TSTP Solution File: SWW473+1 by Vampire-SAT---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW473+1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n023.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 18:52:09 EDT 2024
% Result : Theorem 10.24s 1.86s
% Output : Refutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1791
% Syntax : Number of formulae : 5947 ( 810 unt; 0 def)
% Number of atoms : 17666 (1774 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 20633 (8914 ~;9354 |; 279 &)
% (1468 <=>; 618 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 1390 (1388 usr;1381 prp; 0-2 aty)
% Number of functors : 241 ( 241 usr; 56 con; 0-3 aty)
% Number of variables : 10334 (10270 !; 64 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27241,plain,
$false,
inference(avatar_sat_refutation,[],[f2096,f2101,f2106,f2111,f2116,f2121,f2126,f2131,f2135,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2203,f2207,f2211,f2215,f2219,f2223,f2227,f2231,f2236,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2270,f2276,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2325,f2329,f2333,f2337,f2341,f2345,f2349,f2353,f2357,f2361,f2365,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2397,f2401,f2405,f2409,f2413,f2417,f2421,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2453,f2457,f2461,f2465,f2469,f2473,f2477,f2505,f2516,f2532,f2537,f2541,f2548,f2553,f2557,f2561,f2566,f2570,f2574,f2578,f2582,f2586,f2590,f2595,f2599,f2603,f2607,f2611,f2615,f2621,f2625,f2629,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2785,f2789,f2793,f2797,f2801,f2805,f2809,f2813,f2817,f2821,f2825,f2829,f2833,f2837,f2841,f2849,f2855,f2859,f2863,f2868,f2878,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2992,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3120,f3124,f3128,f3132,f3136,f3140,f3144,f3148,f3152,f3156,f3160,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3205,f3269,f3273,f3277,f3281,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3326,f3370,f3375,f3379,f3383,f3387,f3391,f3395,f3399,f3403,f3407,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3611,f3615,f3619,f3623,f3627,f3631,f3635,f3640,f3678,f3682,f3686,f3691,f3695,f3699,f3703,f3707,f3711,f3715,f3719,f3723,f3727,f3732,f3736,f3740,f3744,f3748,f3752,f3756,f3760,f3764,f3768,f3772,f3777,f3781,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f3813,f3845,f3849,f3853,f3960,f3965,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4037,f4041,f4045,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4235,f4266,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4359,f4363,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4548,f4552,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4608,f4636,f4640,f4644,f4648,f4652,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4765,f4769,f4774,f4784,f4789,f4793,f4804,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4871,f4962,f4966,f4977,f4981,f4999,f5003,f5007,f5011,f5016,f5020,f5025,f5045,f5130,f5134,f5138,f5142,f5146,f5151,f5155,f5160,f5165,f5192,f5196,f5200,f5204,f5208,f5212,f5217,f5223,f5228,f5255,f5283,f5287,f5291,f5295,f5299,f5303,f5307,f5311,f5316,f5320,f5324,f5328,f5370,f5414,f5418,f5429,f5435,f5462,f5466,f5470,f5476,f5502,f5506,f5567,f5573,f5579,f5585,f5604,f5608,f5612,f5629,f5633,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5902,f5906,f5910,f5914,f5918,f5922,f5926,f5930,f5934,f5938,f5942,f5946,f5950,f5954,f5958,f5962,f5966,f5970,f5974,f5978,f6011,f6164,f6266,f6330,f6369,f6406,f6420,f6424,f6431,f6455,f6469,f6473,f6478,f6499,f6503,f6507,f6511,f6524,f6531,f6535,f6540,f6545,f6578,f6610,f6664,f6723,f6771,f6775,f6781,f6785,f7075,f7079,f7083,f7089,f7093,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7125,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7163,f7167,f7173,f7177,f7181,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7215,f7219,f7223,f7230,f7235,f7242,f7247,f7254,f7259,f7264,f7268,f7299,f7304,f7307,f7347,f7490,f7543,f7584,f7634,f7699,f8046,f8079,f8083,f8087,f8091,f8096,f8103,f8107,f8111,f8115,f8119,f8123,f8127,f8131,f8135,f8139,f8143,f8147,f8151,f8217,f8222,f8231,f8235,f8240,f8328,f8333,f8338,f8342,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8384,f8388,f8392,f8396,f8400,f8404,f8408,f8412,f8416,f8420,f8425,f8429,f8433,f8437,f8441,f8445,f8449,f8453,f8457,f8579,f8652,f8656,f8660,f8664,f8668,f8672,f8676,f8680,f8684,f8688,f8692,f8696,f8700,f8706,f8710,f9021,f9056,f9060,f9065,f9069,f9073,f9077,f9081,f9085,f9089,f9093,f9097,f9101,f9105,f9109,f9113,f9117,f9121,f9125,f9129,f9133,f9137,f9141,f9145,f9149,f9153,f9157,f9161,f9165,f9169,f9173,f9177,f9181,f9185,f9189,f9193,f9198,f9202,f9206,f9210,f9214,f9363,f9700,f9782,f9790,f9794,f9798,f9802,f9806,f9810,f9814,f9818,f9825,f9829,f9833,f9837,f9841,f9845,f9849,f9853,f9857,f9861,f9868,f9943,f9947,f9951,f9955,f9959,f10263,f10267,f10272,f10276,f10282,f10379,f10383,f10387,f10391,f10401,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10445,f10449,f10453,f10460,f10462,f10470,f10472,f10477,f10666,f10829,f10831,f10843,f10847,f10851,f10855,f10859,f10864,f10868,f10873,f10938,f10942,f10946,f10950,f10954,f10958,f10962,f10966,f10971,f10976,f10980,f10984,f10988,f10992,f10996,f11000,f11004,f11008,f11016,f11192,f11482,f11645,f11650,f11661,f11716,f11720,f11724,f11728,f11732,f11739,f11744,f11820,f11861,f11864,f11873,f11877,f11884,f11895,f11899,f11906,f11910,f11914,f12162,f12180,f12187,f12230,f12234,f12238,f12242,f12246,f12250,f12254,f12269,f12273,f12277,f12281,f12286,f12290,f12294,f12298,f12302,f12306,f12311,f12315,f12726,f12730,f12734,f12738,f12742,f12746,f12750,f12754,f12758,f12762,f12766,f12770,f12774,f12778,f12782,f12786,f12790,f12794,f12798,f12802,f12806,f12810,f12814,f12818,f12822,f12826,f12830,f12834,f12838,f12842,f12846,f12850,f12854,f12858,f12862,f12866,f12870,f12874,f12878,f12882,f12886,f12890,f12894,f12898,f12902,f12906,f12910,f12914,f12918,f12922,f12926,f12930,f12934,f12938,f12942,f12976,f13258,f13438,f13617,f13776,f13859,f13863,f13867,f13871,f13875,f13998,f14002,f14006,f14010,f14014,f14018,f14022,f14026,f14030,f14034,f14038,f14042,f14046,f14050,f14054,f14058,f14062,f14066,f14070,f14074,f14078,f14082,f14086,f14090,f14094,f14098,f14102,f14110,f14583,f15766,f15898,f16352,f16377,f16381,f16385,f16389,f16393,f16397,f16407,f16411,f16415,f16419,f16423,f16427,f16431,f16435,f16439,f16491,f17061,f17118,f17122,f17126,f17130,f17134,f17138,f17149,f17153,f17157,f17161,f17165,f17169,f17173,f17177,f17181,f17185,f17190,f17194,f17198,f17202,f17206,f17210,f17214,f17218,f17222,f17226,f17230,f17234,f17238,f17242,f17246,f17250,f17254,f17258,f17262,f17266,f17270,f17274,f17278,f17282,f17286,f17290,f17294,f17298,f17302,f17306,f17310,f17314,f17320,f17324,f17328,f17332,f17336,f17340,f17344,f17348,f17352,f17356,f17372,f17376,f17380,f17384,f17389,f17402,f17406,f17410,f17414,f17418,f17422,f17426,f17430,f17434,f17438,f17471,f17767,f17910,f18384,f18400,f18404,f18408,f18412,f18416,f18420,f18424,f18428,f18432,f18436,f18440,f18444,f18448,f18452,f18456,f18460,f18464,f18468,f18472,f18476,f18480,f18484,f18488,f18492,f18496,f18600,f18842,f19131,f19170,f19174,f19178,f19182,f19186,f19190,f19194,f19198,f19202,f19206,f19210,f19214,f19218,f19222,f19226,f19230,f19234,f19238,f19266,f19270,f19274,f19278,f19282,f19286,f19290,f19294,f19298,f19302,f19306,f19310,f20002,f20194,f20252,f20256,f20260,f20264,f20268,f20272,f20277,f20290,f20295,f20328,f20332,f20336,f20340,f20344,f20348,f20352,f20356,f20898,f20974,f20980,f20992,f20996,f21000,f21004,f21011,f21015,f21019,f21023,f21027,f21031,f21035,f21039,f21043,f21047,f21052,f21056,f21060,f21064,f21068,f21072,f21076,f21080,f21084,f21088,f21092,f21099,f21103,f21107,f21111,f21115,f21119,f21123,f21127,f21131,f21135,f21144,f21148,f21152,f21156,f21160,f21164,f21168,f21172,f21176,f21180,f21184,f21188,f21192,f21196,f21200,f21507,f21783,f22049,f22053,f22057,f22061,f22065,f22069,f22073,f22077,f22081,f22085,f22089,f22093,f22097,f22101,f22105,f22109,f22113,f22236,f22766,f22770,f22774,f22778,f22782,f22786,f22790,f22794,f22798,f22802,f22806,f22810,f22814,f22818,f22822,f22826,f22830,f22834,f22838,f22842,f22846,f22850,f22854,f22858,f22862,f22866,f23433,f23658,f23662,f23666,f23670,f23674,f23678,f23682,f23686,f23690,f23694,f23698,f23702,f23708,f23714,f23718,f23722,f23726,f23730,f23734,f23738,f23742,f23746,f24280,f24739,f24783,f24788,f24811,f24815,f24819,f24823,f24827,f24851,f24855,f24859,f24863,f24867,f25130,f25245,f25249,f25253,f25259,f25276,f25280,f25284,f25288,f25292,f25296,f25300,f25304,f25308,f25312,f25313,f25317,f25321,f25325,f25329,f25333,f25337,f25797,f25967,f25972,f26057,f26061,f26067,f26089,f26093,f26097,f26101,f26105,f26109,f26113,f26117,f26121,f26126,f26130,f26435,f26439,f26443,f26447,f26451,f26455,f26459,f26463,f26468,f26472,f26476,f26740,f26764,f26776,f26780,f26784,f26788,f26792,f26796,f26800,f26804,f26962,f26966,f26972,f26989,f26993,f26997,f27001,f27005,f27104,f27168,f27172,f27176,f27180,f27184,f27197,f27201,f27205,f27209,f27213,f27217,f27221,f27225,f27229,f27240]) ).
fof(f27240,plain,
( ~ spl17_44
| ~ spl17_327
| spl17_1366 ),
inference(avatar_split_clause,[],[f27185,f27101,f3803,f2278]) ).
fof(f2278,plain,
( spl17_44
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f3803,plain,
( spl17_327
<=> ! [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,[spl17_327])]) ).
fof(f27101,plain,
( spl17_1366
<=> 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,[spl17_1366])]) ).
fof(f27185,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl17_327
| spl17_1366 ),
inference(resolution,[],[f27103,f3804]) ).
fof(f3804,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)) )
| ~ spl17_327 ),
inference(avatar_component_clause,[],[f3803]) ).
fof(f27103,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| spl17_1366 ),
inference(avatar_component_clause,[],[f27101]) ).
fof(f27229,plain,
( spl17_1380
| ~ spl17_388
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5683,f5631,f4346,f27227]) ).
fof(f27227,plain,
( spl17_1380
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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),X1))),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),X2))))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1380])]) ).
fof(f4346,plain,
( spl17_388
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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,[spl17_388])]) ).
fof(f5631,plain,
( spl17_504
<=> ! [X2,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))) = 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),X1))),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),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_504])]) ).
fof(f5683,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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),X1))),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),X2))))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) )
| ~ spl17_388
| ~ spl17_504 ),
inference(superposition,[],[f4347,f5632]) ).
fof(f5632,plain,
( ! [X2,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))) = 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),X1))),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),X2))))
| ~ spl17_504 ),
inference(avatar_component_clause,[],[f5631]) ).
fof(f4347,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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)))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_388 ),
inference(avatar_component_clause,[],[f4346]) ).
fof(f27225,plain,
( spl17_1379
| ~ spl17_384
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5682,f5631,f4330,f27223]) ).
fof(f27223,plain,
( spl17_1379
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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),X1))),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),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1379])]) ).
fof(f4330,plain,
( spl17_384
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_384])]) ).
fof(f5682,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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),X1))),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),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) )
| ~ spl17_384
| ~ spl17_504 ),
inference(superposition,[],[f4331,f5632]) ).
fof(f4331,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_384 ),
inference(avatar_component_clause,[],[f4330]) ).
fof(f27221,plain,
( spl17_1378
| ~ spl17_389
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5645,f5627,f4357,f27219]) ).
fof(f27219,plain,
( spl17_1378
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1378])]) ).
fof(f4357,plain,
( spl17_389
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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,[spl17_389])]) ).
fof(f5627,plain,
( spl17_503
<=> ! [X2,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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_503])]) ).
fof(f5645,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))) )
| ~ spl17_389
| ~ spl17_503 ),
inference(superposition,[],[f4358,f5628]) ).
fof(f5628,plain,
( ! [X2,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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))
| ~ spl17_503 ),
inference(avatar_component_clause,[],[f5627]) ).
fof(f4358,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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)))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_389 ),
inference(avatar_component_clause,[],[f4357]) ).
fof(f27217,plain,
( spl17_1377
| ~ spl17_385
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5644,f5627,f4334,f27215]) ).
fof(f27215,plain,
( spl17_1377
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1377])]) ).
fof(f4334,plain,
( spl17_385
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_385])]) ).
fof(f5644,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))) )
| ~ spl17_385
| ~ spl17_503 ),
inference(superposition,[],[f4335,f5628]) ).
fof(f4335,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_385 ),
inference(avatar_component_clause,[],[f4334]) ).
fof(f27213,plain,
( spl17_1376
| ~ spl17_405
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5595,f5583,f4587,f27211]) ).
fof(f27211,plain,
( spl17_1376
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1376])]) ).
fof(f4587,plain,
( spl17_405
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_405])]) ).
fof(f5583,plain,
( spl17_499
<=> ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_499])]) ).
fof(f5595,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),X3)) )
| ~ spl17_405
| ~ spl17_499 ),
inference(superposition,[],[f4588,f5584]) ).
fof(f5584,plain,
( ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ spl17_499 ),
inference(avatar_component_clause,[],[f5583]) ).
fof(f4588,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_405 ),
inference(avatar_component_clause,[],[f4587]) ).
fof(f27209,plain,
( spl17_1375
| ~ spl17_404
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5594,f5583,f4583,f27207]) ).
fof(f27207,plain,
( spl17_1375
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1375])]) ).
fof(f4583,plain,
( spl17_404
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_404])]) ).
fof(f5594,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) )
| ~ spl17_404
| ~ spl17_499 ),
inference(superposition,[],[f4584,f5584]) ).
fof(f4584,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_404 ),
inference(avatar_component_clause,[],[f4583]) ).
fof(f27205,plain,
( spl17_1374
| ~ spl17_403
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5593,f5583,f4579,f27203]) ).
fof(f27203,plain,
( spl17_1374
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1374])]) ).
fof(f4579,plain,
( spl17_403
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_403])]) ).
fof(f5593,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) )
| ~ spl17_403
| ~ spl17_499 ),
inference(superposition,[],[f4580,f5584]) ).
fof(f4580,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_403 ),
inference(avatar_component_clause,[],[f4579]) ).
fof(f27201,plain,
( spl17_1373
| ~ spl17_291
| ~ spl17_473 ),
inference(avatar_split_clause,[],[f5346,f5281,f3621,f27199]) ).
fof(f27199,plain,
( spl17_1373
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1373])]) ).
fof(f3621,plain,
( spl17_291
<=> ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_291])]) ).
fof(f5281,plain,
( spl17_473
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_473])]) ).
fof(f5346,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
| ~ spl17_291
| ~ spl17_473 ),
inference(superposition,[],[f5282,f3622]) ).
fof(f3622,plain,
( ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)
| ~ spl17_291 ),
inference(avatar_component_clause,[],[f3621]) ).
fof(f5282,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| 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))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_473 ),
inference(avatar_component_clause,[],[f5281]) ).
fof(f27197,plain,
( spl17_1372
| ~ spl17_291
| ~ spl17_473 ),
inference(avatar_split_clause,[],[f5340,f5281,f3621,f27195]) ).
fof(f27195,plain,
( spl17_1372
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1372])]) ).
fof(f5340,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1))) )
| ~ spl17_291
| ~ spl17_473 ),
inference(superposition,[],[f5282,f3622]) ).
fof(f27184,plain,
( spl17_1371
| ~ spl17_290
| ~ spl17_462 ),
inference(avatar_split_clause,[],[f5167,f5163,f3617,f27182]) ).
fof(f27182,plain,
( spl17_1371
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1371])]) ).
fof(f3617,plain,
( spl17_290
<=> ! [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,[spl17_290])]) ).
fof(f5163,plain,
( spl17_462
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_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,[spl17_462])]) ).
fof(f5167,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))) )
| ~ spl17_290
| ~ spl17_462 ),
inference(resolution,[],[f5164,f3618]) ).
fof(f3618,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl17_290 ),
inference(avatar_component_clause,[],[f3617]) ).
fof(f5164,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_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)) )
| ~ spl17_462 ),
inference(avatar_component_clause,[],[f5163]) ).
fof(f27180,plain,
( spl17_1370
| ~ spl17_288
| ~ spl17_429 ),
inference(avatar_split_clause,[],[f4798,f4791,f3609,f27178]) ).
fof(f27178,plain,
( spl17_1370
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1370])]) ).
fof(f3609,plain,
( spl17_288
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_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,[spl17_288])]) ).
fof(f4791,plain,
( spl17_429
<=> ! [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,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_429])]) ).
fof(f4798,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_288
| ~ spl17_429 ),
inference(resolution,[],[f4792,f3610]) ).
fof(f3610,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 )
| ~ spl17_288 ),
inference(avatar_component_clause,[],[f3609]) ).
fof(f4792,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,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_429 ),
inference(avatar_component_clause,[],[f4791]) ).
fof(f27176,plain,
( spl17_1369
| ~ spl17_289
| ~ spl17_429 ),
inference(avatar_split_clause,[],[f4797,f4791,f3613,f27174]) ).
fof(f27174,plain,
( spl17_1369
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1369])]) ).
fof(f3613,plain,
( spl17_289
<=> ! [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,[spl17_289])]) ).
fof(f4797,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_289
| ~ spl17_429 ),
inference(resolution,[],[f4792,f3614]) ).
fof(f3614,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_289 ),
inference(avatar_component_clause,[],[f3613]) ).
fof(f27172,plain,
( spl17_1368
| ~ spl17_288
| ~ spl17_426 ),
inference(avatar_split_clause,[],[f4779,f4772,f3609,f27170]) ).
fof(f27170,plain,
( spl17_1368
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1368])]) ).
fof(f4772,plain,
( spl17_426
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_426])]) ).
fof(f4779,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_288
| ~ spl17_426 ),
inference(resolution,[],[f4773,f3610]) ).
fof(f4773,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,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_426 ),
inference(avatar_component_clause,[],[f4772]) ).
fof(f27168,plain,
( spl17_1367
| ~ spl17_289
| ~ spl17_426 ),
inference(avatar_split_clause,[],[f4778,f4772,f3613,f27166]) ).
fof(f27166,plain,
( spl17_1367
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1367])]) ).
fof(f4778,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_289
| ~ spl17_426 ),
inference(resolution,[],[f4773,f3614]) ).
fof(f27104,plain,
( ~ spl17_1366
| ~ spl17_100
| spl17_43
| ~ spl17_1295 ),
inference(avatar_split_clause,[],[f25206,f24857,f2273,f2550,f27101]) ).
fof(f2550,plain,
( spl17_100
<=> 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,[spl17_100])]) ).
fof(f2273,plain,
( spl17_43
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f24857,plain,
( spl17_1295
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1295])]) ).
fof(f25206,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)))
| spl17_43
| ~ spl17_1295 ),
inference(resolution,[],[f24858,f2275]) ).
fof(f2275,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u)))
| spl17_43 ),
inference(avatar_component_clause,[],[f2273]) ).
fof(f24858,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X3)) )
| ~ spl17_1295 ),
inference(avatar_component_clause,[],[f24857]) ).
fof(f27005,plain,
( spl17_1365
| ~ spl17_233
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5600,f5583,f3195,f27003]) ).
fof(f27003,plain,
( spl17_1365
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1365])]) ).
fof(f3195,plain,
( spl17_233
<=> ! [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,[spl17_233])]) ).
fof(f5600,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)))) )
| ~ spl17_233
| ~ spl17_499 ),
inference(superposition,[],[f3196,f5584]) ).
fof(f3196,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)) )
| ~ spl17_233 ),
inference(avatar_component_clause,[],[f3195]) ).
fof(f27001,plain,
( spl17_1364
| ~ spl17_399
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5592,f5583,f4550,f26999]) ).
fof(f26999,plain,
( spl17_1364
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X3))
| hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2),X3))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1364])]) ).
fof(f4550,plain,
( spl17_399
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(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)),X2))
| hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_399])]) ).
fof(f5592,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X3))
| hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2),X3))
| X0 = X3 )
| ~ spl17_399
| ~ spl17_499 ),
inference(superposition,[],[f4551,f5584]) ).
fof(f4551,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(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)),X2))
| hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2 )
| ~ spl17_399 ),
inference(avatar_component_clause,[],[f4550]) ).
fof(f26997,plain,
( spl17_1363
| ~ spl17_185
| ~ spl17_490 ),
inference(avatar_split_clause,[],[f5488,f5460,f2909,f26995]) ).
fof(f26995,plain,
( spl17_1363
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1363])]) ).
fof(f2909,plain,
( spl17_185
<=> ! [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,[spl17_185])]) ).
fof(f5460,plain,
( spl17_490
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_490])]) ).
fof(f5488,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) )
| ~ spl17_185
| ~ spl17_490 ),
inference(superposition,[],[f5461,f2910]) ).
fof(f2910,plain,
( ! [X2,X0,X1] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2))
| ~ spl17_185 ),
inference(avatar_component_clause,[],[f2909]) ).
fof(f5461,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ spl17_490 ),
inference(avatar_component_clause,[],[f5460]) ).
fof(f26993,plain,
( spl17_1362
| ~ spl17_452
| ~ spl17_471 ),
inference(avatar_split_clause,[],[f5235,f5226,f5023,f26991]) ).
fof(f26991,plain,
( spl17_1362
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1362])]) ).
fof(f5023,plain,
( spl17_452
<=> ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_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))
| ~ 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,[spl17_452])]) ).
fof(f5226,plain,
( spl17_471
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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))
| 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,[spl17_471])]) ).
fof(f5235,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0)) )
| ~ spl17_452
| ~ spl17_471 ),
inference(duplicate_literal_removal,[],[f5230]) ).
fof(f5230,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_452
| ~ spl17_471 ),
inference(resolution,[],[f5227,f5024]) ).
fof(f5024,plain,
( ! [X0,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,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_452 ),
inference(avatar_component_clause,[],[f5023]) ).
fof(f5227,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_471 ),
inference(avatar_component_clause,[],[f5226]) ).
