.57 % (27442)Instructions burned: 106 (million)
% 1.08/0.57 % (27443)Instruction limit reached!
% 1.08/0.57 % (27443)------------------------------
% 1.08/0.57 % (27443)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.08/0.57 % (27443)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.08/0.57 % (27443)Termination reason: Time limit
% 1.08/0.57 % (27443)Termination phase: Saturation
% 1.08/0.57
% 1.08/0.57 % (27443)Memory used [KB]: 4986
% 1.08/0.57 % (27443)Time elapsed: 0.069 s
% 1.08/0.57 % (27443)Instructions burned: 146 (million)
% 1.08/0.61 % (27432)Running in auto input_syntax mode. Trying TPTP
% 1.08/0.61 % (27454)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2998ds/404Mi)
% 1.08/0.61 % (27432)Running in auto input_syntax mode. Trying TPTP
% 1.08/0.61 % (27455)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 1.08/0.62 % (27432)Running in auto input_syntax mode. Trying TPTP
% 1.08/0.62 % (27456)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 1.47/0.70 % (27455)Instruction limit reached!
% 1.47/0.70 % (27455)------------------------------
% 1.47/0.70 % (27455)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.47/0.70 % (27455)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.47/0.70 % (27455)Termination reason: Time limit
% 1.47/0.70 % (27455)Termination phase: Saturation
% 1.47/0.70
% 1.47/0.70 % (27455)Memory used [KB]: 5387
% 1.47/0.70 % (27455)Time elapsed: 0.085 s
% 1.47/0.70 % (27455)Instructions burned: 176 (million)
% 1.86/0.73 % (27432)Running in auto input_syntax mode. Trying TPTP
% 1.86/0.73 % (27464)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2997ds/900Mi)
% 1.86/0.74 % (27456)Instruction limit reached!
% 1.86/0.74 % (27456)------------------------------
% 1.86/0.74 % (27456)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.86/0.74 % (27456)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.86/0.74 % (27456)Termination reason: Time limit
% 1.86/0.74 % (27456)Termination phase: Saturation
% 1.86/0.74
% 1.86/0.74 % (27456)Memory used [KB]: 6845
% 1.86/0.74 % (27456)Time elapsed: 0.118 s
% 1.86/0.74 % (27456)Instructions burned: 271 (million)
% 2.13/0.77 % (27432)Running in auto input_syntax mode. Trying TPTP
% 2.13/0.77 % (27465)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2997ds/7859Mi)
% 2.13/0.78 % (27454)Instruction limit reached!
% 2.13/0.78 % (27454)------------------------------
% 2.13/0.78 % (27454)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.13/0.78 % (27454)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.13/0.78 % (27454)Termination reason: Time limit
% 2.13/0.78 % (27454)Termination phase: Saturation
% 2.13/0.78
% 2.13/0.78 % (27454)Memory used [KB]: 6978
% 2.13/0.78 % (27454)Time elapsed: 0.200 s
% 2.13/0.78 % (27454)Instructions burned: 405 (million)
% 2.13/0.82 % (27432)Running in auto input_syntax mode. Trying TPTP
% 2.13/0.82 % (27480)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2996ds/2145Mi)
% 3.18/0.97 TRYING [1]
% 3.18/1.02 TRYING [2]
% 3.43/1.04 % (27464)Instruction limit reached!
% 3.43/1.04 % (27464)------------------------------
% 3.43/1.04 % (27464)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 3.43/1.04 % (27464)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 3.43/1.04 % (27464)Termination reason: Time limit
% 3.43/1.04 % (27464)Termination phase: Saturation
% 3.43/1.04
% 3.43/1.04 % (27464)Memory used [KB]: 12474
% 3.43/1.04 % (27464)Time elapsed: 0.309 s
% 3.43/1.04 % (27464)Instructions burned: 900 (million)
% 4.59/1.08 TRYING [1]
% 4.59/1.09 % (27432)Running in auto input_syntax mode. Trying TPTP
% 4.59/1.09 % (27605)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2993ds/1187Mi)
% 4.59/1.12 TRYING [2]
% 6.23/1.33 % (27439)First to succeed.
% 6.59/1.40 % (27439)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27432"
% 6.59/1.41 % (27432)Running in auto input_syntax mode. Trying TPTP
% 6.59/1.41 % (27439)Refutation found. Thanks to Tanya!
% 6.59/1.41 % SZS status Theorem for theBenchmark
% 6.59/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 7.05/1.45 % (27439)------------------------------
% 7.05/1.45 % (27439)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 7.05/1.45 % (27439)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 7.05/1.45 % (27439)Termination reason: Refutation
% 7.05/1.45
% 7.05/1.45 % (27439)Memory used [KB]: 20630
% 7.05/1.45 % (27439)Time elapsed: 0.900 s
% 7.05/1.45 % (27439)Instructions burned: 2310 (million)
% 7.05/1.45 % (27439)------------------------------
% 7.05/1.45 % (27439)------------------------------
% 7.05/1.45 % (27432)Success in time 1.009 s
%------------------------------------------------------------------------------