fof(f26989,plain,
( spl17_1361
| ~ spl17_450
| ~ spl17_469 ),
inference(avatar_split_clause,[],[f5219,f5215,f5014,f26987]) ).
fof(f26987,plain,
( spl17_1361
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1361])]) ).
fof(f5014,plain,
( spl17_450
<=> ! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_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,[spl17_450])]) ).
fof(f5215,plain,
( spl17_469
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_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,[spl17_469])]) ).
fof(f5219,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0)) )
| ~ spl17_450
| ~ spl17_469 ),
inference(duplicate_literal_removal,[],[f5218]) ).
fof(f5218,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_450
| ~ spl17_469 ),
inference(resolution,[],[f5216,f5015]) ).
fof(f5015,plain,
( ! [X0,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,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_450 ),
inference(avatar_component_clause,[],[f5014]) ).
fof(f5216,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_469 ),
inference(avatar_component_clause,[],[f5215]) ).
fof(f26972,plain,
( spl17_1360
| ~ spl17_942
| ~ spl17_1359 ),
inference(avatar_split_clause,[],[f26968,f26964,f12920,f26970]) ).
fof(f26970,plain,
( spl17_1360
<=> ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1360])]) ).
fof(f12920,plain,
( spl17_942
<=> ! [X0,X1] : 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)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_942])]) ).
fof(f26964,plain,
( spl17_1359
<=> ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),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)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1359])]) ).
fof(f26968,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
| ~ spl17_942
| ~ spl17_1359 ),
inference(forward_demodulation,[],[f26967,f12921]) ).
fof(f12921,plain,
( ! [X0,X1] : 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)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)
| ~ spl17_942 ),
inference(avatar_component_clause,[],[f12920]) ).
fof(f26967,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
| ~ spl17_942
| ~ spl17_1359 ),
inference(forward_demodulation,[],[f26965,f12921]) ).
fof(f26965,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),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)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
| ~ spl17_1359 ),
inference(avatar_component_clause,[],[f26964]) ).
fof(f26966,plain,
( spl17_1359
| ~ spl17_390
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f4621,f4579,f4361,f26964]) ).
fof(f4361,plain,
( spl17_390
<=> ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_390])]) ).
fof(f4621,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),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)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
| ~ spl17_390
| ~ spl17_403 ),
inference(forward_demodulation,[],[f4617,f2066]) ).
fof(f2066,plain,
! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(forward_demodulation,[],[f2065,f2025]) ).
fof(f2025,plain,
! [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))) = 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(forward_demodulation,[],[f2024,f1307]) ).
fof(f1307,plain,
! [X0] : collect_nat(X0) = X0,
inference(cnf_transformation,[],[f453]) ).
fof(f453,plain,
! [X0] : collect_nat(X0) = X0,
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X12] : collect_nat(X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2024,plain,
! [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))) = 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(forward_demodulation,[],[f1847,f1307]) ).
fof(f1847,plain,
! [X0,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)) = 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),collect_nat(X1)))),
inference(definition_unfolding,[],[f1391,f1382]) ).
fof(f1382,plain,
! [X0,X1] : 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,[],[f499]) ).
fof(f499,plain,
! [X0,X1] : 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,[],[f345]) ).
fof(f345,axiom,
! [X29,X35] : insert_nat(X29,X35) = 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),X35))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1391,plain,
! [X0,X1] : 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,[],[f508]) ).
fof(f508,plain,
! [X0,X1] : 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,[],[f280]) ).
fof(f280,axiom,
! [X7,X12] : 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(f2065,plain,
! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))) = 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))),
inference(forward_demodulation,[],[f2064,f1307]) ).
fof(f2064,plain,
! [X2,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),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))),
inference(forward_demodulation,[],[f2063,f1307]) ).
fof(f2063,plain,
! [X2,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),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),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),X2))))),
inference(forward_demodulation,[],[f1898,f1307]) ).
fof(f1898,plain,
! [X2,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),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))))) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),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),X2)))))),
inference(definition_unfolding,[],[f1682,f1382,f1382,f1382,f1382]) ).
fof(f1682,plain,
! [X2,X0,X1] : insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)),
inference(cnf_transformation,[],[f711]) ).
fof(f711,plain,
! [X0,X1,X2] : insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X10,X32,X4] : insert_nat(X10,insert_nat(X32,X4)) = insert_nat(X32,insert_nat(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4617,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) )
| ~ spl17_390
| ~ spl17_403 ),
inference(resolution,[],[f4580,f4362]) ).
fof(f4362,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| 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)) = X1 )
| ~ spl17_390 ),
inference(avatar_component_clause,[],[f4361]) ).
fof(f26962,plain,
( spl17_1358
| ~ spl17_350
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4403,f4264,f4051,f26960]) ).
fof(f26960,plain,
( spl17_1358
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))))),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1358])]) ).
fof(f4051,plain,
( spl17_350
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_350])]) ).
fof(f4264,plain,
( spl17_368
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_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,[spl17_368])]) ).
fof(f4403,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))))),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_350
| ~ spl17_368 ),
inference(resolution,[],[f4265,f4052]) ).
fof(f4052,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) )
| ~ spl17_350 ),
inference(avatar_component_clause,[],[f4051]) ).
fof(f4265,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) )
| ~ spl17_368 ),
inference(avatar_component_clause,[],[f4264]) ).
fof(f26804,plain,
( spl17_1357
| ~ spl17_338
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5681,f5631,f3981,f26802]) ).
fof(f26802,plain,
( spl17_1357
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),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),X1))),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),X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1357])]) ).
fof(f3981,plain,
( spl17_338
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_338])]) ).
fof(f5681,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),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),X1))),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),X2))))))
| ~ spl17_338
| ~ spl17_504 ),
inference(superposition,[],[f3982,f5632]) ).
fof(f3982,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ spl17_338 ),
inference(avatar_component_clause,[],[f3981]) ).
fof(f26800,plain,
( spl17_1356
| ~ spl17_341
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5643,f5627,f3993,f26798]) ).
fof(f26798,plain,
( spl17_1356
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1356])]) ).
fof(f3993,plain,
( spl17_341
<=> ! [X0,X1] :
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_341])]) ).
fof(f5643,plain,
( ! [X2,X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))
| ~ is_pname(X0) )
| ~ spl17_341
| ~ spl17_503 ),
inference(superposition,[],[f3994,f5628]) ).
fof(f3994,plain,
( ! [X0,X1] :
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) )
| ~ spl17_341 ),
inference(avatar_component_clause,[],[f3993]) ).
fof(f26796,plain,
( spl17_1355
| ~ spl17_340
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5642,f5627,f3989,f26794]) ).
fof(f26794,plain,
( spl17_1355
<=> ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1355])]) ).
fof(f3989,plain,
( spl17_340
<=> ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_340])]) ).
fof(f5642,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ spl17_340
| ~ spl17_503 ),
inference(superposition,[],[f3990,f5628]) ).
fof(f3990,plain,
( ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| ~ spl17_340 ),
inference(avatar_component_clause,[],[f3989]) ).
fof(f26792,plain,
( spl17_1354
| ~ spl17_619
| ~ spl17_1335 ),
inference(avatar_split_clause,[],[f26356,f26123,f7179,f26790]) ).
fof(f26790,plain,
( spl17_1354
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),image_pname_a(mgt_call,u)))
| is_pname(sK16(mgt_call,X0,sK9(mgt_call,u,image_pname_a(mgt_call,u)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1354])]) ).
fof(f7179,plain,
( spl17_619
<=> ! [X2,X0,X1] :
( is_pname(sK16(X0,X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),image_pname_a(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_619])]) ).
fof(f26123,plain,
( spl17_1335
<=> image_pname_a(mgt_call,u) = image_pname_a(mgt_call,sK9(mgt_call,u,image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1335])]) ).
fof(f26356,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),image_pname_a(mgt_call,u)))
| is_pname(sK16(mgt_call,X0,sK9(mgt_call,u,image_pname_a(mgt_call,u)))) )
| ~ spl17_619
| ~ spl17_1335 ),
inference(superposition,[],[f7180,f26125]) ).
fof(f26125,plain,
( image_pname_a(mgt_call,u) = image_pname_a(mgt_call,sK9(mgt_call,u,image_pname_a(mgt_call,u)))
| ~ spl17_1335 ),
inference(avatar_component_clause,[],[f26123]) ).
fof(f7180,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),image_pname_a(X0,X2)))
| is_pname(sK16(X0,X1,X2)) )
| ~ spl17_619 ),
inference(avatar_component_clause,[],[f7179]) ).
fof(f26788,plain,
( spl17_1353
| ~ spl17_374
| ~ spl17_487 ),
inference(avatar_split_clause,[],[f5421,f5416,f4289,f26786]) ).
fof(f26786,plain,
( spl17_1353
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1353])]) ).
fof(f4289,plain,
( spl17_374
<=> ! [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,[spl17_374])]) ).
fof(f5416,plain,
( spl17_487
<=> ! [X2,X0,X1] : image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_487])]) ).
fof(f5421,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)))) )
| ~ spl17_374
| ~ spl17_487 ),
inference(superposition,[],[f4290,f5417]) ).
fof(f5417,plain,
( ! [X2,X0,X1] : image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2))))
| ~ spl17_487 ),
inference(avatar_component_clause,[],[f5416]) ).
fof(f4290,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))) )
| ~ spl17_374 ),
inference(avatar_component_clause,[],[f4289]) ).
fof(f26784,plain,
( spl17_1352
| ~ spl17_185
| ~ spl17_381
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5382,f5309,f4318,f2909,f26782]) ).
fof(f26782,plain,
( spl17_1352
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X1),sK16(X1,X0,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1352])]) ).
fof(f4318,plain,
( spl17_381
<=> ! [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,sK16(X0,X1,X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_381])]) ).
fof(f5309,plain,
( spl17_480
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) = hAPP_fun_a_bool_nat(finite_card_a,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))))
| 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,[spl17_480])]) ).
fof(f5382,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X1),sK16(X1,X0,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) )
| ~ spl17_185
| ~ spl17_381
| ~ spl17_480 ),
inference(forward_demodulation,[],[f5375,f2910]) ).
fof(f5375,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,sK16(X1,X0,X2)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) )
| ~ spl17_381
| ~ spl17_480 ),
inference(resolution,[],[f5310,f4319]) ).
fof(f4319,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK16(X0,X1,X2))),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) )
| ~ spl17_381 ),
inference(avatar_component_clause,[],[f4318]) ).
fof(f5310,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) = hAPP_fun_a_bool_nat(finite_card_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_480 ),
inference(avatar_component_clause,[],[f5309]) ).
fof(f26780,plain,
( spl17_1351
| ~ spl17_292
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5379,f5309,f3625,f26778]) ).
fof(f26778,plain,
( spl17_1351
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| is_pname(sK7(X2,X0,X1))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1351])]) ).
fof(f3625,plain,
( spl17_292
<=> ! [X2,X0,X1] :
( is_pname(sK7(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,[spl17_292])]) ).
fof(f5379,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| is_pname(sK7(X2,X0,X1))
| ~ is_a(X2) )
| ~ spl17_292
| ~ spl17_480 ),
inference(resolution,[],[f5310,f3626]) ).
fof(f3626,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| is_pname(sK7(X0,X1,X2))
| ~ is_a(X0) )
| ~ spl17_292 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f26776,plain,
( spl17_1350
| ~ spl17_293
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5378,f5309,f3629,f26774]) ).
fof(f26774,plain,
( spl17_1350
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| is_pname(sK8(X2,X0,X1))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1350])]) ).
fof(f3629,plain,
( spl17_293
<=> ! [X2,X0,X1] :
( is_pname(sK8(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,[spl17_293])]) ).
fof(f5378,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| is_pname(sK8(X2,X0,X1))
| ~ is_a(X2) )
| ~ spl17_293
| ~ spl17_480 ),
inference(resolution,[],[f5310,f3630]) ).
fof(f3630,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| is_pname(sK8(X0,X1,X2))
| ~ is_a(X0) )
| ~ spl17_293 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f26764,plain,
( spl17_1349
| ~ spl17_333
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5679,f5631,f3958,f26762]) ).
fof(f26762,plain,
( spl17_1349
<=> ! [X2,X0,X1] :
( is_fun_a_bool(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),X1))),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),X2)))))
| ~ is_fun_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1349])]) ).
fof(f3958,plain,
( spl17_333
<=> ! [X0,X1] :
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_333])]) ).
fof(f5679,plain,
( ! [X2,X0,X1] :
( is_fun_a_bool(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),X1))),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),X2)))))
| ~ is_fun_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))
| ~ is_a(X0) )
| ~ spl17_333
| ~ spl17_504 ),
inference(superposition,[],[f3959,f5632]) ).
fof(f3959,plain,
( ! [X0,X1] :
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) )
| ~ spl17_333 ),
inference(avatar_component_clause,[],[f3958]) ).
fof(f26740,plain,
( ~ spl17_194
| spl17_1348
| ~ spl17_250
| ~ spl17_424 ),
inference(avatar_split_clause,[],[f4807,f4763,f3367,f26738,f3037]) ).
fof(f3037,plain,
( spl17_194
<=> 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,[spl17_194])]) ).
fof(f26738,plain,
( spl17_1348
<=> ! [X0] :
( hAPP_fun_a_bool_nat(finite_card_a,g) != hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1348])]) ).
fof(f3367,plain,
( spl17_250
<=> hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_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,[spl17_250])]) ).
fof(f4763,plain,
( spl17_424
<=> ! [X2,X0,X1] :
( X0 = X2
| hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),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,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_424])]) ).
fof(f4807,plain,
( ! [X0] :
( hAPP_fun_a_bool_nat(finite_card_a,g) != hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))
| hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) = X0
| ~ 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))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) )
| ~ spl17_250
| ~ spl17_424 ),
inference(superposition,[],[f4764,f3369]) ).
fof(f3369,plain,
( hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na))
| ~ spl17_250 ),
inference(avatar_component_clause,[],[f3367]) ).
fof(f4764,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),X1)
| X0 = 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,X1),X2)) )
| ~ spl17_424 ),
inference(avatar_component_clause,[],[f4763]) ).
fof(f26476,plain,
( spl17_1347
| ~ spl17_40
| ~ spl17_495 ),
inference(avatar_split_clause,[],[f5562,f5504,f2259,f26474]) ).
fof(f26474,plain,
( spl17_1347
<=> ! [X0,X1] :
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(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),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,[spl17_1347])]) ).
fof(f2259,plain,
( spl17_40
<=> ! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f5504,plain,
( spl17_495
<=> ! [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))) = 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),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,[spl17_495])]) ).
fof(f5562,plain,
( ! [X0,X1] :
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(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),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)))))) )
| ~ spl17_40
| ~ spl17_495 ),
inference(superposition,[],[f2260,f5505]) ).
fof(f5505,plain,
( ! [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))) = 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),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))))))
| ~ spl17_495 ),
inference(avatar_component_clause,[],[f5504]) ).
fof(f2260,plain,
( ! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) )
| ~ spl17_40 ),
inference(avatar_component_clause,[],[f2259]) ).
fof(f26472,plain,
( spl17_1346
| ~ spl17_41
| ~ spl17_494 ),
inference(avatar_split_clause,[],[f5534,f5500,f2263,f26470]) ).
fof(f26470,plain,
( spl17_1346
<=> ! [X0,X1] :
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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,[spl17_1346])]) ).
fof(f2263,plain,
( spl17_41
<=> ! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f5500,plain,
( spl17_494
<=> ! [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))) = 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),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,[spl17_494])]) ).
fof(f5534,plain,
( ! [X0,X1] :
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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)))))) )
| ~ spl17_41
| ~ spl17_494 ),
inference(superposition,[],[f2264,f5501]) ).
fof(f5501,plain,
( ! [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))) = 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),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))))))
| ~ spl17_494 ),
inference(avatar_component_clause,[],[f5500]) ).
fof(f2264,plain,
( ! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) )
| ~ spl17_41 ),
inference(avatar_component_clause,[],[f2263]) ).
fof(f26468,plain,
( ~ spl17_817
| spl17_1345
| ~ spl17_571
| ~ spl17_1335 ),
inference(avatar_split_clause,[],[f26355,f26123,f6422,f26465,f10818]) ).
fof(f10818,plain,
( spl17_817
<=> is_fun_a_bool(image_pname_a(mgt_call,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_817])]) ).
fof(f26465,plain,
( spl17_1345
<=> is_fun_pname_bool(sK10(image_pname_a(mgt_call,u),mgt_call,sK9(mgt_call,u,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1345])]) ).
fof(f6422,plain,
( spl17_571
<=> ! [X0,X1] :
( is_fun_pname_bool(sK10(image_pname_a(X0,X1),X0,X1))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_571])]) ).
fof(f26355,plain,
( is_fun_pname_bool(sK10(image_pname_a(mgt_call,u),mgt_call,sK9(mgt_call,u,image_pname_a(mgt_call,u))))
| ~ is_fun_a_bool(image_pname_a(mgt_call,u))
| ~ spl17_571
| ~ spl17_1335 ),
inference(superposition,[],[f6423,f26125]) ).
fof(f6423,plain,
( ! [X0,X1] :
( is_fun_pname_bool(sK10(image_pname_a(X0,X1),X0,X1))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_571 ),
inference(avatar_component_clause,[],[f6422]) ).
fof(f26463,plain,
( spl17_1344
| ~ spl17_257
| ~ spl17_491 ),
inference(avatar_split_clause,[],[f5494,f5464,f3397,f26461]) ).
fof(f26461,plain,
( spl17_1344
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1344])]) ).
fof(f3397,plain,
( spl17_257
<=> ! [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,[spl17_257])]) ).
fof(f5464,plain,
( spl17_491
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_491])]) ).
fof(f5494,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))) )
| ~ spl17_257
| ~ spl17_491 ),
inference(resolution,[],[f5465,f3398]) ).
fof(f3398,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_257 ),
inference(avatar_component_clause,[],[f3397]) ).
fof(f5465,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_491 ),
inference(avatar_component_clause,[],[f5464]) ).
fof(f26459,plain,
( spl17_1343
| ~ spl17_256
| ~ spl17_490 ),
inference(avatar_split_clause,[],[f5483,f5460,f3393,f26457]) ).
fof(f26457,plain,
( spl17_1343
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1343])]) ).
fof(f3393,plain,
( spl17_256
<=> ! [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,[spl17_256])]) ).
fof(f5483,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))) )
| ~ spl17_256
| ~ spl17_490 ),
inference(resolution,[],[f5461,f3394]) ).
fof(f3394,plain,
( ! [X0,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))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_256 ),
inference(avatar_component_clause,[],[f3393]) ).
fof(f26455,plain,
( spl17_1342
| ~ spl17_356
| ~ spl17_489 ),
inference(avatar_split_clause,[],[f5456,f5433,f4075,f26453]) ).
fof(f26453,plain,
( spl17_1342
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1342])]) ).
fof(f4075,plain,
( spl17_356
<=> ! [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,[spl17_356])]) ).
fof(f5433,plain,
( spl17_489
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_489])]) ).
fof(f5456,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X0))) )
| ~ spl17_356
| ~ spl17_489 ),
inference(resolution,[],[f5434,f4076]) ).
fof(f4076,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,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_356 ),
inference(avatar_component_clause,[],[f4075]) ).
fof(f5434,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_489 ),
inference(avatar_component_clause,[],[f5433]) ).
fof(f26451,plain,
( spl17_1341
| ~ spl17_185
| ~ spl17_483 ),
inference(avatar_split_clause,[],[f5395,f5322,f2909,f26449]) ).
fof(f26449,plain,
( spl17_1341
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| hAPP_pname_a(X0,X1) = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1341])]) ).
fof(f5322,plain,
( spl17_483
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ is_a(X1)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_483])]) ).
fof(f5395,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| hAPP_pname_a(X0,X1) = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ is_a(X2) )
| ~ spl17_185
| ~ spl17_483 ),
inference(superposition,[],[f5323,f2910]) ).
fof(f5323,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| X0 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ is_a(X1)
| ~ is_a(X0) )
| ~ spl17_483 ),
inference(avatar_component_clause,[],[f5322]) ).
fof(f26447,plain,
( spl17_1340
| ~ spl17_274
| ~ spl17_414 ),
inference(avatar_split_clause,[],[f4729,f4658,f3465,f26445]) ).
fof(f26445,plain,
( spl17_1340
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(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))),X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),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,[spl17_1340])]) ).
fof(f3465,plain,
( spl17_274
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_274])]) ).
fof(f4658,plain,
( spl17_414
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_414])]) ).
fof(f4729,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(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))),X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),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))))) )
| ~ spl17_274
| ~ spl17_414 ),
inference(resolution,[],[f4659,f3466]) ).
fof(f3466,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
| ~ spl17_274 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f4659,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl17_414 ),
inference(avatar_component_clause,[],[f4658]) ).
fof(f26443,plain,
( spl17_1339
| ~ spl17_272
| ~ spl17_411 ),
inference(avatar_split_clause,[],[f4715,f4646,f3457,f26441]) ).
fof(f26441,plain,
( spl17_1339
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(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))),X2)),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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,[spl17_1339])]) ).
fof(f3457,plain,
( spl17_272
<=> ! [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,sK4(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_272])]) ).
fof(f4646,plain,
( spl17_411
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_411])]) ).
fof(f4715,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(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))),X2)),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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))))) )
| ~ spl17_272
| ~ spl17_411 ),
inference(resolution,[],[f4647,f3458]) ).
fof(f3458,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(X0,X1)),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) )
| ~ spl17_272 ),
inference(avatar_component_clause,[],[f3457]) ).
fof(f4647,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) )
| ~ spl17_411 ),
inference(avatar_component_clause,[],[f4646]) ).
fof(f26439,plain,
( spl17_1338
| ~ spl17_371
| ~ spl17_410 ),
inference(avatar_split_clause,[],[f4711,f4642,f4277,f26437]) ).
fof(f26437,plain,
( spl17_1338
<=> ! [X2,X0,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| sK9(X1,X2,X0) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),sK9(X1,X2,X0)))
| ~ is_fun_pname_bool(sK9(X1,X2,X0))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1338])]) ).
fof(f4277,plain,
( spl17_371
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_371])]) ).
fof(f4642,plain,
( spl17_410
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK9(X0,X1,X2)),X1))
| ~ 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,[spl17_410])]) ).
fof(f4711,plain,
( ! [X2,X0,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| sK9(X1,X2,X0) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),sK9(X1,X2,X0)))
| ~ is_fun_pname_bool(sK9(X1,X2,X0))
| ~ is_fun_pname_bool(X2) )
| ~ spl17_371
| ~ spl17_410 ),
inference(resolution,[],[f4643,f4278]) ).
fof(f4278,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) )
| ~ spl17_371 ),
inference(avatar_component_clause,[],[f4277]) ).
fof(f4643,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK9(X0,X1,X2)),X1))
| ~ 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) )
| ~ spl17_410 ),
inference(avatar_component_clause,[],[f4642]) ).
fof(f26435,plain,
( spl17_1337
| ~ spl17_350
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4402,f4264,f4051,f26433]) ).
fof(f26433,plain,
( spl17_1337
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X2)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1337])]) ).
fof(f4402,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X2)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ spl17_350
| ~ spl17_368 ),
inference(resolution,[],[f4265,f4052]) ).
fof(f26130,plain,
( spl17_1336
| ~ spl17_365
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5591,f5583,f4111,f26128]) ).
fof(f26128,plain,
( spl17_1336
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1336])]) ).
fof(f4111,plain,
( spl17_365
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(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)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_365])]) ).
fof(f5591,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2),X3)) )
| ~ spl17_365
| ~ spl17_499 ),
inference(superposition,[],[f4112,f5584]) ).
fof(f4112,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(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)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) )
| ~ spl17_365 ),
inference(avatar_component_clause,[],[f4111]) ).
fof(f26126,plain,
( ~ spl17_817
| spl17_1335
| ~ spl17_938
| ~ spl17_1299 ),
inference(avatar_split_clause,[],[f25530,f25127,f12904,f26123,f10818]) ).
fof(f12904,plain,
( spl17_938
<=> ! [X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_938])]) ).
fof(f25127,plain,
( spl17_1299
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1299])]) ).
fof(f25530,plain,
( image_pname_a(mgt_call,u) = image_pname_a(mgt_call,sK9(mgt_call,u,image_pname_a(mgt_call,u)))
| ~ is_fun_a_bool(image_pname_a(mgt_call,u))
| ~ spl17_938
| ~ spl17_1299 ),
inference(resolution,[],[f25128,f12905]) ).
fof(f12905,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| image_pname_a(X0,X1) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_938 ),
inference(avatar_component_clause,[],[f12904]) ).
fof(f25128,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(mgt_call,u)))
| ~ spl17_1299 ),
inference(avatar_component_clause,[],[f25127]) ).
fof(f26121,plain,
( spl17_1334
| ~ spl17_364
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5590,f5583,f4107,f26119]) ).
fof(f26119,plain,
( spl17_1334
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1334])]) ).
fof(f4107,plain,
( spl17_364
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_364])]) ).
fof(f5590,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) )
| ~ spl17_364
| ~ spl17_499 ),
inference(superposition,[],[f4108,f5584]) ).
fof(f4108,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_364 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f26117,plain,
( spl17_1333
| ~ spl17_362
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5589,f5583,f4099,f26115]) ).
fof(f26115,plain,
( spl17_1333
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1333])]) ).
fof(f4099,plain,
( spl17_362
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_362])]) ).
fof(f5589,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))) )
| ~ spl17_362
| ~ spl17_499 ),
inference(superposition,[],[f4100,f5584]) ).
fof(f4100,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_362 ),
inference(avatar_component_clause,[],[f4099]) ).
fof(f26113,plain,
( spl17_1332
| ~ spl17_359
| ~ spl17_467 ),
inference(avatar_split_clause,[],[f5274,f5206,f4087,f26111]) ).
fof(f26111,plain,
( spl17_1332
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1332])]) ).
fof(f4087,plain,
( spl17_359
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_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,[spl17_359])]) ).
fof(f5206,plain,
( spl17_467
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),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,[spl17_467])]) ).
fof(f5274,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) )
| ~ spl17_359
| ~ spl17_467 ),
inference(resolution,[],[f5207,f4088]) ).
fof(f4088,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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)) )
| ~ spl17_359 ),
inference(avatar_component_clause,[],[f4087]) ).
fof(f5207,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ spl17_467 ),
inference(avatar_component_clause,[],[f5206]) ).
fof(f26109,plain,
( spl17_1331
| ~ spl17_360
| ~ spl17_467 ),
inference(avatar_split_clause,[],[f5273,f5206,f4091,f26107]) ).
fof(f26107,plain,
( spl17_1331
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1331])]) ).
fof(f4091,plain,
( spl17_360
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_360])]) ).
fof(f5273,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) )
| ~ spl17_360
| ~ spl17_467 ),
inference(resolution,[],[f5207,f4092]) ).
fof(f4092,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,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_360 ),
inference(avatar_component_clause,[],[f4091]) ).
fof(f26105,plain,
( spl17_1330
| ~ spl17_325
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5268,f5202,f3795,f26103]) ).
fof(f26103,plain,
( spl17_1330
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1330])]) ).
fof(f3795,plain,
( spl17_325
<=> ! [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,[spl17_325])]) ).
fof(f5202,plain,
( spl17_466
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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,[spl17_466])]) ).
fof(f5268,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
| ~ spl17_325
| ~ spl17_466 ),
inference(resolution,[],[f5203,f3796]) ).
fof(f3796,plain,
( ! [X2,X0,X1] :
( ~ 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))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
| ~ spl17_325 ),
inference(avatar_component_clause,[],[f3795]) ).
fof(f5203,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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)) )
| ~ spl17_466 ),
inference(avatar_component_clause,[],[f5202]) ).
fof(f26101,plain,
( spl17_1329
| ~ spl17_357
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5258,f5202,f4079,f26099]) ).
fof(f26099,plain,
( spl17_1329
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| 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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1329])]) ).
fof(f4079,plain,
( spl17_357
<=> ! [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,[spl17_357])]) ).
fof(f5258,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| 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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) )
| ~ spl17_357
| ~ spl17_466 ),
inference(resolution,[],[f5203,f4080]) ).
fof(f4080,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_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) )
| ~ spl17_357 ),
inference(avatar_component_clause,[],[f4079]) ).
fof(f26097,plain,
( spl17_1328
| ~ spl17_358
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5257,f5202,f4083,f26095]) ).
fof(f26095,plain,
( spl17_1328
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ 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,X3),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1328])]) ).
fof(f4083,plain,
( spl17_358
<=> ! [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,[spl17_358])]) ).
fof(f5257,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ 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,X3),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) )
| ~ spl17_358
| ~ spl17_466 ),
inference(resolution,[],[f5203,f4084]) ).
fof(f4084,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,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ spl17_358 ),
inference(avatar_component_clause,[],[f4083]) ).
fof(f26093,plain,
( spl17_1327
| ~ spl17_378
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f5183,f5140,f4305,f26091]) ).
fof(f26091,plain,
( spl17_1327
<=> ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0)))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1327])]) ).
fof(f4305,plain,
( spl17_378
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK8(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,[spl17_378])]) ).
fof(f5140,plain,
( spl17_457
<=> ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,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))))
| ~ 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,[spl17_457])]) ).
fof(f5183,plain,
( ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0)))
| ~ is_a(X1) )
| ~ spl17_378
| ~ spl17_457 ),
inference(resolution,[],[f5141,f4306]) ).
fof(f4306,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK8(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) )
| ~ spl17_378 ),
inference(avatar_component_clause,[],[f4305]) ).
fof(f5141,plain,
( ! [X0,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,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))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_457 ),
inference(avatar_component_clause,[],[f5140]) ).
fof(f26089,plain,
( spl17_1326
| ~ spl17_377
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f5182,f5140,f4301,f26087]) ).
fof(f26087,plain,
( spl17_1326
<=> ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0)))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1326])]) ).
fof(f4301,plain,
( spl17_377
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(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,[spl17_377])]) ).
fof(f5182,plain,
( ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0)))
| ~ is_a(X1) )
| ~ spl17_377
| ~ spl17_457 ),
inference(resolution,[],[f5141,f4302]) ).
fof(f4302,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) )
| ~ spl17_377 ),
inference(avatar_component_clause,[],[f4301]) ).
fof(f26067,plain,
( spl17_1325
| ~ spl17_942
| ~ spl17_1324 ),
inference(avatar_split_clause,[],[f26063,f26059,f12920,f26065]) ).
fof(f26065,plain,
( spl17_1325
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)),X0))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1325])]) ).
fof(f26059,plain,
( spl17_1324
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1324])]) ).
fof(f26063,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)),X0))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl17_942
| ~ spl17_1324 ),
inference(forward_demodulation,[],[f26062,f12921]) ).
fof(f26062,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X0)) )
| ~ spl17_942
| ~ spl17_1324 ),
inference(forward_demodulation,[],[f26060,f12921]) ).
fof(f26060,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X0)) )
| ~ spl17_1324 ),
inference(avatar_component_clause,[],[f26059]) ).
fof(f26061,plain,
( spl17_1324
| ~ spl17_290
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f4623,f4583,f3617,f26059]) ).
fof(f4623,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = X0
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X0)) )
| ~ spl17_290
| ~ spl17_404 ),
inference(resolution,[],[f4584,f3618]) ).
fof(f26057,plain,
( spl17_1323
| ~ spl17_261
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4132,f4051,f3413,f26055]) ).
fof(f26055,plain,
( spl17_1323
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = hAPP_nat_nat(suc,sK3(hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1323])]) ).
fof(f3413,plain,
( spl17_261
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,sK3(X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_261])]) ).
fof(f4132,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = hAPP_nat_nat(suc,sK3(hAPP_nat_nat(minus_minus_nat(X1),X2))) )
| ~ spl17_261
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3414]) ).
fof(f3414,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,sK3(X1)) = X1 )
| ~ spl17_261 ),
inference(avatar_component_clause,[],[f3413]) ).
fof(f25972,plain,
( spl17_1322
| ~ spl17_376
| ~ spl17_667
| ~ spl17_1321 ),
inference(avatar_split_clause,[],[f25968,f25965,f8214,f4297,f25970]) ).
fof(f25970,plain,
( spl17_1322
<=> ! [X0] :
( hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),na)),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1322])]) ).
fof(f4297,plain,
( spl17_376
<=> ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_376])]) ).
fof(f8214,plain,
( spl17_667
<=> hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) = hAPP_nat_nat(suc,sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_667])]) ).
fof(f25965,plain,
( spl17_1321
<=> ! [X0] :
( hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1321])]) ).
fof(f25968,plain,
( ! [X0] :
( hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),na)),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) )
| ~ spl17_376
| ~ spl17_667
| ~ spl17_1321 ),
inference(forward_demodulation,[],[f25966,f8282]) ).
fof(f8282,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),X0)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_nat_nat(suc,X1))
| ~ spl17_376
| ~ spl17_667 ),
inference(superposition,[],[f4298,f8216]) ).
fof(f8216,plain,
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) = hAPP_nat_nat(suc,sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl17_667 ),
inference(avatar_component_clause,[],[f8214]) ).
fof(f4298,plain,
( ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2))
| ~ spl17_376 ),
inference(avatar_component_clause,[],[f4297]) ).
fof(f25966,plain,
( ! [X0] :
( hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) )
| ~ spl17_1321 ),
inference(avatar_component_clause,[],[f25965]) ).
fof(f25967,plain,
( spl17_1321
| ~ spl17_194
| ~ spl17_237
| ~ spl17_376
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5122,f5005,f4297,f3271,f3037,f25965]) ).
fof(f3271,plain,
( spl17_237
<=> ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_237])]) ).
fof(f5005,plain,
( spl17_448
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_448])]) ).
fof(f5122,plain,
( ! [X0] :
( hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) )
| ~ spl17_194
| ~ spl17_237
| ~ spl17_376
| ~ spl17_448 ),
inference(forward_demodulation,[],[f5094,f4438]) ).
fof(f4438,plain,
( ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,X1))),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(suc,X2))
| ~ spl17_237
| ~ spl17_376 ),
inference(superposition,[],[f4298,f3272]) ).
fof(f3272,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))
| ~ spl17_237 ),
inference(avatar_component_clause,[],[f3271]) ).
fof(f5094,plain,
( ! [X0] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0))
| hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na))),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))) )
| ~ spl17_194
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3039]) ).
fof(f3039,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))))
| ~ spl17_194 ),
inference(avatar_component_clause,[],[f3037]) ).
fof(f5006,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,X1),X0))
| hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) )
| ~ spl17_448 ),
inference(avatar_component_clause,[],[f5005]) ).
fof(f25797,plain,
( spl17_1320
| ~ spl17_620
| ~ spl17_1299 ),
inference(avatar_split_clause,[],[f25533,f25127,f7183,f25795]) ).
fof(f25795,plain,
( spl17_1320
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| is_a(sK4(image_pname_a(mgt_call,u),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1320])]) ).
fof(f7183,plain,
( spl17_620
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| is_a(sK4(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_620])]) ).
fof(f25533,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| is_a(sK4(image_pname_a(mgt_call,u),X0)) )
| ~ spl17_620
| ~ spl17_1299 ),
inference(resolution,[],[f25128,f7184]) ).
fof(f7184,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| is_a(sK4(X1,X0)) )
| ~ spl17_620 ),
inference(avatar_component_clause,[],[f7183]) ).
fof(f25337,plain,
( spl17_1319
| ~ spl17_434
| ~ spl17_495 ),
inference(avatar_split_clause,[],[f5539,f5504,f4840,f25335]) ).
fof(f25335,plain,
( spl17_1319
<=> ! [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))) = 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))),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,[spl17_1319])]) ).
fof(f4840,plain,
( spl17_434
<=> ! [X0,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)) = 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),collect_a(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_434])]) ).
fof(f5539,plain,
( ! [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))) = 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))),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))))
| ~ spl17_434
| ~ spl17_495 ),
inference(superposition,[],[f5505,f4841]) ).
fof(f4841,plain,
( ! [X0,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)) = 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),collect_a(X1))))
| ~ spl17_434 ),
inference(avatar_component_clause,[],[f4840]) ).
fof(f25333,plain,
( spl17_1318
| ~ spl17_434
| ~ spl17_495 ),
inference(avatar_split_clause,[],[f5537,f5504,f4840,f25331]) ).
fof(f25331,plain,
( spl17_1318
<=> ! [X0,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)) = 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),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,[spl17_1318])]) ).
fof(f5537,plain,
( ! [X0,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)) = 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),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)))))
| ~ spl17_434
| ~ spl17_495 ),
inference(superposition,[],[f5505,f4841]) ).
fof(f25329,plain,
( spl17_1317
| ~ spl17_433
| ~ spl17_494 ),
inference(avatar_split_clause,[],[f5511,f5500,f4836,f25327]) ).
fof(f25327,plain,
( spl17_1317
<=> ! [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))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),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,[spl17_1317])]) ).
fof(f4836,plain,
( spl17_433
<=> ! [X0,X1] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),collect_pname(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_433])]) ).
fof(f5511,plain,
( ! [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))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),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))))
| ~ spl17_433
| ~ spl17_494 ),
inference(superposition,[],[f5501,f4837]) ).
fof(f4837,plain,
( ! [X0,X1] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),collect_pname(X1))))
| ~ spl17_433 ),
inference(avatar_component_clause,[],[f4836]) ).
fof(f25325,plain,
( spl17_1316
| ~ spl17_433
| ~ spl17_494 ),
inference(avatar_split_clause,[],[f5509,f5500,f4836,f25323]) ).
fof(f25323,plain,
( spl17_1316
<=> ! [X0,X1] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1316])]) ).
fof(f5509,plain,
( ! [X0,X1] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))))
| ~ spl17_433
| ~ spl17_494 ),
inference(superposition,[],[f5501,f4837]) ).
fof(f25321,plain,
( spl17_1315
| ~ spl17_433
| ~ spl17_491 ),
inference(avatar_split_clause,[],[f5498,f5464,f4836,f25319]) ).
fof(f25319,plain,
( spl17_1315
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X2)))),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1315])]) ).
fof(f5498,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X2)))),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1))) )
| ~ spl17_433
| ~ spl17_491 ),
inference(superposition,[],[f5465,f4837]) ).
fof(f25317,plain,
( spl17_1314
| ~ spl17_433
| ~ spl17_491 ),
inference(avatar_split_clause,[],[f5497,f5464,f4836,f25315]) ).
fof(f25315,plain,
( spl17_1314
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1314])]) ).
fof(f5497,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2)) )
| ~ spl17_433
| ~ spl17_491 ),
inference(superposition,[],[f5465,f4837]) ).
fof(f25313,plain,
( ~ spl17_8
| ~ spl17_159
| spl17_1299 ),
inference(avatar_split_clause,[],[f25271,f25127,f2791,f2128]) ).
fof(f2128,plain,
( spl17_8
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f2791,plain,
( spl17_159
<=> ! [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,[spl17_159])]) ).
fof(f25271,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_159
| spl17_1299 ),
inference(resolution,[],[f25129,f2792]) ).
fof(f2792,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)) )
| ~ spl17_159 ),
inference(avatar_component_clause,[],[f2791]) ).
fof(f25129,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(mgt_call,u)))
| spl17_1299 ),
inference(avatar_component_clause,[],[f25127]) ).
fof(f25312,plain,
( spl17_1313
| ~ spl17_434
| ~ spl17_490 ),
inference(avatar_split_clause,[],[f5489,f5460,f4840,f25310]) ).
fof(f25310,plain,
( spl17_1313
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X2)))),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1313])]) ).
fof(f5489,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X2)))),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1))) )
| ~ spl17_434
| ~ spl17_490 ),
inference(superposition,[],[f5461,f4841]) ).
fof(f25308,plain,
( spl17_1312
| ~ spl17_434
| ~ spl17_490 ),
inference(avatar_split_clause,[],[f5487,f5460,f4840,f25306]) ).
fof(f25306,plain,
( spl17_1312
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1312])]) ).
fof(f5487,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2)) )
| ~ spl17_434
| ~ spl17_490 ),
inference(superposition,[],[f5461,f4841]) ).
fof(f25304,plain,
( spl17_1311
| ~ spl17_11
| ~ spl17_390
| ~ spl17_423
| ~ spl17_471 ),
inference(avatar_split_clause,[],[f5236,f5226,f4694,f4361,f2141,f25302]) ).
fof(f25302,plain,
( spl17_1311
<=> ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0) = X0
| hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1311])]) ).
fof(f2141,plain,
( spl17_11
<=> ! [X0] : collect_nat(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f4694,plain,
( spl17_423
<=> ! [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))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_423])]) ).
fof(f5236,plain,
( ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0) = X0
| hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_11
| ~ spl17_390
| ~ spl17_423
| ~ spl17_471 ),
inference(forward_demodulation,[],[f5231,f4760]) ).
fof(f4760,plain,
( ! [X0,X1] : 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)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)
| ~ spl17_11
| ~ spl17_423 ),
inference(superposition,[],[f4695,f2142]) ).
fof(f2142,plain,
( ! [X0] : collect_nat(X0) = X0
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f4695,plain,
( ! [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))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)
| ~ spl17_423 ),
inference(avatar_component_clause,[],[f4694]) ).
fof(f5231,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) = X0 )
| ~ spl17_390
| ~ spl17_471 ),
inference(resolution,[],[f5227,f4362]) ).
fof(f25300,plain,
( spl17_1310
| ~ spl17_354
| ~ spl17_471 ),
inference(avatar_split_clause,[],[f5232,f5226,f4067,f25298]) ).
fof(f25298,plain,
( spl17_1310
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1310])]) ).
fof(f4067,plain,
( spl17_354
<=> ! [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,[spl17_354])]) ).
fof(f5232,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_354
| ~ spl17_471 ),
inference(resolution,[],[f5227,f4068]) ).
fof(f4068,plain,
( ! [X2,X0,X1] :
( ~ 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)) )
| ~ spl17_354 ),
inference(avatar_component_clause,[],[f4067]) ).
fof(f25296,plain,
( spl17_1309
| ~ spl17_185
| ~ spl17_327
| ~ spl17_456 ),
inference(avatar_split_clause,[],[f5176,f5136,f3803,f2909,f25294]) ).
fof(f25294,plain,
( spl17_1309
<=> ! [X2,X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1)) = hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1309])]) ).
fof(f5136,plain,
( spl17_456
<=> ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,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))))
| ~ 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,[spl17_456])]) ).
fof(f5176,plain,
( ! [X2,X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1)) = hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ~ spl17_185
| ~ spl17_327
| ~ spl17_456 ),
inference(forward_demodulation,[],[f5175,f2069]) ).
fof(f2069,plain,
! [X2,X0,X1] : image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))),
inference(forward_demodulation,[],[f1901,f1679]) ).
fof(f1679,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,[],[f708]) ).
fof(f708,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,[],[f416]) ).
fof(f416,axiom,
! [X43,X44,X45] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X43,X44),X45) = hAPP_a_fun_a_bool(X43,hAPP_pname_a(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1901,plain,
! [X2,X0,X1] : image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))),
inference(definition_unfolding,[],[f1710,f1384,f1386]) ).
fof(f1386,plain,
! [X0,X1] : 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,[],[f503]) ).
fof(f503,plain,
! [X0,X1] : 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,[],[f276]) ).
fof(f276,axiom,
! [X7,X9] : insert_a(X7,X9) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X7)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1384,plain,
! [X0,X1] : 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,[],[f501]) ).
fof(f501,plain,
! [X0,X1] : 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,[],[f275]) ).
fof(f275,axiom,
! [X7,X9] : insert_pname(X7,X9) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X7)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1710,plain,
! [X2,X0,X1] : image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)),
inference(cnf_transformation,[],[f739]) ).
fof(f739,plain,
! [X0,X1,X2] : image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X8,X7,X9] : image_pname_a(X8,insert_pname(X7,X9)) = insert_a(hAPP_pname_a(X8,X7),image_pname_a(X8,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5175,plain,
( ! [X2,X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ~ spl17_185
| ~ spl17_327
| ~ spl17_456 ),
inference(forward_demodulation,[],[f5172,f2910]) ).
fof(f5172,plain,
( ! [X2,X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X0,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ~ spl17_327
| ~ spl17_456 ),
inference(resolution,[],[f5137,f3804]) ).
fof(f5137,plain,
( ! [X0,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,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_456 ),
inference(avatar_component_clause,[],[f5136]) ).
fof(f25292,plain,
( spl17_1308
| ~ spl17_237
| ~ spl17_424 ),
inference(avatar_split_clause,[],[f4805,f4763,f3271,f25290]) ).
fof(f25290,plain,
( spl17_1308
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))
| hAPP_nat_nat(suc,X0) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1308])]) ).
fof(f4805,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))
| hAPP_nat_nat(suc,X0) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) )
| ~ spl17_237
| ~ spl17_424 ),
inference(superposition,[],[f4764,f3272]) ).
fof(f25288,plain,
( spl17_1307
| ~ spl17_415
| ~ spl17_421 ),
inference(avatar_split_clause,[],[f4756,f4686,f4662,f25286]) ).
fof(f25286,plain,
( spl17_1307
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X3)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1307])]) ).
fof(f4662,plain,
( spl17_415
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_415])]) ).
fof(f4686,plain,
( spl17_421
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_421])]) ).
fof(f4756,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X3)))),X2)) )
| ~ spl17_415
| ~ spl17_421 ),
inference(resolution,[],[f4687,f4663]) ).
fof(f4663,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_415 ),
inference(avatar_component_clause,[],[f4662]) ).
fof(f4687,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ spl17_421 ),
inference(avatar_component_clause,[],[f4686]) ).
fof(f25284,plain,
( spl17_1306
| ~ spl17_415
| ~ spl17_420 ),
inference(avatar_split_clause,[],[f4751,f4682,f4662,f25282]) ).
fof(f25282,plain,
( spl17_1306
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1306])]) ).
fof(f4682,plain,
( spl17_420
<=> ! [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,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)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_420])]) ).
fof(f4751,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))),X2)) )
| ~ spl17_415
| ~ spl17_420 ),
inference(resolution,[],[f4683,f4663]) ).
fof(f4683,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_420 ),
inference(avatar_component_clause,[],[f4682]) ).
fof(f25280,plain,
( spl17_1305
| ~ spl17_412
| ~ spl17_419 ),
inference(avatar_split_clause,[],[f4745,f4678,f4650,f25278]) ).
fof(f25278,plain,
( spl17_1305
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X3)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1305])]) ).
fof(f4650,plain,
( spl17_412
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_412])]) ).
fof(f4678,plain,
( spl17_419
<=> ! [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,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)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_419])]) ).
fof(f4745,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X3)))),X2)) )
| ~ spl17_412
| ~ spl17_419 ),
inference(resolution,[],[f4679,f4651]) ).
fof(f4651,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ spl17_412 ),
inference(avatar_component_clause,[],[f4650]) ).
fof(f4679,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl17_419 ),
inference(avatar_component_clause,[],[f4678]) ).
fof(f25276,plain,
( spl17_1304
| ~ spl17_412
| ~ spl17_418 ),
inference(avatar_split_clause,[],[f4739,f4674,f4650,f25274]) ).
fof(f25274,plain,
( spl17_1304
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1304])]) ).
fof(f4674,plain,
( spl17_418
<=> ! [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,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)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_418])]) ).
fof(f4739,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))),X2)) )
| ~ spl17_412
| ~ spl17_418 ),
inference(resolution,[],[f4675,f4651]) ).
fof(f4675,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) )
| ~ spl17_418 ),
inference(avatar_component_clause,[],[f4674]) ).
fof(f25259,plain,
( spl17_1303
| ~ spl17_942
| ~ spl17_1302 ),
inference(avatar_split_clause,[],[f25255,f25251,f12920,f25257]) ).
fof(f25257,plain,
( spl17_1303
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1303])]) ).
fof(f25251,plain,
( spl17_1302
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(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)),X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1302])]) ).
fof(f25255,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1),X2)),X1)) )
| ~ spl17_942
| ~ spl17_1302 ),
inference(forward_demodulation,[],[f25254,f12921]) ).
fof(f25254,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1),X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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)))) )
| ~ spl17_942
| ~ spl17_1302 ),
inference(forward_demodulation,[],[f25252,f12921]) ).
fof(f25252,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(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)),X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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)))) )
| ~ spl17_1302 ),
inference(avatar_component_clause,[],[f25251]) ).
fof(f25253,plain,
( spl17_1302
| ~ spl17_276
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f4620,f4579,f3473,f25251]) ).
fof(f3473,plain,
( spl17_276
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_276])]) ).
fof(f4620,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(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)),X2)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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)))) )
| ~ spl17_276
| ~ spl17_403 ),
inference(resolution,[],[f4580,f3474]) ).
fof(f3474,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) )
| ~ spl17_276 ),
inference(avatar_component_clause,[],[f3473]) ).
fof(f25249,plain,
( spl17_1301
| ~ spl17_288
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4143,f4051,f3609,f25247]) ).
fof(f25247,plain,
( spl17_1301
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1301])]) ).
fof(f4143,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0)) = X0 )
| ~ spl17_288
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3610]) ).
fof(f25245,plain,
( spl17_1300
| ~ spl17_289
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4142,f4051,f3613,f25243]) ).
fof(f25243,plain,
( spl17_1300
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1300])]) ).
fof(f4142,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))),X0)) )
| ~ spl17_289
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3614]) ).
fof(f25130,plain,
( spl17_1298
| ~ spl17_1299
| spl17_43
| ~ spl17_1278 ),
inference(avatar_split_clause,[],[f24675,f23724,f2273,f25127,f25123]) ).
fof(f25123,plain,
( spl17_1298
<=> hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(mgt_call,u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1298])]) ).
fof(f23724,plain,
( spl17_1278
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1278])]) ).
fof(f24675,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(mgt_call,u)))
| hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(mgt_call,u)))))
| spl17_43
| ~ spl17_1278 ),
inference(resolution,[],[f23725,f2275]) ).
fof(f23725,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) )
| ~ spl17_1278 ),
inference(avatar_component_clause,[],[f23724]) ).
fof(f24867,plain,
( spl17_1297
| ~ spl17_330
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5588,f5583,f3843,f24865]) ).
fof(f24865,plain,
( spl17_1297
<=> ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1297])]) ).
fof(f3843,plain,
( spl17_330
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_330])]) ).
fof(f5588,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ spl17_330
| ~ spl17_499 ),
inference(superposition,[],[f3844,f5584]) ).
fof(f3844,plain,
( ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))))
| ~ spl17_330 ),
inference(avatar_component_clause,[],[f3843]) ).
fof(f24863,plain,
( spl17_1296
| ~ spl17_177
| ~ spl17_490 ),
inference(avatar_split_clause,[],[f5484,f5460,f2876,f24861]) ).
fof(f24861,plain,
( spl17_1296
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1296])]) ).
fof(f2876,plain,
( spl17_177
<=> ! [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,[spl17_177])]) ).
fof(f5484,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) )
| ~ spl17_177
| ~ spl17_490 ),
inference(resolution,[],[f5461,f2877]) ).
fof(f2877,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)) )
| ~ spl17_177 ),
inference(avatar_component_clause,[],[f2876]) ).
fof(f24859,plain,
( spl17_1295
| ~ spl17_185
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5270,f5202,f2909,f24857]) ).
fof(f5270,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X3)) )
| ~ spl17_185
| ~ spl17_466 ),
inference(superposition,[],[f5203,f2910]) ).
fof(f24855,plain,
( spl17_1294
| ~ spl17_185
| ~ spl17_463 ),
inference(avatar_split_clause,[],[f5242,f5190,f2909,f24853]) ).
fof(f24853,plain,
( spl17_1294
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1294])]) ).
fof(f5190,plain,
( spl17_463
<=> ! [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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_463])]) ).
fof(f5242,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X2)) )
| ~ spl17_185
| ~ spl17_463 ),
inference(superposition,[],[f5191,f2910]) ).
fof(f5191,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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)) )
| ~ spl17_463 ),
inference(avatar_component_clause,[],[f5190]) ).
fof(f24851,plain,
( spl17_1293
| ~ spl17_336
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f5181,f5140,f3973,f24849]) ).
fof(f24849,plain,
( spl17_1293
<=> ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1293])]) ).
fof(f3973,plain,
( spl17_336
<=> ! [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,sK16(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_336])]) ).
fof(f5181,plain,
( ! [X2,X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X1,X2,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X0)),X2)) )
| ~ spl17_336
| ~ spl17_457 ),
inference(resolution,[],[f5141,f3974]) ).
fof(f3974,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(X0,X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) )
| ~ spl17_336 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f24827,plain,
( spl17_1292
| ~ spl17_356
| ~ spl17_462 ),
inference(avatar_split_clause,[],[f5166,f5163,f4075,f24825]) ).
fof(f24825,plain,
( spl17_1292
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1292])]) ).
fof(f5166,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))) )
| ~ spl17_356
| ~ spl17_462 ),
inference(resolution,[],[f5164,f4076]) ).
fof(f24823,plain,
( spl17_1291
| ~ spl17_237
| ~ spl17_291
| ~ spl17_324
| ~ spl17_376
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5125,f5005,f4297,f3791,f3621,f3271,f24821]) ).
fof(f24821,plain,
( spl17_1291
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1291])]) ).
fof(f3791,plain,
( spl17_324
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,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,[spl17_324])]) ).
fof(f5125,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
| ~ spl17_237
| ~ spl17_291
| ~ spl17_324
| ~ spl17_376
| ~ spl17_448 ),
inference(forward_demodulation,[],[f5124,f3622]) ).
fof(f5124,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0)))),X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
| ~ spl17_237
| ~ spl17_291
| ~ spl17_324
| ~ spl17_376
| ~ spl17_448 ),
inference(forward_demodulation,[],[f5123,f3657]) ).
fof(f3657,plain,
( ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)),hAPP_nat_nat(suc,X1))
| ~ spl17_237
| ~ spl17_291 ),
inference(superposition,[],[f3622,f3272]) ).
fof(f5123,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X0)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
| ~ spl17_237
| ~ spl17_324
| ~ spl17_376
| ~ spl17_448 ),
inference(forward_demodulation,[],[f5114,f4438]) ).
fof(f5114,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),hAPP_nat_nat(suc,X0))),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
| ~ spl17_324
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3792]) ).
fof(f3792,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_324 ),
inference(avatar_component_clause,[],[f3791]) ).
fof(f24819,plain,
( spl17_1290
| ~ spl17_237
| ~ spl17_277
| ~ spl17_376
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5121,f5005,f4297,f3477,f3271,f24817]) ).
fof(f24817,plain,
( spl17_1290
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1290])]) ).
fof(f3477,plain,
( spl17_277
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_277])]) ).
fof(f5121,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ spl17_237
| ~ spl17_277
| ~ spl17_376
| ~ spl17_448 ),
inference(forward_demodulation,[],[f5073,f4438]) ).
fof(f5073,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X0))),hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X0)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ spl17_277
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3478]) ).
fof(f3478,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)) )
| ~ spl17_277 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f24815,plain,
( spl17_1289
| ~ spl17_335
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5118,f5005,f3969,f24813]) ).
fof(f24813,plain,
( spl17_1289
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(sK1(X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(sK1(X2)),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1289])]) ).
fof(f3969,plain,
( spl17_335
<=> ! [X4,X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(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,[spl17_335])]) ).
fof(f5118,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(sK1(X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(sK1(X2)),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) )
| ~ spl17_335
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3970]) ).
fof(f3970,plain,
( ! [X0,X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_335 ),
inference(avatar_component_clause,[],[f3969]) ).
fof(f24811,plain,
( spl17_1288
| ~ spl17_291
| ~ spl17_424 ),
inference(avatar_split_clause,[],[f4808,f4763,f3621,f24809]) ).
fof(f24809,plain,
( spl17_1288
<=> ! [X0,X3,X2,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) != hAPP_nat_nat(minus_minus_nat(X3),X2)
| hAPP_nat_nat(minus_minus_nat(X0),X1) = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1288])]) ).
fof(f4808,plain,
( ! [X2,X3,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) != hAPP_nat_nat(minus_minus_nat(X3),X2)
| hAPP_nat_nat(minus_minus_nat(X0),X1) = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
| ~ spl17_291
| ~ spl17_424 ),
inference(superposition,[],[f4764,f3622]) ).
fof(f24788,plain,
( spl17_1287
| ~ spl17_942
| ~ spl17_1286 ),
inference(avatar_split_clause,[],[f24784,f24781,f12920,f24786]) ).
fof(f24786,plain,
( spl17_1287
<=> ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1287])]) ).
fof(f24781,plain,
( spl17_1286
<=> ! [X0,X1] : 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)) = 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),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)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1286])]) ).
fof(f24784,plain,
( ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)))
| ~ spl17_942
| ~ spl17_1286 ),
inference(forward_demodulation,[],[f24782,f12921]) ).
fof(f24782,plain,
( ! [X0,X1] : 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)) = 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),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))))
| ~ spl17_1286 ),
inference(avatar_component_clause,[],[f24781]) ).
fof(f24783,plain,
( spl17_1286
| ~ spl17_329
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f4490,f4361,f3811,f24781]) ).
fof(f3811,plain,
( spl17_329
<=> ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),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)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_329])]) ).
fof(f4490,plain,
( ! [X0,X1] : 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)) = 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),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))))
| ~ spl17_329
| ~ spl17_390 ),
inference(resolution,[],[f4362,f3812]) ).
fof(f3812,plain,
( ! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),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))))
| ~ spl17_329 ),
inference(avatar_component_clause,[],[f3811]) ).
fof(f24739,plain,
( spl17_1285
| ~ spl17_334
| spl17_674
| ~ spl17_1278 ),
inference(avatar_split_clause,[],[f24688,f23724,f8335,f3962,f24736]) ).
fof(f24736,plain,
( spl17_1285
<=> hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1285])]) ).
fof(f3962,plain,
( spl17_334
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_334])]) ).
fof(f8335,plain,
( spl17_674
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_674])]) ).
fof(f24688,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))
| spl17_674
| ~ spl17_1278 ),
inference(resolution,[],[f23725,f8337]) ).
fof(f8337,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),g))
| spl17_674 ),
inference(avatar_component_clause,[],[f8335]) ).
fof(f24280,plain,
( spl17_1284
| ~ spl17_49
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3595,f2807,f2299,f24278]) ).
fof(f24278,plain,
( spl17_1284
<=> ! [X0,X1] :
( p(image_pname_a(X0,X1)) = collect_fun_a_bool(p(image_pname_a(X0,X1)))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1284])]) ).
fof(f2299,plain,
( spl17_49
<=> ! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f2807,plain,
( spl17_163
<=> ! [X0] :
( p(X0) = collect_fun_a_bool(p(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_163])]) ).
fof(f3595,plain,
( ! [X0,X1] :
( p(image_pname_a(X0,X1)) = collect_fun_a_bool(p(image_pname_a(X0,X1)))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_49
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2300]) ).
fof(f2300,plain,
( ! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_49 ),
inference(avatar_component_clause,[],[f2299]) ).
fof(f2808,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| p(X0) = collect_fun_a_bool(p(X0)) )
| ~ spl17_163 ),
inference(avatar_component_clause,[],[f2807]) ).
fof(f23746,plain,
( spl17_1283
| ~ spl17_419
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5688,f5631,f4678,f23744]) ).
fof(f23744,plain,
( spl17_1283
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X1))),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),X2))))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1283])]) ).
fof(f5688,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X1))),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),X2))))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X3)) )
| ~ spl17_419
| ~ spl17_504 ),
inference(superposition,[],[f4679,f5632]) ).
fof(f23742,plain,
( spl17_1282
| ~ spl17_421
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5650,f5627,f4686,f23740]) ).
fof(f23740,plain,
( spl17_1282
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1282])]) ).
fof(f5650,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X3)) )
| ~ spl17_421
| ~ spl17_503 ),
inference(superposition,[],[f4687,f5628]) ).
fof(f23738,plain,
( spl17_1281
| ~ spl17_255
| ~ spl17_489 ),
inference(avatar_split_clause,[],[f5458,f5433,f3389,f23736]) ).
fof(f23736,plain,
( spl17_1281
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1281])]) ).
fof(f3389,plain,
( spl17_255
<=> ! [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,[spl17_255])]) ).
fof(f5458,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1))) )
| ~ spl17_255
| ~ spl17_489 ),
inference(resolution,[],[f5434,f3390]) ).
fof(f3390,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_255 ),
inference(avatar_component_clause,[],[f3389]) ).
fof(f23734,plain,
( spl17_1280
| ~ spl17_274
| ~ spl17_482 ),
inference(avatar_split_clause,[],[f5384,f5318,f3465,f23732]) ).
fof(f23732,plain,
( spl17_1280
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0)) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1280])]) ).
fof(f5318,plain,
( spl17_482
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) = hAPP_f921600141ol_nat(finite_card_pname,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))))
| 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,[spl17_482])]) ).
fof(f5384,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0)) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
| ~ spl17_274
| ~ spl17_482 ),
inference(resolution,[],[f5319,f3466]) ).
fof(f5319,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) = hAPP_f921600141ol_nat(finite_card_pname,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))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_482 ),
inference(avatar_component_clause,[],[f5318]) ).
fof(f23730,plain,
( spl17_1279
| ~ spl17_48
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f3562,f2719,f2295,f23728]) ).
fof(f23728,plain,
( spl17_1279
<=> ! [X0,X1] :
( collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1)) = collect_fun_a_bool(collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1)))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1279])]) ).
fof(f2295,plain,
( spl17_48
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f2719,plain,
( spl17_141
<=> ! [X0] :
( collect_fun_a_bool(X0) = collect_fun_a_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_141])]) ).
fof(f3562,plain,
( ! [X0,X1] :
( collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1)) = collect_fun_a_bool(collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1)))
| ~ is_fun_a_bool(X1) )
| ~ spl17_48
| ~ spl17_141 ),
inference(resolution,[],[f2720,f2296]) ).
fof(f2296,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl17_48 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f2720,plain,
( ! [X0] :
( ~ is_fun949378684l_bool(X0)
| collect_fun_a_bool(X0) = collect_fun_a_bool(collect_fun_a_bool(X0)) )
| ~ spl17_141 ),
inference(avatar_component_clause,[],[f2719]) ).
fof(f23726,plain,
( spl17_1278
| ~ spl17_272
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5371,f5309,f3457,f23724]) ).
fof(f5371,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) )
| ~ spl17_272
| ~ spl17_480 ),
inference(resolution,[],[f5310,f3458]) ).
fof(f23722,plain,
( spl17_1277
| ~ spl17_248
| ~ spl17_463 ),
inference(avatar_split_clause,[],[f5241,f5190,f3318,f23720]) ).
fof(f23720,plain,
( spl17_1277
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X0,X1)))
| is_pname(sK16(X0,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1277])]) ).
fof(f3318,plain,
( spl17_248
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| is_pname(sK16(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_248])]) ).
fof(f5241,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X0,X1)))
| is_pname(sK16(X0,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X1)) )
| ~ spl17_248
| ~ spl17_463 ),
inference(resolution,[],[f5191,f3319]) ).
fof(f3319,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| is_pname(sK16(X0,X1,X2)) )
| ~ spl17_248 ),
inference(avatar_component_clause,[],[f3318]) ).
fof(f23718,plain,
( spl17_1276
| ~ spl17_185
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4968,f4960,f2909,f23716]) ).
fof(f23716,plain,
( spl17_1276
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X3))
| hAPP_pname_a(X0,X1) = X3
| hBOOL(hAPP_a_bool(X2,X3))
| ~ is_a(X3)
| ~ is_a(hAPP_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1276])]) ).
fof(f4960,plain,
( spl17_442
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(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))),X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_442])]) ).
fof(f4968,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X3))
| hAPP_pname_a(X0,X1) = X3
| hBOOL(hAPP_a_bool(X2,X3))
| ~ is_a(X3)
| ~ is_a(hAPP_pname_a(X0,X1)) )
| ~ spl17_185
| ~ spl17_442 ),
inference(superposition,[],[f4961,f2910]) ).
fof(f4961,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(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))),X2))
| X0 = X2
| hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) )
| ~ spl17_442 ),
inference(avatar_component_clause,[],[f4960]) ).
fof(f23714,plain,
( spl17_1275
| ~ spl17_171
| ~ spl17_409 ),
inference(avatar_split_clause,[],[f4709,f4638,f2839,f23712]) ).
fof(f23712,plain,
( spl17_1275
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),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,[spl17_1275])]) ).
fof(f2839,plain,
( spl17_171
<=> ! [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,[spl17_171])]) ).
fof(f4638,plain,
( spl17_409
<=> ! [X0,X1] :
( 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,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,[spl17_409])]) ).
fof(f4709,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_409 ),
inference(superposition,[],[f4639,f2840]) ).
fof(f2840,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))
| ~ spl17_171 ),
inference(avatar_component_clause,[],[f2839]) ).
fof(f4639,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,X0)))
| X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_409 ),
inference(avatar_component_clause,[],[f4638]) ).
fof(f23708,plain,
( spl17_1274
| ~ spl17_404
| ~ spl17_406 ),
inference(avatar_split_clause,[],[f4631,f4591,f4583,f23706]) ).
fof(f23706,plain,
( spl17_1274
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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),X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1274])]) ).
fof(f4591,plain,
( spl17_406
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_406])]) ).
fof(f4631,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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),X3))),X2)) )
| ~ spl17_404
| ~ spl17_406 ),
inference(resolution,[],[f4592,f4584]) ).
fof(f4592,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ spl17_406 ),
inference(avatar_component_clause,[],[f4591]) ).
fof(f23702,plain,
( spl17_1273
| ~ spl17_404
| ~ spl17_405 ),
inference(avatar_split_clause,[],[f4627,f4587,f4583,f23700]) ).
fof(f23700,plain,
( spl17_1273
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1273])]) ).
fof(f4627,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))),X2)) )
| ~ spl17_404
| ~ spl17_405 ),
inference(resolution,[],[f4588,f4584]) ).
fof(f23698,plain,
( spl17_1272
| ~ spl17_371
| ~ spl17_380 ),
inference(avatar_split_clause,[],[f4462,f4314,f4277,f23696]) ).
fof(f23696,plain,
( spl17_1272
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| sK10(X0,X1,X2) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),sK10(X0,X1,X2)))
| ~ is_fun_pname_bool(sK10(X0,X1,X2))
| ~ is_fun_pname_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1272])]) ).
fof(f4314,plain,
( spl17_380
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK10(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,[spl17_380])]) ).
fof(f4462,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| sK10(X0,X1,X2) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),sK10(X0,X1,X2)))
| ~ is_fun_pname_bool(sK10(X0,X1,X2))
| ~ is_fun_pname_bool(X2) )
| ~ spl17_371
| ~ spl17_380 ),
inference(resolution,[],[f4315,f4278]) ).
fof(f4315,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK10(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) )
| ~ spl17_380 ),
inference(avatar_component_clause,[],[f4314]) ).
fof(f23694,plain,
( spl17_1271
| ~ spl17_350
| ~ spl17_369 ),
inference(avatar_split_clause,[],[f4417,f4269,f4051,f23692]) ).
fof(f23692,plain,
( spl17_1271
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1271])]) ).
fof(f4269,plain,
( spl17_369
<=> ! [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,[spl17_369])]) ).
fof(f4417,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0))) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_350
| ~ spl17_369 ),
inference(resolution,[],[f4270,f4052]) ).
fof(f4270,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 )
| ~ spl17_369 ),
inference(avatar_component_clause,[],[f4269]) ).
fof(f23690,plain,
( spl17_1270
| ~ spl17_350
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4225,f4063,f4051,f23688]) ).
fof(f23688,plain,
( spl17_1270
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,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),hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1270])]) ).
fof(f4063,plain,
( spl17_353
<=> ! [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,[spl17_353])]) ).
fof(f4225,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,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),hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_350
| ~ spl17_353 ),
inference(resolution,[],[f4064,f4052]) ).
fof(f4064,plain,
( ! [X2,X0,X1] :
( ~ 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))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_353 ),
inference(avatar_component_clause,[],[f4063]) ).
fof(f23686,plain,
( spl17_1269
| ~ spl17_350
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4224,f4063,f4051,f23684]) ).
fof(f23684,plain,
( spl17_1269
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X3)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1269])]) ).
fof(f4224,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X3)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) )
| ~ spl17_350
| ~ spl17_353 ),
inference(resolution,[],[f4064,f4052]) ).
fof(f23682,plain,
( spl17_1268
| ~ spl17_45
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f3561,f2719,f2283,f23680]) ).
fof(f23680,plain,
( spl17_1268
<=> ! [X0,X1] :
( collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1)) = collect_fun_a_bool(collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1)))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1268])]) ).
fof(f2283,plain,
( spl17_45
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f3561,plain,
( ! [X0,X1] :
( collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1)) = collect_fun_a_bool(collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1)))
| ~ is_a(X1) )
| ~ spl17_45
| ~ spl17_141 ),
inference(resolution,[],[f2720,f2284]) ).
fof(f2284,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f23678,plain,
( spl17_1267
| ~ spl17_260
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4141,f4051,f3409,f23676]) ).
fof(f23676,plain,
( spl17_1267
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1267])]) ).
fof(f3409,plain,
( spl17_260
<=> ! [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,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_260])]) ).
fof(f4141,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)))))) )
| ~ spl17_260
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3410]) ).
fof(f3410,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_260 ),
inference(avatar_component_clause,[],[f3409]) ).
fof(f23674,plain,
( spl17_1266
| ~ spl17_278
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4139,f4051,f3481,f23672]) ).
fof(f23672,plain,
( spl17_1266
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1266])]) ).
fof(f3481,plain,
( spl17_278
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_278])]) ).
fof(f4139,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))),X0)) )
| ~ spl17_278
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3482]) ).
fof(f3482,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)) )
| ~ spl17_278 ),
inference(avatar_component_clause,[],[f3481]) ).
fof(f23670,plain,
( spl17_1265
| ~ spl17_288
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4136,f4051,f3609,f23668]) ).
fof(f23668,plain,
( spl17_1265
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1265])]) ).
fof(f4136,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) = X0 )
| ~ spl17_288
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3610]) ).
fof(f23666,plain,
( spl17_1264
| ~ spl17_289
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4135,f4051,f3613,f23664]) ).
fof(f23664,plain,
( spl17_1264
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1264])]) ).
fof(f4135,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) )
| ~ spl17_289
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3614]) ).
fof(f23662,plain,
( spl17_1263
| ~ spl17_260
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4133,f4051,f3409,f23660]) ).
fof(f23660,plain,
( spl17_1263
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1263])]) ).
fof(f4133,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2))) )
| ~ spl17_260
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3410]) ).
fof(f23658,plain,
( spl17_1262
| ~ spl17_278
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4131,f4051,f3481,f23656]) ).
fof(f23656,plain,
( spl17_1262
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1262])]) ).
fof(f4131,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X0)) )
| ~ spl17_278
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3482]) ).
fof(f23433,plain,
( spl17_1261
| ~ spl17_47
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f3495,f2631,f2291,f23431]) ).
fof(f23431,plain,
( spl17_1261
<=> ! [X0,X1] :
( collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1)) = collec1974731493e_bool(collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1)))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1261])]) ).
fof(f2291,plain,
( spl17_47
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f2631,plain,
( spl17_119
<=> ! [X0] :
( collec1974731493e_bool(X0) = collec1974731493e_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
fof(f3495,plain,
( ! [X0,X1] :
( collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1)) = collec1974731493e_bool(collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1)))
| ~ is_pname(X1) )
| ~ spl17_47
| ~ spl17_119 ),
inference(resolution,[],[f2632,f2292]) ).
fof(f2292,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) )
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f2291]) ).
fof(f2632,plain,
( ! [X0] :
( ~ is_fun1661590463l_bool(X0)
| collec1974731493e_bool(X0) = collec1974731493e_bool(collec1974731493e_bool(X0)) )
| ~ spl17_119 ),
inference(avatar_component_clause,[],[f2631]) ).
fof(f22866,plain,
( spl17_1260
| ~ spl17_40
| ~ spl17_487 ),
inference(avatar_split_clause,[],[f5425,f5416,f2259,f22864]) ).
fof(f22864,plain,
( spl17_1260
<=> ! [X2,X0,X1] :
( is_fun_a_bool(image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_fun_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1260])]) ).
fof(f5425,plain,
( ! [X2,X0,X1] :
( is_fun_a_bool(image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_fun_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2)))) )
| ~ spl17_40
| ~ spl17_487 ),
inference(superposition,[],[f2260,f5417]) ).
fof(f22862,plain,
( spl17_1259
| ~ spl17_257
| ~ spl17_467 ),
inference(avatar_split_clause,[],[f5275,f5206,f3397,f22860]) ).
fof(f22860,plain,
( spl17_1259
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1259])]) ).
fof(f5275,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_257
| ~ spl17_467 ),
inference(resolution,[],[f5207,f3398]) ).
fof(f22858,plain,
( spl17_1258
| ~ spl17_256
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5259,f5202,f3393,f22856]) ).
fof(f22856,plain,
( spl17_1258
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1258])]) ).
fof(f5259,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_256
| ~ spl17_466 ),
inference(resolution,[],[f5203,f3394]) ).
fof(f22854,plain,
( spl17_1257
| ~ spl17_259
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5113,f5005,f3405,f22852]) ).
fof(f22852,plain,
( spl17_1257
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1257])]) ).
fof(f3405,plain,
( spl17_259
<=> ! [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,[spl17_259])]) ).
fof(f5113,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) )
| ~ spl17_259
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3406]) ).
fof(f3406,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)) )
| ~ spl17_259 ),
inference(avatar_component_clause,[],[f3405]) ).
fof(f22850,plain,
( spl17_1256
| ~ spl17_353
| ~ spl17_439 ),
inference(avatar_split_clause,[],[f4955,f4860,f4063,f22848]) ).
fof(f22848,plain,
( spl17_1256
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f921600141ol_nat(finite_card_pname,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1256])]) ).
fof(f4860,plain,
( spl17_439
<=> ! [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,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))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_439])]) ).
fof(f4955,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f921600141ol_nat(finite_card_pname,X0))) )
| ~ spl17_353
| ~ spl17_439 ),
inference(resolution,[],[f4861,f4064]) ).
fof(f4861,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,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))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_439 ),
inference(avatar_component_clause,[],[f4860]) ).
fof(f22846,plain,
( spl17_1255
| ~ spl17_353
| ~ spl17_438 ),
inference(avatar_split_clause,[],[f4949,f4856,f4063,f22844]) ).
fof(f22844,plain,
( spl17_1255
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_fun_a_bool_nat(finite_card_a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1255])]) ).
fof(f4856,plain,
( spl17_438
<=> ! [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,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))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_438])]) ).
fof(f4949,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_fun_a_bool_nat(finite_card_a,X0))) )
| ~ spl17_353
| ~ spl17_438 ),
inference(resolution,[],[f4857,f4064]) ).
fof(f4857,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,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))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_438 ),
inference(avatar_component_clause,[],[f4856]) ).
fof(f22842,plain,
( spl17_1254
| ~ spl17_353
| ~ spl17_437 ),
inference(avatar_split_clause,[],[f4944,f4852,f4063,f22840]) ).
fof(f22840,plain,
( spl17_1254
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1254])]) ).
fof(f4852,plain,
( spl17_437
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_437])]) ).
fof(f4944,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) )
| ~ spl17_353
| ~ spl17_437 ),
inference(resolution,[],[f4853,f4064]) ).
fof(f4853,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,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_437 ),
inference(avatar_component_clause,[],[f4852]) ).
fof(f22838,plain,
( spl17_1253
| ~ spl17_353
| ~ spl17_435 ),
inference(avatar_split_clause,[],[f4939,f4844,f4063,f22836]) ).
fof(f22836,plain,
( spl17_1253
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1253])]) ).
fof(f4844,plain,
( spl17_435
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_435])]) ).
fof(f4939,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) )
| ~ spl17_353
| ~ spl17_435 ),
inference(resolution,[],[f4845,f4064]) ).
fof(f4845,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,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_435 ),
inference(avatar_component_clause,[],[f4844]) ).
fof(f22834,plain,
( spl17_1252
| ~ spl17_374
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4933,f4840,f4289,f22832]) ).
fof(f22832,plain,
( spl17_1252
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1252])]) ).
fof(f4933,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)))) )
| ~ spl17_374
| ~ spl17_434 ),
inference(superposition,[],[f4290,f4841]) ).
fof(f22830,plain,
( spl17_1251
| ~ spl17_375
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4916,f4836,f4293,f22828]) ).
fof(f22828,plain,
( spl17_1251
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1251])]) ).
fof(f4293,plain,
( spl17_375
<=> ! [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,[spl17_375])]) ).
fof(f4916,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)))) )
| ~ spl17_375
| ~ spl17_433 ),
inference(superposition,[],[f4294,f4837]) ).
fof(f4294,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))) )
| ~ spl17_375 ),
inference(avatar_component_clause,[],[f4293]) ).
fof(f22826,plain,
( spl17_1250
| ~ spl17_621
| ~ spl17_1214 ),
inference(avatar_split_clause,[],[f21601,f21504,f7187,f22824]) ).
fof(f22824,plain,
( spl17_1250
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1250])]) ).
fof(f7187,plain,
( spl17_621
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_pname(sK5(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_621])]) ).
fof(f21504,plain,
( spl17_1214
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1214])]) ).
fof(f21601,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u),X0)) )
| ~ spl17_621
| ~ spl17_1214 ),
inference(resolution,[],[f21506,f7188]) ).
fof(f7188,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(X1,X0)) )
| ~ spl17_621 ),
inference(avatar_component_clause,[],[f7187]) ).
fof(f21506,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u)))
| ~ spl17_1214 ),
inference(avatar_component_clause,[],[f21504]) ).
fof(f22822,plain,
( spl17_1249
| ~ spl17_373
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4893,f4832,f4285,f22820]) ).
fof(f22820,plain,
( spl17_1249
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1249])]) ).
fof(f4285,plain,
( spl17_373
<=> ! [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,[spl17_373])]) ).
fof(f4832,plain,
( spl17_432
<=> ! [X0,X1] : collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_432])]) ).
fof(f4893,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)))) )
| ~ spl17_373
| ~ spl17_432 ),
inference(superposition,[],[f4286,f4833]) ).
fof(f4833,plain,
( ! [X0,X1] : collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1))))
| ~ spl17_432 ),
inference(avatar_component_clause,[],[f4832]) ).
fof(f4286,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))) )
| ~ spl17_373 ),
inference(avatar_component_clause,[],[f4285]) ).
fof(f22818,plain,
( spl17_1248
| ~ spl17_372
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4881,f4828,f4281,f22816]) ).
fof(f22816,plain,
( spl17_1248
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1248])]) ).
fof(f4281,plain,
( spl17_372
<=> ! [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,[spl17_372])]) ).
fof(f4828,plain,
( spl17_431
<=> ! [X0,X1] : collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_431])]) ).
fof(f4881,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)))) )
| ~ spl17_372
| ~ spl17_431 ),
inference(superposition,[],[f4282,f4829]) ).
fof(f4829,plain,
( ! [X0,X1] : collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1))))
| ~ spl17_431 ),
inference(avatar_component_clause,[],[f4828]) ).
fof(f4282,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))) )
| ~ spl17_372 ),
inference(avatar_component_clause,[],[f4281]) ).
fof(f22814,plain,
( spl17_1247
| ~ spl17_378
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4822,f4802,f4305,f22812]) ).
fof(f22812,plain,
( spl17_1247
<=> ! [X0,X3,X2,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),image_pname_a(X3,X1)))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1247])]) ).
fof(f4802,plain,
( spl17_430
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X2) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_430])]) ).
fof(f4822,plain,
( ! [X2,X3,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),image_pname_a(X3,X1)))
| ~ is_a(X2) )
| ~ spl17_378
| ~ spl17_430 ),
inference(resolution,[],[f4803,f4306]) ).
fof(f4803,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| image_pname_a(X0,X2) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))) )
| ~ spl17_430 ),
inference(avatar_component_clause,[],[f4802]) ).
fof(f22810,plain,
( spl17_1246
| ~ spl17_377
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4821,f4802,f4301,f22808]) ).
fof(f22808,plain,
( spl17_1246
<=> ! [X0,X3,X2,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),image_pname_a(X3,X1)))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1246])]) ).
fof(f4821,plain,
( ! [X2,X3,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),image_pname_a(X3,X1)))
| ~ is_a(X2) )
| ~ spl17_377
| ~ spl17_430 ),
inference(resolution,[],[f4803,f4302]) ).
fof(f22806,plain,
( spl17_1245
| ~ spl17_408
| ~ spl17_426 ),
inference(avatar_split_clause,[],[f4780,f4772,f4634,f22804]) ).
fof(f22804,plain,
( spl17_1245
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0) = X0
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1245])]) ).
fof(f4634,plain,
( spl17_408
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_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,[spl17_408])]) ).
fof(f4780,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0) = X0
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0)),X0)) )
| ~ spl17_408
| ~ spl17_426 ),
inference(duplicate_literal_removal,[],[f4775]) ).
fof(f4775,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0) = X0
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X0)),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_408
| ~ spl17_426 ),
inference(resolution,[],[f4773,f4635]) ).
fof(f4635,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,X0)))
| X0 = X1
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_408 ),
inference(avatar_component_clause,[],[f4634]) ).
fof(f22802,plain,
( spl17_1244
| ~ spl17_368
| ~ spl17_397 ),
inference(avatar_split_clause,[],[f4541,f4516,f4264,f22800]) ).
fof(f22800,plain,
( spl17_1244
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))),hAPP_f921600141ol_nat(finite_card_pname,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1244])]) ).
fof(f4516,plain,
( spl17_397
<=> ! [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,[spl17_397])]) ).
fof(f4541,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))),hAPP_f921600141ol_nat(finite_card_pname,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) )
| ~ spl17_368
| ~ spl17_397 ),
inference(resolution,[],[f4517,f4265]) ).
fof(f4517,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)) )
| ~ spl17_397 ),
inference(avatar_component_clause,[],[f4516]) ).
fof(f22798,plain,
( spl17_1243
| ~ spl17_368
| ~ spl17_395 ),
inference(avatar_split_clause,[],[f4537,f4508,f4264,f22796]) ).
fof(f22796,plain,
( spl17_1243
<=> ! [X0,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))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))),hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1243])]) ).
fof(f4508,plain,
( spl17_395
<=> ! [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,[spl17_395])]) ).
fof(f4537,plain,
( ! [X0,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))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))),hAPP_fun_a_bool_nat(finite_card_a,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X0))) )
| ~ spl17_368
| ~ spl17_395 ),
inference(resolution,[],[f4509,f4265]) ).
fof(f4509,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)) )
| ~ spl17_395 ),
inference(avatar_component_clause,[],[f4508]) ).
fof(f22794,plain,
( spl17_1242
| ~ spl17_368
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4531,f4504,f4264,f22792]) ).
fof(f22792,plain,
( spl17_1242
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))),hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1242])]) ).
fof(f4504,plain,
( spl17_394
<=> ! [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,[spl17_394])]) ).
fof(f4531,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))),hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_368
| ~ spl17_394 ),
inference(resolution,[],[f4505,f4265]) ).
fof(f4505,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)) )
| ~ spl17_394 ),
inference(avatar_component_clause,[],[f4504]) ).
fof(f22790,plain,
( spl17_1241
| ~ spl17_368
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f4527,f4500,f4264,f22788]) ).
fof(f22788,plain,
( spl17_1241
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1241])]) ).
fof(f4500,plain,
( spl17_393
<=> ! [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,[spl17_393])]) ).
fof(f4527,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) )
| ~ spl17_368
| ~ spl17_393 ),
inference(resolution,[],[f4501,f4265]) ).
fof(f4501,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)) )
| ~ spl17_393 ),
inference(avatar_component_clause,[],[f4500]) ).
fof(f22786,plain,
( spl17_1240
| ~ spl17_368
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f4523,f4496,f4264,f22784]) ).
fof(f22784,plain,
( spl17_1240
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1240])]) ).
fof(f4496,plain,
( spl17_392
<=> ! [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,[spl17_392])]) ).
fof(f4523,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) )
| ~ spl17_368
| ~ spl17_392 ),
inference(resolution,[],[f4497,f4265]) ).
fof(f4497,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)) )
| ~ spl17_392 ),
inference(avatar_component_clause,[],[f4496]) ).
fof(f22782,plain,
( spl17_1239
| ~ spl17_621
| ~ spl17_642 ),
inference(avatar_split_clause,[],[f7947,f7344,f7187,f22780]) ).
fof(f22780,plain,
( spl17_1239
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1239])]) ).
fof(f7344,plain,
( spl17_642
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_642])]) ).
fof(f7947,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn),X0)) )
| ~ spl17_621
| ~ spl17_642 ),
inference(resolution,[],[f7188,f7346]) ).
fof(f7346,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)))
| ~ spl17_642 ),
inference(avatar_component_clause,[],[f7344]) ).
fof(f22778,plain,
( spl17_1238
| ~ spl17_368
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f4519,f4492,f4264,f22776]) ).
fof(f22776,plain,
( spl17_1238
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1238])]) ).
fof(f4492,plain,
( spl17_391
<=> ! [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,[spl17_391])]) ).
fof(f4519,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_368
| ~ spl17_391 ),
inference(resolution,[],[f4493,f4265]) ).
fof(f4493,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)) )
| ~ spl17_391 ),
inference(avatar_component_clause,[],[f4492]) ).
fof(f22774,plain,
( spl17_1237
| ~ spl17_328
| ~ spl17_370 ),
inference(avatar_split_clause,[],[f4423,f4273,f3807,f22772]) ).
fof(f22772,plain,
( spl17_1237
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1237])]) ).
fof(f3807,plain,
( spl17_328
<=> ! [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,[spl17_328])]) ).
fof(f4273,plain,
( spl17_370
<=> ! [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,[spl17_370])]) ).
fof(f4423,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) )
| ~ spl17_328
| ~ spl17_370 ),
inference(resolution,[],[f4274,f3808]) ).
fof(f3808,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)) )
| ~ spl17_328 ),
inference(avatar_component_clause,[],[f3807]) ).
fof(f4274,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) )
| ~ spl17_370 ),
inference(avatar_component_clause,[],[f4273]) ).
fof(f22770,plain,
( spl17_1236
| ~ spl17_352
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4400,f4264,f4059,f22768]) ).
fof(f22768,plain,
( spl17_1236
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1236])]) ).
fof(f4059,plain,
( spl17_352
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_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,[spl17_352])]) ).
fof(f4400,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ spl17_352
| ~ spl17_368 ),
inference(resolution,[],[f4265,f4060]) ).
fof(f4060,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_352 ),
inference(avatar_component_clause,[],[f4059]) ).
fof(f22766,plain,
( spl17_1235
| ~ spl17_351
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4399,f4264,f4055,f22764]) ).
fof(f22764,plain,
( spl17_1235
<=> ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X0),X2)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1235])]) ).
fof(f4055,plain,
( spl17_351
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_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,[spl17_351])]) ).
fof(f4399,plain,
( ! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X0),X2)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X0),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_351
| ~ spl17_368 ),
inference(resolution,[],[f4265,f4056]) ).
fof(f4056,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_351 ),
inference(avatar_component_clause,[],[f4055]) ).
fof(f22236,plain,
( spl17_1234
| ~ spl17_556
| ~ spl17_1110 ),
inference(avatar_split_clause,[],[f20300,f19129,f5948,f22234]) ).
fof(f22234,plain,
( spl17_1234
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X1),X2)))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1234])]) ).
fof(f5948,plain,
( spl17_556
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_556])]) ).
fof(f19129,plain,
( spl17_1110
<=> ! [X0,X1] :
( hBOOL(hAPP_a_bool(X0,sK4(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1110])]) ).
fof(f20300,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X1),X2)))
| hBOOL(X1) )
| ~ spl17_556
| ~ spl17_1110 ),
inference(resolution,[],[f19130,f5949]) ).
fof(f5949,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_556 ),
inference(avatar_component_clause,[],[f5948]) ).
fof(f19130,plain,
( ! [X0,X1] :
( hBOOL(hAPP_a_bool(X0,sK4(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) )
| ~ spl17_1110 ),
inference(avatar_component_clause,[],[f19129]) ).
fof(f22113,plain,
( spl17_1233
| ~ spl17_406
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5596,f5583,f4591,f22111]) ).
fof(f22111,plain,
( spl17_1233
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1233])]) ).
fof(f5596,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) )
| ~ spl17_406
| ~ spl17_499 ),
inference(superposition,[],[f4592,f5584]) ).
fof(f22109,plain,
( spl17_1232
| ~ spl17_11
| ~ spl17_493 ),
inference(avatar_split_clause,[],[f5477,f5474,f2141,f22107]) ).
fof(f22107,plain,
( spl17_1232
<=> ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1232])]) ).
fof(f5474,plain,
( spl17_493
<=> ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),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))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_493])]) ).
fof(f5477,plain,
( ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))
| ~ spl17_11
| ~ spl17_493 ),
inference(superposition,[],[f5475,f2142]) ).
fof(f5475,plain,
( ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),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))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)))
| ~ spl17_493 ),
inference(avatar_component_clause,[],[f5474]) ).
fof(f22105,plain,
( spl17_1231
| ~ spl17_433
| ~ spl17_484 ),
inference(avatar_split_clause,[],[f5408,f5326,f4836,f22103]) ).
fof(f22103,plain,
( spl17_1231
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| X0 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(X1)))
| ~ is_pname(X0)
| ~ is_pname(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1231])]) ).
fof(f5326,plain,
( spl17_484
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_pname(X1)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_484])]) ).
fof(f5408,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| X0 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(X1)))
| ~ is_pname(X0)
| ~ is_pname(X2) )
| ~ spl17_433
| ~ spl17_484 ),
inference(superposition,[],[f5327,f4837]) ).
fof(f5327,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| X0 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ is_pname(X1)
| ~ is_pname(X0) )
| ~ spl17_484 ),
inference(avatar_component_clause,[],[f5326]) ).
fof(f22101,plain,
( spl17_1230
| ~ spl17_434
| ~ spl17_483 ),
inference(avatar_split_clause,[],[f5396,f5322,f4840,f22099]) ).
fof(f22099,plain,
( spl17_1230
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),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))))
| X0 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(X1)))
| ~ is_a(X0)
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1230])]) ).
fof(f5396,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),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))))
| X0 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(X1)))
| ~ is_a(X0)
| ~ is_a(X2) )
| ~ spl17_434
| ~ spl17_483 ),
inference(superposition,[],[f5323,f4841]) ).
fof(f22097,plain,
( spl17_1229
| ~ spl17_206
| ~ spl17_473 ),
inference(avatar_split_clause,[],[f5333,f5281,f3086,f22095]) ).
fof(f22095,plain,
( spl17_1229
<=> ! [X2,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,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1229])]) ).
fof(f3086,plain,
( spl17_206
<=> ! [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,[spl17_206])]) ).
fof(f5333,plain,
( ! [X2,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,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) )
| ~ spl17_206
| ~ spl17_473 ),
inference(resolution,[],[f5282,f3087]) ).
fof(f3087,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)) )
| ~ spl17_206 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f22093,plain,
( spl17_1228
| ~ spl17_276
| ~ spl17_471 ),
inference(avatar_split_clause,[],[f5229,f5226,f3473,f22091]) ).
fof(f22091,plain,
( spl17_1228
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X0,X1)))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1228])]) ).
fof(f5229,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X0,X1)))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) )
| ~ spl17_276
| ~ spl17_471 ),
inference(resolution,[],[f5227,f3474]) ).
fof(f22089,plain,
( spl17_1227
| ~ spl17_273
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f5179,f5140,f3461,f22087]) ).
fof(f22087,plain,
( spl17_1227
<=> ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X1,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1227])]) ).
fof(f3461,plain,
( spl17_273
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_273])]) ).
fof(f5179,plain,
( ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X1,X0))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) )
| ~ spl17_273
| ~ spl17_457 ),
inference(resolution,[],[f5141,f3462]) ).
fof(f3462,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
| ~ spl17_273 ),
inference(avatar_component_clause,[],[f3461]) ).
fof(f22085,plain,
( spl17_1226
| ~ spl17_271
| ~ spl17_456 ),
inference(avatar_split_clause,[],[f5171,f5136,f3453,f22083]) ).
fof(f22083,plain,
( spl17_1226
<=> ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X1,X0))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1226])]) ).
fof(f3453,plain,
( spl17_271
<=> ! [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,sK4(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_271])]) ).
fof(f5171,plain,
( ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X1,X0))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
| ~ spl17_271
| ~ spl17_456 ),
inference(resolution,[],[f5137,f3454]) ).
fof(f3454,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(X0,X1)),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) )
| ~ spl17_271 ),
inference(avatar_component_clause,[],[f3453]) ).
fof(f22081,plain,
( spl17_1225
| ~ spl17_113
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5070,f5005,f2605,f22079]) ).
fof(f22079,plain,
( spl17_1225
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1225])]) ).
fof(f2605,plain,
( spl17_113
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
fof(f5070,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X2))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1))),hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(minus_minus_nat(X0),X1))) )
| ~ spl17_113
| ~ spl17_448 ),
inference(resolution,[],[f5006,f2606]) ).
fof(f2606,plain,
( ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0))
| ~ spl17_113 ),
inference(avatar_component_clause,[],[f2605]) ).
fof(f22077,plain,
( spl17_1224
| ~ spl17_346
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4819,f4802,f4035,f22075]) ).
fof(f22075,plain,
( spl17_1224
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK2(X2,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1224])]) ).
fof(f4035,plain,
( spl17_346
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(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,[spl17_346])]) ).
fof(f4819,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK2(X2,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_346
| ~ spl17_430 ),
inference(resolution,[],[f4803,f4036]) ).
fof(f4036,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(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)) )
| ~ spl17_346 ),
inference(avatar_component_clause,[],[f4035]) ).
fof(f22073,plain,
( spl17_1223
| ~ spl17_323
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4138,f4051,f3787,f22071]) ).
fof(f22071,plain,
( spl17_1223
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1223])]) ).
fof(f3787,plain,
( spl17_323
<=> ! [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,X0)),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_323])]) ).
fof(f4138,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0))))) )
| ~ spl17_323
| ~ spl17_350 ),
inference(resolution,[],[f4052,f3788]) ).
fof(f3788,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_323 ),
inference(avatar_component_clause,[],[f3787]) ).
fof(f22069,plain,
( spl17_1222
| ~ spl17_271
| ~ spl17_348 ),
inference(avatar_split_clause,[],[f4124,f4043,f3453,f22067]) ).
fof(f22067,plain,
( spl17_1222
<=> ! [X2,X0,X1] :
( sK4(X1,image_pname_a(X0,X2)) = hAPP_pname_a(X0,sK8(sK4(X1,image_pname_a(X0,X2)),X0,X2))
| ~ is_a(sK4(X1,image_pname_a(X0,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1222])]) ).
fof(f4043,plain,
( spl17_348
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X1,sK8(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,[spl17_348])]) ).
fof(f4124,plain,
( ! [X2,X0,X1] :
( sK4(X1,image_pname_a(X0,X2)) = hAPP_pname_a(X0,sK8(sK4(X1,image_pname_a(X0,X2)),X0,X2))
| ~ is_a(sK4(X1,image_pname_a(X0,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) )
| ~ spl17_271
| ~ spl17_348 ),
inference(resolution,[],[f4044,f3454]) ).
fof(f4044,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| hAPP_pname_a(X1,sK8(X0,X1,X2)) = X0
| ~ is_a(X0) )
| ~ spl17_348 ),
inference(avatar_component_clause,[],[f4043]) ).
fof(f22065,plain,
( spl17_1221
| ~ spl17_271
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f4121,f4039,f3453,f22063]) ).
fof(f22063,plain,
( spl17_1221
<=> ! [X2,X0,X1] :
( sK4(X1,image_pname_a(X0,X2)) = hAPP_pname_a(X0,sK7(sK4(X1,image_pname_a(X0,X2)),X0,X2))
| ~ is_a(sK4(X1,image_pname_a(X0,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1221])]) ).
fof(f4039,plain,
( spl17_347
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X1,sK7(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,[spl17_347])]) ).
fof(f4121,plain,
( ! [X2,X0,X1] :
( sK4(X1,image_pname_a(X0,X2)) = hAPP_pname_a(X0,sK7(sK4(X1,image_pname_a(X0,X2)),X0,X2))
| ~ is_a(sK4(X1,image_pname_a(X0,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) )
| ~ spl17_271
| ~ spl17_347 ),
inference(resolution,[],[f4040,f3454]) ).
fof(f4040,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| hAPP_pname_a(X1,sK7(X0,X1,X2)) = X0
| ~ is_a(X0) )
| ~ spl17_347 ),
inference(avatar_component_clause,[],[f4039]) ).
fof(f22061,plain,
( spl17_1220
| ~ spl17_56
| ~ spl17_343 ),
inference(avatar_split_clause,[],[f4033,f4001,f2327,f22059]) ).
fof(f22059,plain,
( spl17_1220
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| ~ is_fun_pname_bool(X1)
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))) = collec1974731493e_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1220])]) ).
fof(f2327,plain,
( spl17_56
<=> ! [X0] :
( collec1974731493e_bool(X0) = X0
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f4001,plain,
( spl17_343
<=> ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_343])]) ).
fof(f4033,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| ~ is_fun_pname_bool(X1)
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))) = collec1974731493e_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0)))) )
| ~ spl17_56
| ~ spl17_343 ),
inference(resolution,[],[f4002,f2328]) ).
fof(f2328,plain,
( ! [X0] :
( ~ is_fun1661590463l_bool(X0)
| collec1974731493e_bool(X0) = X0 )
| ~ spl17_56 ),
inference(avatar_component_clause,[],[f2327]) ).
fof(f4002,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) )
| ~ spl17_343 ),
inference(avatar_component_clause,[],[f4001]) ).
fof(f22057,plain,
( spl17_1219
| ~ spl17_57
| ~ spl17_342 ),
inference(avatar_split_clause,[],[f4030,f3997,f2331,f22055]) ).
fof(f22055,plain,
( spl17_1219
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| ~ is_fun_a_bool(X1)
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))) = collect_fun_a_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1219])]) ).
fof(f2331,plain,
( spl17_57
<=> ! [X0] :
( collect_fun_a_bool(X0) = X0
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f3997,plain,
( spl17_342
<=> ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_342])]) ).
fof(f4030,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| ~ is_fun_a_bool(X1)
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))) = collect_fun_a_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0)))) )
| ~ spl17_57
| ~ spl17_342 ),
inference(resolution,[],[f3998,f2332]) ).
fof(f2332,plain,
( ! [X0] :
( ~ is_fun949378684l_bool(X0)
| collect_fun_a_bool(X0) = X0 )
| ~ spl17_57 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f3998,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) )
| ~ spl17_342 ),
inference(avatar_component_clause,[],[f3997]) ).
fof(f22053,plain,
( spl17_1218
| ~ spl17_58
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f4028,f3993,f2335,f22051]) ).
fof(f22051,plain,
( spl17_1218
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| ~ is_pname(X1)
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))) = collect_pname(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1218])]) ).
fof(f2335,plain,
( spl17_58
<=> ! [X0] :
( collect_pname(X0) = X0
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f4028,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| ~ is_pname(X1)
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))) = collect_pname(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) )
| ~ spl17_58
| ~ spl17_341 ),
inference(resolution,[],[f3994,f2336]) ).
fof(f2336,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| collect_pname(X0) = X0 )
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f2335]) ).
fof(f22049,plain,
( spl17_1217
| ~ spl17_277
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3933,f3799,f3477,f22047]) ).
fof(f22047,plain,
( spl17_1217
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1217])]) ).
fof(f3799,plain,
( spl17_326
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK11(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_326])]) ).
fof(f3933,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK11(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)))),X0)) )
| ~ spl17_277
| ~ spl17_326 ),
inference(resolution,[],[f3800,f3478]) ).
fof(f3800,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(X1,sK11(X1)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) )
| ~ spl17_326 ),
inference(avatar_component_clause,[],[f3799]) ).
fof(f21783,plain,
( ~ spl17_1215
| spl17_1216
| ~ spl17_629
| ~ spl17_644 ),
inference(avatar_split_clause,[],[f8071,f7541,f7221,f21780,f21776]) ).
fof(f21776,plain,
( spl17_1215
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,finite_finite_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1215])]) ).
fof(f21780,plain,
( spl17_1216
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),finite_finite_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1216])]) ).
fof(f7221,plain,
( spl17_629
<=> ! [X0] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_629])]) ).
fof(f7541,plain,
( spl17_644
<=> ! [X0] : hAPP_f2117159681l_bool(X0,finite_finite_a) = collect_fun_a_bool(hAPP_f2117159681l_bool(X0,finite_finite_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_644])]) ).
fof(f8071,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),finite_finite_a)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,finite_finite_a))
| ~ spl17_629
| ~ spl17_644 ),
inference(superposition,[],[f7222,f7542]) ).
fof(f7542,plain,
( ! [X0] : hAPP_f2117159681l_bool(X0,finite_finite_a) = collect_fun_a_bool(hAPP_f2117159681l_bool(X0,finite_finite_a))
| ~ spl17_644 ),
inference(avatar_component_clause,[],[f7541]) ).
fof(f7222,plain,
( ! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) )
| ~ spl17_629 ),
inference(avatar_component_clause,[],[f7221]) ).
fof(f21507,plain,
( ~ spl17_8
| spl17_1214
| ~ spl17_588
| ~ spl17_639 ),
inference(avatar_split_clause,[],[f8075,f7262,f6662,f21504,f2128]) ).
fof(f6662,plain,
( spl17_588
<=> ! [X0] : hAPP_f759274231e_bool(X0,u) = collect_pname(hAPP_f759274231e_bool(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_588])]) ).
fof(f7262,plain,
( spl17_639
<=> ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_639])]) ).
fof(f8075,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_588
| ~ spl17_639 ),
inference(superposition,[],[f7263,f6663]) ).
fof(f6663,plain,
( ! [X0] : hAPP_f759274231e_bool(X0,u) = collect_pname(hAPP_f759274231e_bool(X0,u))
| ~ spl17_588 ),
inference(avatar_component_clause,[],[f6662]) ).
fof(f7263,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_639 ),
inference(avatar_component_clause,[],[f7262]) ).
fof(f21200,plain,
( spl17_1213
| ~ spl17_433
| ~ spl17_467 ),
inference(avatar_split_clause,[],[f5279,f5206,f4836,f21198]) ).
fof(f21198,plain,
( spl17_1213
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1213])]) ).
fof(f5279,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ spl17_433
| ~ spl17_467 ),
inference(superposition,[],[f5207,f4837]) ).
fof(f21196,plain,
( spl17_1212
| ~ spl17_434
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5271,f5202,f4840,f21194]) ).
fof(f21194,plain,
( spl17_1212
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1212])]) ).
fof(f5271,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl17_434
| ~ spl17_466 ),
inference(superposition,[],[f5203,f4841]) ).
fof(f21192,plain,
( spl17_1211
| ~ spl17_433
| ~ spl17_464 ),
inference(avatar_split_clause,[],[f5250,f5194,f4836,f21190]) ).
fof(f21190,plain,
( spl17_1211
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1211])]) ).
fof(f5194,plain,
( spl17_464
<=> ! [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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_464])]) ).
fof(f5250,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ spl17_433
| ~ spl17_464 ),
inference(superposition,[],[f5195,f4837]) ).
fof(f5195,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl17_464 ),
inference(avatar_component_clause,[],[f5194]) ).
fof(f21188,plain,
( spl17_1210
| ~ spl17_434
| ~ spl17_463 ),
inference(avatar_split_clause,[],[f5243,f5190,f4840,f21186]) ).
fof(f21186,plain,
( spl17_1210
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1210])]) ).
fof(f5243,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl17_434
| ~ spl17_463 ),
inference(superposition,[],[f5191,f4841]) ).
fof(f21184,plain,
( spl17_1209
| ~ spl17_255
| ~ spl17_462 ),
inference(avatar_split_clause,[],[f5168,f5163,f3389,f21182]) ).
fof(f21182,plain,
( spl17_1209
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1209])]) ).
fof(f5168,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_255
| ~ spl17_462 ),
inference(resolution,[],[f5164,f3390]) ).
fof(f21180,plain,
( spl17_1208
| ~ spl17_321
| ~ spl17_447 ),
inference(avatar_split_clause,[],[f5061,f5001,f3779,f21178]) ).
fof(f21178,plain,
( spl17_1208
<=> ! [X0,X1] :
( image_pname_pname(X1,X0) = X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X0)))
| ~ is_fun_pname_bool(image_pname_pname(X1,X0))
| ~ is_fun_pname_bool(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1208])]) ).
fof(f3779,plain,
( spl17_321
<=> ! [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,[spl17_321])]) ).
fof(f5001,plain,
( spl17_447
<=> ! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_447])]) ).
fof(f5061,plain,
( ! [X0,X1] :
( image_pname_pname(X1,X0) = X0
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X0)))
| ~ is_fun_pname_bool(image_pname_pname(X1,X0))
| ~ is_fun_pname_bool(X0)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_321
| ~ spl17_447 ),
inference(resolution,[],[f5002,f3780]) ).
fof(f3780,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)) )
| ~ spl17_321 ),
inference(avatar_component_clause,[],[f3779]) ).
fof(f5002,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,X0)))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) )
| ~ spl17_447 ),
inference(avatar_component_clause,[],[f5001]) ).
fof(f21176,plain,
( spl17_1207
| ~ spl17_316
| ~ spl17_446 ),
inference(avatar_split_clause,[],[f5053,f4997,f3758,f21174]) ).
fof(f21174,plain,
( spl17_1207
<=> ! [X0,X1] :
( image_a_a(X1,X0) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X0)))
| ~ is_fun_a_bool(image_a_a(X1,X0))
| ~ is_fun_a_bool(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1207])]) ).
fof(f3758,plain,
( spl17_316
<=> ! [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,[spl17_316])]) ).
fof(f4997,plain,
( spl17_446
<=> ! [X0,X1] :
( 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,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))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_446])]) ).
fof(f5053,plain,
( ! [X0,X1] :
( image_a_a(X1,X0) = X0
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X0)))
| ~ is_fun_a_bool(image_a_a(X1,X0))
| ~ is_fun_a_bool(X0)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) )
| ~ spl17_316
| ~ spl17_446 ),
inference(resolution,[],[f4998,f3759]) ).
fof(f3759,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)) )
| ~ spl17_316 ),
inference(avatar_component_clause,[],[f3758]) ).
fof(f4998,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,X0)))
| X0 = 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))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) )
| ~ spl17_446 ),
inference(avatar_component_clause,[],[f4997]) ).
fof(f21172,plain,
( spl17_1206
| ~ spl17_185
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4921,f4840,f2909,f21170]) ).
fof(f21170,plain,
( spl17_1206
<=> ! [X2,X0,X1] : collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1))),X2)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1206])]) ).
fof(f4921,plain,
( ! [X2,X0,X1] : collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1))),X2)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X2))))
| ~ spl17_185
| ~ spl17_434 ),
inference(superposition,[],[f4841,f2910]) ).
fof(f21168,plain,
( spl17_1205
| ~ spl17_336
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4820,f4802,f3973,f21166]) ).
fof(f21166,plain,
( spl17_1205
<=> ! [X0,X3,X2,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X2,X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1205])]) ).
fof(f4820,plain,
( ! [X2,X3,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X2,X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X2,X1)),X3)) )
| ~ spl17_336
| ~ spl17_430 ),
inference(resolution,[],[f4803,f3974]) ).
fof(f21164,plain,
( spl17_1204
| ~ spl17_171
| ~ spl17_429 ),
inference(avatar_split_clause,[],[f4799,f4791,f2839,f21162]) ).
fof(f21162,plain,
( spl17_1204
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),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,[spl17_1204])]) ).
fof(f4799,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_429 ),
inference(superposition,[],[f4792,f2840]) ).
fof(f21160,plain,
( spl17_1203
| ~ spl17_353
| ~ spl17_429 ),
inference(avatar_split_clause,[],[f4796,f4791,f4063,f21158]) ).
fof(f21158,plain,
( spl17_1203
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1203])]) ).
fof(f4796,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_353
| ~ spl17_429 ),
inference(resolution,[],[f4792,f4064]) ).
fof(f21156,plain,
( spl17_1202
| ~ spl17_353
| ~ spl17_426 ),
inference(avatar_split_clause,[],[f4777,f4772,f4063,f21154]) ).
fof(f21154,plain,
( spl17_1202
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2))),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1202])]) ).
fof(f4777,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2))),X0))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_353
| ~ spl17_426 ),
inference(resolution,[],[f4773,f4064]) ).
fof(f21152,plain,
( spl17_1201
| ~ spl17_359
| ~ spl17_415 ),
inference(avatar_split_clause,[],[f4733,f4662,f4087,f21150]) ).
fof(f21150,plain,
( spl17_1201
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1201])]) ).
fof(f4733,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) )
| ~ spl17_359
| ~ spl17_415 ),
inference(resolution,[],[f4663,f4088]) ).
fof(f21148,plain,
( spl17_1200
| ~ spl17_360
| ~ spl17_415 ),
inference(avatar_split_clause,[],[f4732,f4662,f4091,f21146]) ).
fof(f21146,plain,
( spl17_1200
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1200])]) ).
fof(f4732,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
| ~ spl17_360
| ~ spl17_415 ),
inference(resolution,[],[f4663,f4092]) ).
fof(f21144,plain,
( ~ spl17_1198
| spl17_1199
| ~ spl17_566
| ~ spl17_632 ),
inference(avatar_split_clause,[],[f8072,f7233,f6264,f21141,f21137]) ).
fof(f21137,plain,
( spl17_1198
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,finite_finite_pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1198])]) ).
fof(f21141,plain,
( spl17_1199
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),finite_finite_pname))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1199])]) ).
fof(f6264,plain,
( spl17_566
<=> ! [X0] : hAPP_f559147733l_bool(X0,finite_finite_pname) = collec1974731493e_bool(hAPP_f559147733l_bool(X0,finite_finite_pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_566])]) ).
fof(f7233,plain,
( spl17_632
<=> ! [X0] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_632])]) ).
fof(f8072,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),finite_finite_pname)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,finite_finite_pname))
| ~ spl17_566
| ~ spl17_632 ),
inference(superposition,[],[f7234,f6265]) ).
fof(f6265,plain,
( ! [X0] : hAPP_f559147733l_bool(X0,finite_finite_pname) = collec1974731493e_bool(hAPP_f559147733l_bool(X0,finite_finite_pname))
| ~ spl17_566 ),
inference(avatar_component_clause,[],[f6264]) ).
fof(f7234,plain,
( ! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) )
| ~ spl17_632 ),
inference(avatar_component_clause,[],[f7233]) ).
fof(f21135,plain,
( spl17_1197
| ~ spl17_357
| ~ spl17_412 ),
inference(avatar_split_clause,[],[f4723,f4650,f4079,f21133]) ).
fof(f21133,plain,
( spl17_1197
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1197])]) ).
fof(f4723,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) )
| ~ spl17_357
| ~ spl17_412 ),
inference(resolution,[],[f4651,f4080]) ).
fof(f21131,plain,
( spl17_1196
| ~ spl17_358
| ~ spl17_412 ),
inference(avatar_split_clause,[],[f4722,f4650,f4083,f21129]) ).
fof(f21129,plain,
( spl17_1196
<=> ! [X0,X3,X2,X1] :
( ~ 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,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1196])]) ).
fof(f4722,plain,
( ! [X2,X3,X0,X1] :
( ~ 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,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
| ~ spl17_358
| ~ spl17_412 ),
inference(resolution,[],[f4651,f4084]) ).
fof(f21127,plain,
( spl17_1195
| ~ spl17_359
| ~ spl17_410 ),
inference(avatar_split_clause,[],[f4713,f4642,f4087,f21125]) ).
fof(f21125,plain,
( spl17_1195
<=> ! [X0,X3,X2,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),sK9(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1195])]) ).
fof(f4713,plain,
( ! [X2,X3,X0,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),sK9(X1,X2,X0))) )
| ~ spl17_359
| ~ spl17_410 ),
inference(resolution,[],[f4643,f4088]) ).
fof(f21123,plain,
( spl17_1194
| ~ spl17_360
| ~ spl17_410 ),
inference(avatar_split_clause,[],[f4712,f4642,f4091,f21121]) ).
fof(f21121,plain,
( spl17_1194
<=> ! [X0,X3,X2,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),sK9(X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1194])]) ).
fof(f4712,plain,
( ! [X2,X3,X0,X1] :
( ~ 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))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),sK9(X1,X2,X0))) )
| ~ spl17_360
| ~ spl17_410 ),
inference(resolution,[],[f4643,f4092]) ).
fof(f21119,plain,
( spl17_1193
| ~ spl17_171
| ~ spl17_409 ),
inference(avatar_split_clause,[],[f4710,f4638,f2839,f21117]) ).
fof(f21117,plain,
( spl17_1193
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(suc,X0)))
| hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1193])]) ).
fof(f4710,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(suc,X0)))
| hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_171
| ~ spl17_409 ),
inference(superposition,[],[f4639,f2840]) ).
fof(f21115,plain,
( spl17_1192
| ~ spl17_378
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4614,f4575,f4305,f21113]) ).
fof(f21113,plain,
( spl17_1192
<=> ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(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,[spl17_1192])]) ).
fof(f4575,plain,
( spl17_402
<=> ! [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))) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_402])]) ).
fof(f4614,plain,
( ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK8(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) )
| ~ spl17_378
| ~ spl17_402 ),
inference(resolution,[],[f4576,f4306]) ).
fof(f4576,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_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))) = X1
| ~ is_fun_pname_bool(X1) )
| ~ spl17_402 ),
inference(avatar_component_clause,[],[f4575]) ).
fof(f21111,plain,
( spl17_1191
| ~ spl17_377
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4613,f4575,f4301,f21109]) ).
fof(f21109,plain,
( spl17_1191
<=> ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(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,[spl17_1191])]) ).
fof(f4613,plain,
( ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK7(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0) )
| ~ spl17_377
| ~ spl17_402 ),
inference(resolution,[],[f4576,f4302]) ).
fof(f21107,plain,
( spl17_1190
| ~ spl17_248
| ~ spl17_400 ),
inference(avatar_split_clause,[],[f4598,f4567,f3318,f21105]) ).
fof(f21105,plain,
( spl17_1190
<=> ! [X0,X3,X2,X1] :
( image_pname_a(X2,X3) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1190])]) ).
fof(f4567,plain,
( spl17_400
<=> ! [X2,X0,X1] :
( image_pname_a(X0,sK9(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,[spl17_400])]) ).
fof(f4598,plain,
( ! [X2,X3,X0,X1] :
( image_pname_a(X2,X3) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) )
| ~ spl17_248
| ~ spl17_400 ),
inference(resolution,[],[f4568,f3319]) ).
fof(f4568,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| image_pname_a(X0,sK9(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) )
| ~ spl17_400 ),
inference(avatar_component_clause,[],[f4567]) ).
fof(f21103,plain,
( spl17_1189
| ~ spl17_298
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4395,f4264,f3684,f21101]) ).
fof(f21101,plain,
( spl17_1189
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f1253658590ol_nat(finite1659325229l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1189])]) ).
fof(f3684,plain,
( spl17_298
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_298])]) ).
fof(f4395,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f1253658590ol_nat(finite1659325229l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) )
| ~ spl17_298
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3685]) ).
fof(f3685,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) )
| ~ spl17_298 ),
inference(avatar_component_clause,[],[f3684]) ).
fof(f21099,plain,
( spl17_1188
| ~ spl17_297
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4394,f4264,f3680,f21097]) ).
fof(f21097,plain,
( spl17_1188
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f98387925ol_nat(finite269641166l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1188])]) ).
fof(f3680,plain,
( spl17_297
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_297])]) ).
fof(f4394,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f98387925ol_nat(finite269641166l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) )
| ~ spl17_297
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3681]) ).
fof(f3681,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) )
| ~ spl17_297 ),
inference(avatar_component_clause,[],[f3680]) ).
fof(f21092,plain,
( spl17_1187
| ~ spl17_296
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4393,f4264,f3676,f21090]) ).
fof(f21090,plain,
( spl17_1187
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f1690079119ol_nat(finite1352710292l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1187])]) ).
fof(f3676,plain,
( spl17_296
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_296])]) ).
fof(f4393,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f1690079119ol_nat(finite1352710292l_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) )
| ~ spl17_296
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3677]) ).
fof(f3677,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) )
| ~ spl17_296 ),
inference(avatar_component_clause,[],[f3676]) ).
fof(f21088,plain,
( spl17_1186
| ~ spl17_305
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4392,f4264,f3713,f21086]) ).
fof(f21086,plain,
( spl17_1186
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1186])]) ).
fof(f3713,plain,
( spl17_305
<=> ! [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,[spl17_305])]) ).
fof(f4392,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) )
| ~ spl17_305
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3714]) ).
fof(f3714,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)) )
| ~ spl17_305 ),
inference(avatar_component_clause,[],[f3713]) ).
fof(f21084,plain,
( spl17_1185
| ~ spl17_304
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4391,f4264,f3709,f21082]) ).
fof(f21082,plain,
( spl17_1185
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1185])]) ).
fof(f3709,plain,
( spl17_304
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_304])]) ).
fof(f4391,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) )
| ~ spl17_304
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3710]) ).
fof(f3710,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_304 ),
inference(avatar_component_clause,[],[f3709]) ).
fof(f21080,plain,
( spl17_1184
| ~ spl17_300
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4390,f4264,f3693,f21078]) ).
fof(f21078,plain,
( spl17_1184
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1184])]) ).
fof(f3693,plain,
( spl17_300
<=> ! [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,[spl17_300])]) ).
fof(f4390,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) )
| ~ spl17_300
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3694]) ).
fof(f3694,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)) )
| ~ spl17_300 ),
inference(avatar_component_clause,[],[f3693]) ).
fof(f21076,plain,
( spl17_1183
| ~ spl17_306
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4389,f4264,f3717,f21074]) ).
fof(f21074,plain,
( spl17_1183
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1183])]) ).
fof(f3717,plain,
( spl17_306
<=> ! [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,[spl17_306])]) ).
fof(f4389,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) )
| ~ spl17_306
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3718]) ).
fof(f3718,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)) )
| ~ spl17_306 ),
inference(avatar_component_clause,[],[f3717]) ).
fof(f21072,plain,
( spl17_1182
| ~ spl17_302
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4388,f4264,f3701,f21070]) ).
fof(f21070,plain,
( spl17_1182
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1182])]) ).
fof(f3701,plain,
( spl17_302
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_302])]) ).
fof(f4388,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) )
| ~ spl17_302
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3702]) ).
fof(f3702,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_302 ),
inference(avatar_component_clause,[],[f3701]) ).
fof(f21068,plain,
( spl17_1181
| ~ spl17_301
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4387,f4264,f3697,f21066]) ).
fof(f21066,plain,
( spl17_1181
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1181])]) ).
fof(f3697,plain,
( spl17_301
<=> ! [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,[spl17_301])]) ).
fof(f4387,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) )
| ~ spl17_301
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3698]) ).
fof(f3698,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)) )
| ~ spl17_301 ),
inference(avatar_component_clause,[],[f3697]) ).
fof(f21064,plain,
( spl17_1180
| ~ spl17_307
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4386,f4264,f3721,f21062]) ).
fof(f21062,plain,
( spl17_1180
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1180])]) ).
fof(f3721,plain,
( spl17_307
<=> ! [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,[spl17_307])]) ).
fof(f4386,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_307
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3722]) ).
fof(f3722,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)) )
| ~ spl17_307 ),
inference(avatar_component_clause,[],[f3721]) ).
fof(f21060,plain,
( spl17_1179
| ~ spl17_303
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4385,f4264,f3705,f21058]) ).
fof(f21058,plain,
( spl17_1179
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1179])]) ).
fof(f3705,plain,
( spl17_303
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_303])]) ).
fof(f4385,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_303
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3706]) ).
fof(f3706,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_303 ),
inference(avatar_component_clause,[],[f3705]) ).
fof(f21056,plain,
( spl17_1178
| ~ spl17_299
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4384,f4264,f3689,f21054]) ).
fof(f21054,plain,
( spl17_1178
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1178])]) ).
fof(f3689,plain,
( spl17_299
<=> ! [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,[spl17_299])]) ).
fof(f4384,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_299
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3690]) ).
fof(f3690,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)) )
| ~ spl17_299 ),
inference(avatar_component_clause,[],[f3689]) ).
fof(f21052,plain,
( ~ spl17_8
| spl17_1177
| ~ spl17_202
| ~ spl17_584 ),
inference(avatar_split_clause,[],[f7042,f6538,f3070,f21049,f2128]) ).
fof(f21049,plain,
( spl17_1177
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1177])]) ).
fof(f3070,plain,
( spl17_202
<=> ! [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,[spl17_202])]) ).
fof(f6538,plain,
( spl17_584
<=> ! [X0] : hAPP_f434788991l_bool(X0,u) = collec1974731493e_bool(hAPP_f434788991l_bool(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_584])]) ).
fof(f7042,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),u)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_202
| ~ spl17_584 ),
inference(superposition,[],[f3071,f6539]) ).
fof(f6539,plain,
( ! [X0] : hAPP_f434788991l_bool(X0,u) = collec1974731493e_bool(hAPP_f434788991l_bool(X0,u))
| ~ spl17_584 ),
inference(avatar_component_clause,[],[f6538]) ).
fof(f3071,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)) )
| ~ spl17_202 ),
inference(avatar_component_clause,[],[f3070]) ).
fof(f21047,plain,
( spl17_1176
| ~ spl17_316
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4382,f4264,f3758,f21045]) ).
fof(f21045,plain,
( spl17_1176
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1176])]) ).
fof(f4382,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) )
| ~ spl17_316
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3759]) ).
fof(f21043,plain,
( spl17_1175
| ~ spl17_315
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4381,f4264,f3754,f21041]) ).
fof(f21041,plain,
( spl17_1175
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1175])]) ).
fof(f3754,plain,
( spl17_315
<=> ! [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,[spl17_315])]) ).
fof(f4381,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) )
| ~ spl17_315
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3755]) ).
fof(f3755,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)) )
| ~ spl17_315 ),
inference(avatar_component_clause,[],[f3754]) ).
fof(f21039,plain,
( spl17_1174
| ~ spl17_314
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4380,f4264,f3750,f21037]) ).
fof(f21037,plain,
( spl17_1174
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1174])]) ).
fof(f3750,plain,
( spl17_314
<=> ! [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,[spl17_314])]) ).
fof(f4380,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) )
| ~ spl17_314
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3751]) ).
fof(f3751,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)) )
| ~ spl17_314 ),
inference(avatar_component_clause,[],[f3750]) ).
fof(f21035,plain,
( spl17_1173
| ~ spl17_319
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4379,f4264,f3770,f21033]) ).
fof(f21033,plain,
( spl17_1173
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1173])]) ).
fof(f3770,plain,
( spl17_319
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_319])]) ).
fof(f4379,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_319
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3771]) ).
fof(f3771,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_319 ),
inference(avatar_component_clause,[],[f3770]) ).
fof(f21031,plain,
( spl17_1172
| ~ spl17_318
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4378,f4264,f3766,f21029]) ).
fof(f21029,plain,
( spl17_1172
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1172])]) ).
fof(f3766,plain,
( spl17_318
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_318])]) ).
fof(f4378,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_318
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3767]) ).
fof(f3767,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_318 ),
inference(avatar_component_clause,[],[f3766]) ).
fof(f21027,plain,
( spl17_1171
| ~ spl17_317
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4377,f4264,f3762,f21025]) ).
fof(f21025,plain,
( spl17_1171
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1171])]) ).
fof(f3762,plain,
( spl17_317
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_317])]) ).
fof(f4377,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_317
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3763]) ).
fof(f3763,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_317 ),
inference(avatar_component_clause,[],[f3762]) ).
fof(f21023,plain,
( spl17_1170
| ~ spl17_322
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4376,f4264,f3783,f21021]) ).
fof(f21021,plain,
( spl17_1170
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1170])]) ).
fof(f3783,plain,
( spl17_322
<=> ! [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,[spl17_322])]) ).
fof(f4376,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_322
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3784]) ).
fof(f3784,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)) )
| ~ spl17_322 ),
inference(avatar_component_clause,[],[f3783]) ).
fof(f21019,plain,
( spl17_1169
| ~ spl17_321
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4375,f4264,f3779,f21017]) ).
fof(f21017,plain,
( spl17_1169
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1169])]) ).
fof(f4375,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_321
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3780]) ).
fof(f21015,plain,
( spl17_1168
| ~ spl17_320
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4374,f4264,f3775,f21013]) ).
fof(f21013,plain,
( spl17_1168
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1168])]) ).
fof(f3775,plain,
( spl17_320
<=> ! [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,[spl17_320])]) ).
fof(f4374,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
| ~ spl17_320
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3776]) ).
fof(f3776,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)) )
| ~ spl17_320 ),
inference(avatar_component_clause,[],[f3775]) ).
fof(f21011,plain,
( spl17_1167
| ~ spl17_311
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4373,f4264,f3738,f21009]) ).
fof(f21009,plain,
( spl17_1167
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1167])]) ).
fof(f3738,plain,
( spl17_311
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_311])]) ).
fof(f4373,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_311
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3739]) ).
fof(f3739,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_311 ),
inference(avatar_component_clause,[],[f3738]) ).
fof(f21004,plain,
( spl17_1166
| ~ spl17_310
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4372,f4264,f3734,f21002]) ).
fof(f21002,plain,
( spl17_1166
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1166])]) ).
fof(f3734,plain,
( spl17_310
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_310])]) ).
fof(f4372,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_310
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3735]) ).
fof(f3735,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_310 ),
inference(avatar_component_clause,[],[f3734]) ).
fof(f21000,plain,
( spl17_1165
| ~ spl17_308
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4371,f4264,f3725,f20998]) ).
fof(f20998,plain,
( spl17_1165
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1165])]) ).
fof(f3725,plain,
( spl17_308
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_308])]) ).
fof(f4371,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_308
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3726]) ).
fof(f3726,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_308 ),
inference(avatar_component_clause,[],[f3725]) ).
fof(f20996,plain,
( spl17_1164
| ~ spl17_313
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4370,f4264,f3746,f20994]) ).
fof(f20994,plain,
( spl17_1164
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1164])]) ).
fof(f3746,plain,
( spl17_313
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_313])]) ).
fof(f4370,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_313
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3747]) ).
fof(f3747,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_313 ),
inference(avatar_component_clause,[],[f3746]) ).
fof(f20992,plain,
( spl17_1163
| ~ spl17_312
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4369,f4264,f3742,f20990]) ).
fof(f20990,plain,
( spl17_1163
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1163])]) ).
fof(f3742,plain,
( spl17_312
<=> ! [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,[spl17_312])]) ).
fof(f4369,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0))),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_312
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3743]) ).
fof(f3743,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)) )
| ~ spl17_312 ),
inference(avatar_component_clause,[],[f3742]) ).
fof(f20980,plain,
( spl17_1162
| ~ spl17_942
| ~ spl17_1161 ),
inference(avatar_split_clause,[],[f20976,f20972,f12920,f20978]) ).
fof(f20978,plain,
( spl17_1162
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1162])]) ).
fof(f20972,plain,
( spl17_1161
<=> ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1161])]) ).
fof(f20976,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),X1))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = X1 )
| ~ spl17_942
| ~ spl17_1161 ),
inference(forward_demodulation,[],[f20975,f12921]) ).
fof(f20975,plain,
( ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X1)) )
| ~ spl17_942
| ~ spl17_1161 ),
inference(forward_demodulation,[],[f20973,f12921]) ).
fof(f20973,plain,
( ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X1)) )
| ~ spl17_1161 ),
inference(avatar_component_clause,[],[f20972]) ).
fof(f20974,plain,
( spl17_1161
| ~ spl17_290
| ~ spl17_330 ),
inference(avatar_split_clause,[],[f3951,f3843,f3617,f20972]) ).
fof(f3951,plain,
( ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X1)) )
| ~ spl17_290
| ~ spl17_330 ),
inference(resolution,[],[f3844,f3618]) ).
fof(f20898,plain,
( ~ spl17_334
| spl17_1160
| ~ spl17_201
| ~ spl17_515 ),
inference(avatar_split_clause,[],[f5824,f5781,f3066,f20895,f3962]) ).
fof(f20895,plain,
( spl17_1160
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1160])]) ).
fof(f3066,plain,
( spl17_201
<=> ! [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,[spl17_201])]) ).
fof(f5781,plain,
( spl17_515
<=> ! [X0] : hAPP_f1631501043l_bool(X0,g) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_515])]) ).
fof(f5824,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),g)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ spl17_201
| ~ spl17_515 ),
inference(superposition,[],[f3067,f5782]) ).
fof(f5782,plain,
( ! [X0] : hAPP_f1631501043l_bool(X0,g) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,g))
| ~ spl17_515 ),
inference(avatar_component_clause,[],[f5781]) ).
fof(f3067,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)) )
| ~ spl17_201 ),
inference(avatar_component_clause,[],[f3066]) ).
fof(f20356,plain,
( spl17_1159
| ~ spl17_170
| ~ spl17_484 ),
inference(avatar_split_clause,[],[f5402,f5326,f2835,f20354]) ).
fof(f20354,plain,
( spl17_1159
<=> ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ is_pname(X1)
| ~ is_pname(X0)
| ~ hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1159])]) ).
fof(f2835,plain,
( spl17_170
<=> ! [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,[spl17_170])]) ).
fof(f5402,plain,
( ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ is_pname(X1)
| ~ is_pname(X0)
| ~ hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),X0)) )
| ~ spl17_170
| ~ spl17_484 ),
inference(resolution,[],[f5327,f2836]) ).
fof(f2836,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_170 ),
inference(avatar_component_clause,[],[f2835]) ).
fof(f20352,plain,
( spl17_1158
| ~ spl17_168
| ~ spl17_483 ),
inference(avatar_split_clause,[],[f5393,f5322,f2827,f20350]) ).
fof(f20350,plain,
( spl17_1158
<=> ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ is_a(X1)
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1158])]) ).
fof(f2827,plain,
( spl17_168
<=> ! [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,[spl17_168])]) ).
fof(f5393,plain,
( ! [X2,X0,X1] :
( X0 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ is_a(X1)
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X0)) )
| ~ spl17_168
| ~ spl17_483 ),
inference(resolution,[],[f5323,f2828]) ).
fof(f2828,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
| ~ spl17_168 ),
inference(avatar_component_clause,[],[f2827]) ).
fof(f20348,plain,
( spl17_1157
| ~ spl17_169
| ~ spl17_482 ),
inference(avatar_split_clause,[],[f5388,f5318,f2831,f20346]) ).
fof(f20346,plain,
( spl17_1157
<=> ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1157])]) ).
fof(f2831,plain,
( spl17_169
<=> ! [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,[spl17_169])]) ).
fof(f5388,plain,
( ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_169
| ~ spl17_482 ),
inference(resolution,[],[f5319,f2832]) ).
fof(f2832,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_169 ),
inference(avatar_component_clause,[],[f2831]) ).
fof(f20344,plain,
( spl17_1156
| ~ spl17_167
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5374,f5309,f2823,f20342]) ).
fof(f20342,plain,
( spl17_1156
<=> ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1156])]) ).
fof(f2823,plain,
( spl17_167
<=> ! [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,[spl17_167])]) ).
fof(f5374,plain,
( ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_167
| ~ spl17_480 ),
inference(resolution,[],[f5310,f2824]) ).
fof(f2824,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| hBOOL(hAPP_a_bool(X1,X0)) )
| ~ spl17_167 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f20340,plain,
( spl17_1155
| ~ spl17_164
| ~ spl17_477 ),
inference(avatar_split_clause,[],[f5361,f5297,f2811,f20338]) ).
fof(f20338,plain,
( spl17_1155
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| is_pname(sK5(hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))),hAPP_n1025906991e_bool(X2,sK15(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1155])]) ).
fof(f2811,plain,
( spl17_164
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| is_pname(sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_164])]) ).
fof(f5297,plain,
( spl17_477
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,sK15(X2))),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_477])]) ).
fof(f5361,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| is_pname(sK5(hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))),hAPP_n1025906991e_bool(X2,sK15(X2)))) )
| ~ spl17_164
| ~ spl17_477 ),
inference(resolution,[],[f5298,f2812]) ).
fof(f2812,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| is_pname(sK5(X0,X1)) )
| ~ spl17_164 ),
inference(avatar_component_clause,[],[f2811]) ).
fof(f5298,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,sK15(X2))),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1))) )
| ~ spl17_477 ),
inference(avatar_component_clause,[],[f5297]) ).
fof(f20336,plain,
( spl17_1154
| ~ spl17_162
| ~ spl17_476 ),
inference(avatar_split_clause,[],[f5360,f5293,f2803,f20334]) ).
fof(f20334,plain,
( spl17_1154
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| is_a(sK4(hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))),hAPP_nat_fun_a_bool(X2,sK14(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1154])]) ).
fof(f2803,plain,
( spl17_162
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_162])]) ).
fof(f5293,plain,
( spl17_476
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,sK14(X2))),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_476])]) ).
fof(f5360,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| is_a(sK4(hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))),hAPP_nat_fun_a_bool(X2,sK14(X2)))) )
| ~ spl17_162
| ~ spl17_476 ),
inference(resolution,[],[f5294,f2804]) ).
fof(f2804,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK4(X0,X1)) )
| ~ spl17_162 ),
inference(avatar_component_clause,[],[f2803]) ).
fof(f5294,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,sK14(X2))),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1))) )
| ~ spl17_476 ),
inference(avatar_component_clause,[],[f5293]) ).
fof(f20332,plain,
( spl17_1153
| ~ spl17_177
| ~ spl17_466 ),
inference(avatar_split_clause,[],[f5260,f5202,f2876,f20330]) ).
fof(f20330,plain,
( spl17_1153
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1153])]) ).
fof(f5260,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) )
| ~ spl17_177
| ~ spl17_466 ),
inference(resolution,[],[f5203,f2877]) ).
fof(f20328,plain,
( spl17_1152
| ~ spl17_275
| ~ spl17_452 ),
inference(avatar_split_clause,[],[f5027,f5023,f3469,f20326]) ).
fof(f20326,plain,
( spl17_1152
<=> ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X1,X0)))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1152])]) ).
fof(f3469,plain,
( spl17_275
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_275])]) ).
fof(f5027,plain,
( ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X1,X0)))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
| ~ spl17_275
| ~ spl17_452 ),
inference(resolution,[],[f5024,f3470]) ).
fof(f3470,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) )
| ~ spl17_275 ),
inference(avatar_component_clause,[],[f3469]) ).
fof(f20295,plain,
( spl17_1151
| ~ spl17_942
| ~ spl17_1150 ),
inference(avatar_split_clause,[],[f20291,f20288,f12920,f20293]) ).
fof(f20293,plain,
( spl17_1151
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1151])]) ).
fof(f20288,plain,
( spl17_1150
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1150])]) ).
fof(f20291,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
| ~ spl17_942
| ~ spl17_1150 ),
inference(forward_demodulation,[],[f20289,f12921]) ).
fof(f20289,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
| ~ spl17_1150 ),
inference(avatar_component_clause,[],[f20288]) ).
fof(f20290,plain,
( spl17_1150
| ~ spl17_356
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f4622,f4583,f4075,f20288]) ).
fof(f4622,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
| ~ spl17_356
| ~ spl17_404 ),
inference(resolution,[],[f4584,f4076]) ).
fof(f20277,plain,
( spl17_1149
| ~ spl17_942
| ~ spl17_1148 ),
inference(avatar_split_clause,[],[f20273,f20270,f12920,f20275]) ).
fof(f20275,plain,
( spl17_1149
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1149])]) ).
fof(f20270,plain,
( spl17_1148
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1148])]) ).
fof(f20273,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) )
| ~ spl17_942
| ~ spl17_1148 ),
inference(forward_demodulation,[],[f20271,f12921]) ).
fof(f20271,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) )
| ~ spl17_1148 ),
inference(avatar_component_clause,[],[f20270]) ).
fof(f20272,plain,
( spl17_1148
| ~ spl17_354
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f4618,f4579,f4067,f20270]) ).
fof(f4618,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X3)) )
| ~ spl17_354
| ~ spl17_403 ),
inference(resolution,[],[f4580,f4068]) ).
fof(f20268,plain,
( spl17_1147
| ~ spl17_346
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4611,f4575,f4035,f20266]) ).
fof(f20266,plain,
( spl17_1147
<=> ! [X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK2(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) = X1
| ~ is_fun_pname_bool(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,[spl17_1147])]) ).
fof(f4611,plain,
( ! [X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK2(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_346
| ~ spl17_402 ),
inference(resolution,[],[f4576,f4036]) ).
fof(f20264,plain,
( spl17_1146
| ~ spl17_328
| ~ spl17_400 ),
inference(avatar_split_clause,[],[f4597,f4567,f3807,f20262]) ).
fof(f20262,plain,
( spl17_1146
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X2) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1146])]) ).
fof(f4597,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X2) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) )
| ~ spl17_328
| ~ spl17_400 ),
inference(resolution,[],[f4568,f3808]) ).
fof(f20260,plain,
( spl17_1145
| ~ spl17_352
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4448,f4297,f4059,f20258]) ).
fof(f20258,plain,
( spl17_1145
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,X2))),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1145])]) ).
fof(f4448,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,X2))),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))) )
| ~ spl17_352
| ~ spl17_376 ),
inference(superposition,[],[f4060,f4298]) ).
fof(f20256,plain,
( spl17_1144
| ~ spl17_352
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4447,f4297,f4059,f20254]) ).
fof(f20254,plain,
( spl17_1144
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1144])]) ).
fof(f4447,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)) )
| ~ spl17_352
| ~ spl17_376 ),
inference(superposition,[],[f4060,f4298]) ).
fof(f20252,plain,
( spl17_1143
| ~ spl17_351
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4446,f4297,f4055,f20250]) ).
fof(f20250,plain,
( spl17_1143
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1143])]) ).
fof(f4446,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(suc,X2))) )
| ~ spl17_351
| ~ spl17_376 ),
inference(superposition,[],[f4056,f4298]) ).
fof(f20194,plain,
( spl17_1142
| ~ spl17_351
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4445,f4297,f4055,f20192]) ).
fof(f20192,plain,
( spl17_1142
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1142])]) ).
fof(f4445,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X3)) )
| ~ spl17_351
| ~ spl17_376 ),
inference(superposition,[],[f4056,f4298]) ).
fof(f20002,plain,
( spl17_1141
| ~ spl17_277
| ~ spl17_1108 ),
inference(avatar_split_clause,[],[f19242,f18598,f3477,f20000]) ).
fof(f20000,plain,
( spl17_1141
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK3(hAPP_nat_nat(suc,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1141])]) ).
fof(f18598,plain,
( spl17_1108
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),sK3(hAPP_nat_nat(suc,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1108])]) ).
fof(f19242,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK3(hAPP_nat_nat(suc,X0))),X0))
| ~ spl17_277
| ~ spl17_1108 ),
inference(resolution,[],[f18599,f3478]) ).
fof(f18599,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),sK3(hAPP_nat_nat(suc,X0))))
| ~ spl17_1108 ),
inference(avatar_component_clause,[],[f18598]) ).
fof(f19310,plain,
( spl17_1140
| ~ spl17_284
| ~ spl17_487 ),
inference(avatar_split_clause,[],[f5422,f5416,f3518,f19308]) ).
fof(f19308,plain,
( spl17_1140
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1140])]) ).
fof(f3518,plain,
( spl17_284
<=> ! [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,[spl17_284])]) ).
fof(f5422,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2))))) )
| ~ spl17_284
| ~ spl17_487 ),
inference(superposition,[],[f3519,f5417]) ).
fof(f3519,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))) )
| ~ spl17_284 ),
inference(avatar_component_clause,[],[f3518]) ).
fof(f19306,plain,
( spl17_1139
| ~ spl17_237
| ~ spl17_288
| ~ spl17_355
| ~ spl17_563
| ~ spl17_712
| ~ spl17_1108 ),
inference(avatar_split_clause,[],[f19253,f18598,f8678,f5976,f4071,f3609,f3271,f19304]) ).
fof(f19304,plain,
( spl17_1139
<=> ! [X0] : sK3(hAPP_nat_nat(suc,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1139])]) ).
fof(f4071,plain,
( spl17_355
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_355])]) ).
fof(f5976,plain,
( spl17_563
<=> ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,sK3(hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_563])]) ).
fof(f8678,plain,
( spl17_712
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_712])]) ).
fof(f19253,plain,
( ! [X0] : sK3(hAPP_nat_nat(suc,X0)) = X0
| ~ spl17_237
| ~ spl17_288
| ~ spl17_355
| ~ spl17_563
| ~ spl17_712
| ~ spl17_1108 ),
inference(forward_demodulation,[],[f19252,f4355]) ).
fof(f4355,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X0)) = X0
| ~ spl17_288
| ~ spl17_355 ),
inference(resolution,[],[f4072,f3610]) ).
fof(f4072,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X0)))
| ~ spl17_355 ),
inference(avatar_component_clause,[],[f4071]) ).
fof(f19252,plain,
( ! [X0] : sK3(hAPP_nat_nat(suc,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X0))
| ~ spl17_237
| ~ spl17_563
| ~ spl17_712
| ~ spl17_1108 ),
inference(forward_demodulation,[],[f19246,f6399]) ).
fof(f6399,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X1),X0) = hAPP_nat_nat(minus_minus_nat(X1),sK3(hAPP_nat_nat(suc,X0)))
| ~ spl17_237
| ~ spl17_563 ),
inference(forward_demodulation,[],[f6383,f3272]) ).
fof(f6383,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0)) = hAPP_nat_nat(minus_minus_nat(X1),sK3(hAPP_nat_nat(suc,X0)))
| ~ spl17_237
| ~ spl17_563 ),
inference(superposition,[],[f3272,f5977]) ).
fof(f5977,plain,
( ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,sK3(hAPP_nat_nat(suc,X0)))
| ~ spl17_563 ),
inference(avatar_component_clause,[],[f5976]) ).
fof(f19246,plain,
( ! [X0] : sK3(hAPP_nat_nat(suc,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),sK3(hAPP_nat_nat(suc,X0))))
| ~ spl17_712
| ~ spl17_1108 ),
inference(resolution,[],[f18599,f8679]) ).
fof(f8679,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X1 )
| ~ spl17_712 ),
inference(avatar_component_clause,[],[f8678]) ).
fof(f19302,plain,
( spl17_1138
| ~ spl17_164
| ~ spl17_464 ),
inference(avatar_split_clause,[],[f5247,f5194,f2811,f19300]) ).
fof(f19300,plain,
( spl17_1138
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
| is_pname(sK5(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1138])]) ).
fof(f5247,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
| is_pname(sK5(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X0)) )
| ~ spl17_164
| ~ spl17_464 ),
inference(resolution,[],[f5195,f2812]) ).
fof(f19298,plain,
( spl17_1137
| ~ spl17_162
| ~ spl17_463 ),
inference(avatar_split_clause,[],[f5240,f5190,f2803,f19296]) ).
fof(f19296,plain,
( spl17_1137
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
| is_a(sK4(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1137])]) ).
fof(f5240,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
| is_a(sK4(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X0)) )
| ~ spl17_162
| ~ spl17_463 ),
inference(resolution,[],[f5191,f2804]) ).
fof(f19294,plain,
( spl17_1136
| ~ spl17_206
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5071,f5005,f3086,f19292]) ).
fof(f19292,plain,
( spl17_1136
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1136])]) ).
fof(f5071,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
| ~ spl17_206
| ~ spl17_448 ),
inference(resolution,[],[f5006,f3087]) ).
fof(f19290,plain,
( spl17_1135
| ~ spl17_392
| ~ spl17_445 ),
inference(avatar_split_clause,[],[f5046,f4979,f4496,f19288]) ).
fof(f19288,plain,
( spl17_1135
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0)
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1135])]) ).
fof(f4979,plain,
( spl17_445
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_445])]) ).
fof(f5046,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0)
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) )
| ~ spl17_392
| ~ spl17_445 ),
inference(resolution,[],[f4980,f4497]) ).
fof(f4980,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,X0)))
| X0 = X1
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0) )
| ~ spl17_445 ),
inference(avatar_component_clause,[],[f4979]) ).
fof(f19286,plain,
( spl17_1134
| ~ spl17_393
| ~ spl17_444 ),
inference(avatar_split_clause,[],[f5035,f4975,f4500,f19284]) ).
fof(f19284,plain,
( spl17_1134
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0)
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1134])]) ).
fof(f4975,plain,
( spl17_444
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_444])]) ).
fof(f5035,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0)
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) )
| ~ spl17_393
| ~ spl17_444 ),
inference(resolution,[],[f4976,f4501]) ).
fof(f4976,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,X0)))
| X0 = X1
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0) )
| ~ spl17_444 ),
inference(avatar_component_clause,[],[f4975]) ).
fof(f19282,plain,
( spl17_1133
| ~ spl17_185
| ~ spl17_438 ),
inference(avatar_split_clause,[],[f4952,f4856,f2909,f19280]) ).
fof(f19280,plain,
( spl17_1133
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1133])]) ).
fof(f4952,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) )
| ~ spl17_185
| ~ spl17_438 ),
inference(superposition,[],[f4857,f2910]) ).
fof(f19278,plain,
( spl17_1132
| ~ spl17_185
| ~ spl17_419 ),
inference(avatar_split_clause,[],[f4746,f4678,f2909,f19276]) ).
fof(f19276,plain,
( spl17_1132
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1132])]) ).
fof(f4746,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),X3)) )
| ~ spl17_185
| ~ spl17_419 ),
inference(superposition,[],[f4679,f2910]) ).
fof(f19274,plain,
( spl17_1131
| ~ spl17_185
| ~ spl17_416 ),
inference(avatar_split_clause,[],[f4735,f4666,f2909,f19272]) ).
fof(f19272,plain,
( spl17_1131
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X3))
| ~ hBOOL(hAPP_a_bool(X2,X3))
| ~ is_a(X3)
| ~ is_a(hAPP_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1131])]) ).
fof(f4666,plain,
( spl17_416
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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))),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_416])]) ).
fof(f4735,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),X3))
| ~ hBOOL(hAPP_a_bool(X2,X3))
| ~ is_a(X3)
| ~ is_a(hAPP_pname_a(X0,X1)) )
| ~ spl17_185
| ~ spl17_416 ),
inference(superposition,[],[f4667,f2910]) ).
fof(f4667,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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))),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) )
| ~ spl17_416 ),
inference(avatar_component_clause,[],[f4666]) ).
fof(f19270,plain,
( spl17_1130
| ~ spl17_336
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4612,f4575,f3973,f19268]) ).
fof(f19268,plain,
( spl17_1130
<=> ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1130])]) ).
fof(f4612,plain,
( ! [X2,X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK16(X0,X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = X2
| ~ is_fun_pname_bool(X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) )
| ~ spl17_336
| ~ spl17_402 ),
inference(resolution,[],[f4576,f3974]) ).
fof(f19266,plain,
( spl17_1129
| ~ spl17_288
| ~ spl17_397 ),
inference(avatar_split_clause,[],[f4544,f4516,f3609,f19264]) ).
fof(f19264,plain,
( spl17_1129
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1129])]) ).
fof(f4544,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) )
| ~ spl17_288
| ~ spl17_397 ),
inference(resolution,[],[f4517,f3610]) ).
fof(f19238,plain,
( spl17_1128
| ~ spl17_289
| ~ spl17_397 ),
inference(avatar_split_clause,[],[f4543,f4516,f3613,f19236]) ).
fof(f19236,plain,
( spl17_1128
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1128])]) ).
fof(f4543,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0))) )
| ~ spl17_289
| ~ spl17_397 ),
inference(resolution,[],[f4517,f3614]) ).
fof(f19234,plain,
( spl17_1127
| ~ spl17_288
| ~ spl17_395 ),
inference(avatar_split_clause,[],[f4540,f4508,f3609,f19232]) ).
fof(f19232,plain,
( spl17_1127
<=> ! [X0,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))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1127])]) ).
fof(f4540,plain,
( ! [X0,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))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X0))) )
| ~ spl17_288
| ~ spl17_395 ),
inference(resolution,[],[f4509,f3610]) ).
fof(f19230,plain,
( spl17_1126
| ~ spl17_289
| ~ spl17_395 ),
inference(avatar_split_clause,[],[f4539,f4508,f3613,f19228]) ).
fof(f19228,plain,
( spl17_1126
<=> ! [X0,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))
| hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,X0)
| ~ 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,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1126])]) ).
fof(f4539,plain,
( ! [X0,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))
| hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,X0)
| ~ 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,X0))) )
| ~ spl17_289
| ~ spl17_395 ),
inference(resolution,[],[f4509,f3614]) ).
fof(f19226,plain,
( spl17_1125
| ~ spl17_288
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4534,f4504,f3609,f19224]) ).
fof(f19224,plain,
( spl17_1125
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1125])]) ).
fof(f4534,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_288
| ~ spl17_394 ),
inference(resolution,[],[f4505,f3610]) ).
fof(f19222,plain,
( spl17_1124
| ~ spl17_289
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4533,f4504,f3613,f19220]) ).
fof(f19220,plain,
( spl17_1124
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1124])]) ).
fof(f4533,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_289
| ~ spl17_394 ),
inference(resolution,[],[f4505,f3614]) ).
fof(f19218,plain,
( spl17_1123
| ~ spl17_288
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f4530,f4500,f3609,f19216]) ).
fof(f19216,plain,
( spl17_1123
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1123])]) ).
fof(f4530,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) )
| ~ spl17_288
| ~ spl17_393 ),
inference(resolution,[],[f4501,f3610]) ).
fof(f19214,plain,
( spl17_1122
| ~ spl17_289
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f4529,f4500,f3613,f19212]) ).
fof(f19212,plain,
( spl17_1122
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1122])]) ).
fof(f4529,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) )
| ~ spl17_289
| ~ spl17_393 ),
inference(resolution,[],[f4501,f3614]) ).
fof(f19210,plain,
( spl17_1121
| ~ spl17_288
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f4526,f4496,f3609,f19208]) ).
fof(f19208,plain,
( spl17_1121
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1121])]) ).
fof(f4526,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) )
| ~ spl17_288
| ~ spl17_392 ),
inference(resolution,[],[f4497,f3610]) ).
fof(f19206,plain,
( spl17_1120
| ~ spl17_289
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f4525,f4496,f3613,f19204]) ).
fof(f19204,plain,
( spl17_1120
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1120])]) ).
fof(f4525,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) )
| ~ spl17_289
| ~ spl17_392 ),
inference(resolution,[],[f4497,f3614]) ).
fof(f19202,plain,
( spl17_1119
| ~ spl17_288
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f4522,f4492,f3609,f19200]) ).
fof(f19200,plain,
( spl17_1119
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1119])]) ).
fof(f4522,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_288
| ~ spl17_391 ),
inference(resolution,[],[f4493,f3610]) ).
fof(f19198,plain,
( spl17_1118
| ~ spl17_166
| ~ spl17_665 ),
inference(avatar_split_clause,[],[f8186,f8145,f2819,f19196]) ).
fof(f19196,plain,
( spl17_1118
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK1(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1118])]) ).
fof(f2819,plain,
( spl17_166
<=> ! [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,[spl17_166])]) ).
fof(f8145,plain,
( spl17_665
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,sK1(X0))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_665])]) ).
fof(f8186,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK1(X0)))) )
| ~ spl17_166
| ~ spl17_665 ),
inference(resolution,[],[f8146,f2820]) ).
fof(f2820,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_166 ),
inference(avatar_component_clause,[],[f2819]) ).
fof(f8146,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,sK1(X0))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_665 ),
inference(avatar_component_clause,[],[f8145]) ).
fof(f19194,plain,
( spl17_1117
| ~ spl17_289
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f4521,f4492,f3613,f19192]) ).
fof(f19192,plain,
( spl17_1117
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1117])]) ).
fof(f4521,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_289
| ~ spl17_391 ),
inference(resolution,[],[f4493,f3614]) ).
fof(f19190,plain,
( spl17_1116
| ~ spl17_288
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4178,f4059,f3609,f19188]) ).
fof(f19188,plain,
( spl17_1116
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1116])]) ).
fof(f4178,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) )
| ~ spl17_288
| ~ spl17_352 ),
inference(resolution,[],[f4060,f3610]) ).
fof(f19186,plain,
( spl17_1115
| ~ spl17_289
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4177,f4059,f3613,f19184]) ).
fof(f19184,plain,
( spl17_1115
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(X1),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1115])]) ).
fof(f4177,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X2) = hAPP_nat_nat(minus_minus_nat(X1),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X0),X2))) )
| ~ spl17_289
| ~ spl17_352 ),
inference(resolution,[],[f4060,f3614]) ).
fof(f19182,plain,
( spl17_1114
| ~ spl17_288
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4168,f4055,f3609,f19180]) ).
fof(f19180,plain,
( spl17_1114
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1114])]) ).
fof(f4168,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X2),X1))) )
| ~ spl17_288
| ~ spl17_351 ),
inference(resolution,[],[f4056,f3610]) ).
fof(f19178,plain,
( spl17_1113
| ~ spl17_289
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4167,f4055,f3613,f19176]) ).
fof(f19176,plain,
( spl17_1113
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(X2),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1113])]) ).
fof(f4167,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(X2),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X0)),hAPP_nat_nat(minus_minus_nat(X2),X1))) )
| ~ spl17_289
| ~ spl17_351 ),
inference(resolution,[],[f4056,f3614]) ).
fof(f19174,plain,
( spl17_1112
| ~ spl17_219
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4160,f4051,f3138,f19172]) ).
fof(f19172,plain,
( spl17_1112
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)))),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1112])]) ).
fof(f3138,plain,
( spl17_219
<=> ! [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,[spl17_219])]) ).
fof(f4160,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)))),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1)) )
| ~ spl17_219
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4159,f3139]) ).
fof(f3139,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)
| ~ spl17_219 ),
inference(avatar_component_clause,[],[f3138]) ).
fof(f4159,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)))),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2)) )
| ~ spl17_219
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4151,f3139]) ).
fof(f4151,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2)) )
| ~ spl17_219
| ~ spl17_350 ),
inference(superposition,[],[f4052,f3139]) ).
fof(f19170,plain,
( spl17_1111
| ~ spl17_218
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4158,f4051,f3134,f19168]) ).
fof(f19168,plain,
( spl17_1111
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)))),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1111])]) ).
fof(f3134,plain,
( spl17_218
<=> ! [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,[spl17_218])]) ).
fof(f4158,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)))),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1)) )
| ~ spl17_218
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4157,f3135]) ).
fof(f3135,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)
| ~ spl17_218 ),
inference(avatar_component_clause,[],[f3134]) ).
fof(f4157,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(suc,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)))),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2)) )
| ~ spl17_218
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4150,f3135]) ).
fof(f4150,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),hAPP_nat_nat(suc,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2)) )
| ~ spl17_218
| ~ spl17_350 ),
inference(superposition,[],[f4052,f3135]) ).
fof(f19131,plain,
( spl17_1110
| ~ spl17_177
| ~ spl17_622 ),
inference(avatar_split_clause,[],[f7953,f7191,f2876,f19129]) ).
fof(f7191,plain,
( spl17_622
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_a_bool(X0,sK4(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_622])]) ).
fof(f7953,plain,
( ! [X0,X1] :
( hBOOL(hAPP_a_bool(X0,sK4(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) )
| ~ spl17_177
| ~ spl17_622 ),
inference(resolution,[],[f7192,f2877]) ).
fof(f7192,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_a_bool(X0,sK4(X1,X0))) )
| ~ spl17_622 ),
inference(avatar_component_clause,[],[f7191]) ).
fof(f18842,plain,
( spl17_1109
| ~ spl17_355
| ~ spl17_563 ),
inference(avatar_split_clause,[],[f6393,f5976,f4071,f18840]) ).
fof(f18840,plain,
( spl17_1109
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK3(hAPP_nat_nat(suc,X0))),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1109])]) ).
fof(f6393,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK3(hAPP_nat_nat(suc,X0))),hAPP_nat_nat(suc,X0)))
| ~ spl17_355
| ~ spl17_563 ),
inference(superposition,[],[f4072,f5977]) ).
fof(f18600,plain,
( spl17_1108
| ~ spl17_104
| ~ spl17_563 ),
inference(avatar_split_clause,[],[f6379,f5976,f2568,f18598]) ).
fof(f2568,plain,
( spl17_104
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
fof(f6379,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),sK3(hAPP_nat_nat(suc,X0))))
| ~ spl17_104
| ~ spl17_563 ),
inference(superposition,[],[f2569,f5977]) ).
fof(f2569,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0))
| ~ spl17_104 ),
inference(avatar_component_clause,[],[f2568]) ).
fof(f18496,plain,
( spl17_1107
| ~ spl17_337
| ~ spl17_504 ),
inference(avatar_split_clause,[],[f5680,f5631,f3977,f18494]) ).
fof(f18494,plain,
( spl17_1107
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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),X1))),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),X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1107])]) ).
fof(f3977,plain,
( spl17_337
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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,[spl17_337])]) ).
fof(f5680,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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),X1))),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),X2))))))
| ~ spl17_337
| ~ spl17_504 ),
inference(superposition,[],[f3978,f5632]) ).
fof(f3978,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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)))))
| ~ spl17_337 ),
inference(avatar_component_clause,[],[f3977]) ).
fof(f18492,plain,
( spl17_1106
| ~ spl17_339
| ~ spl17_503 ),
inference(avatar_split_clause,[],[f5641,f5627,f3985,f18490]) ).
fof(f18490,plain,
( spl17_1106
<=> ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1106])]) ).
fof(f3985,plain,
( spl17_339
<=> ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),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,[spl17_339])]) ).
fof(f5641,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))))
| ~ spl17_339
| ~ spl17_503 ),
inference(superposition,[],[f3986,f5628]) ).
fof(f3986,plain,
( ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),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)))))
| ~ spl17_339 ),
inference(avatar_component_clause,[],[f3985]) ).
fof(f18488,plain,
( spl17_1105
| ~ spl17_165
| ~ spl17_471 ),
inference(avatar_split_clause,[],[f5233,f5226,f2815,f18486]) ).
fof(f18486,plain,
( spl17_1105
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1105])]) ).
fof(f2815,plain,
( spl17_165
<=> ! [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,[spl17_165])]) ).
fof(f5233,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X0)) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_165
| ~ spl17_471 ),
inference(resolution,[],[f5227,f2816]) ).
fof(f2816,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_165 ),
inference(avatar_component_clause,[],[f2815]) ).
fof(f18484,plain,
( spl17_1104
| ~ spl17_170
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f5178,f5140,f2835,f18482]) ).
fof(f18482,plain,
( spl17_1104
<=> ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1104])]) ).
fof(f5178,plain,
( ! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_170
| ~ spl17_457 ),
inference(resolution,[],[f5141,f2836]) ).
fof(f18480,plain,
( spl17_1103
| ~ spl17_168
| ~ spl17_456 ),
inference(avatar_split_clause,[],[f5170,f5136,f2827,f18478]) ).
fof(f18478,plain,
( spl17_1103
<=> ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1103])]) ).
fof(f5170,plain,
( ! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_168
| ~ spl17_456 ),
inference(resolution,[],[f5137,f2828]) ).
fof(f18476,plain,
( spl17_1102
| ~ spl17_433
| ~ spl17_443 ),
inference(avatar_split_clause,[],[f4972,f4964,f4836,f18474]) ).
fof(f18474,plain,
( spl17_1102
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),X2))
| X0 = X2
| hBOOL(hAPP_pname_bool(collect_pname(X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1102])]) ).
fof(f4964,plain,
( spl17_443
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_pname_bool(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))),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_443])]) ).
fof(f4972,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),X2))
| X0 = X2
| hBOOL(hAPP_pname_bool(collect_pname(X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) )
| ~ spl17_433
| ~ spl17_443 ),
inference(superposition,[],[f4965,f4837]) ).
fof(f4965,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(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))),X2))
| X0 = X2
| hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_pname(X0) )
| ~ spl17_443 ),
inference(avatar_component_clause,[],[f4964]) ).
fof(f18472,plain,
( spl17_1101
| ~ spl17_434
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4969,f4960,f4840,f18470]) ).
fof(f18470,plain,
( spl17_1101
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(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)),X2))
| X0 = X2
| hBOOL(hAPP_a_bool(collect_a(X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1101])]) ).
fof(f4969,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(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)),X2))
| X0 = X2
| hBOOL(hAPP_a_bool(collect_a(X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) )
| ~ spl17_434
| ~ spl17_442 ),
inference(superposition,[],[f4961,f4841]) ).
fof(f18468,plain,
( spl17_1100
| ~ spl17_433
| ~ spl17_439 ),
inference(avatar_split_clause,[],[f4958,f4860,f4836,f18466]) ).
fof(f18466,plain,
( spl17_1100
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,collect_pname(X1))),hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1100])]) ).
fof(f4958,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,collect_pname(X1))),hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
| ~ spl17_433
| ~ spl17_439 ),
inference(superposition,[],[f4861,f4837]) ).
fof(f18464,plain,
( spl17_1099
| ~ spl17_434
| ~ spl17_438 ),
inference(avatar_split_clause,[],[f4953,f4856,f4840,f18462]) ).
fof(f18462,plain,
( spl17_1099
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,collect_a(X1))),hAPP_fun_a_bool_nat(finite_card_a,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)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1099])]) ).
fof(f4953,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,collect_a(X1))),hAPP_fun_a_bool_nat(finite_card_a,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)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
| ~ spl17_434
| ~ spl17_438 ),
inference(superposition,[],[f4857,f4841]) ).
fof(f18460,plain,
( spl17_1098
| ~ spl17_431
| ~ spl17_437 ),
inference(avatar_split_clause,[],[f4947,f4852,f4828,f18458]) ).
fof(f18458,plain,
( spl17_1098
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1098])]) ).
fof(f4947,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
| ~ spl17_431
| ~ spl17_437 ),
inference(superposition,[],[f4853,f4829]) ).
fof(f18456,plain,
( spl17_1097
| ~ spl17_432
| ~ spl17_435 ),
inference(avatar_split_clause,[],[f4942,f4844,f4832,f18454]) ).
fof(f18454,plain,
( spl17_1097
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1097])]) ).
fof(f4942,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
| ~ spl17_432
| ~ spl17_435 ),
inference(superposition,[],[f4845,f4833]) ).
fof(f18452,plain,
( spl17_1096
| ~ spl17_273
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4818,f4802,f3461,f18450]) ).
fof(f18450,plain,
( spl17_1096
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X2,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1096])]) ).
fof(f4818,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X2,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_273
| ~ spl17_430 ),
inference(resolution,[],[f4803,f3462]) ).
fof(f18448,plain,
( spl17_1095
| ~ spl17_340
| ~ spl17_420 ),
inference(avatar_split_clause,[],[f4752,f4682,f3989,f18446]) ).
fof(f18446,plain,
( spl17_1095
<=> ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1095])]) ).
fof(f4752,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))))
| ~ spl17_340
| ~ spl17_420 ),
inference(forward_demodulation,[],[f4750,f2067]) ).
fof(f2067,plain,
! [X2,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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))),
inference(forward_demodulation,[],[f1899,f1848]) ).
fof(f1848,plain,
! [X0,X1] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_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),collect_pname(X1)))),
inference(definition_unfolding,[],[f1392,f1384]) ).
fof(f1392,plain,
! [X0,X1] : insert_pname(X0,collect_pname(X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),
inference(cnf_transformation,[],[f509]) ).
fof(f509,plain,
! [X0,X1] : insert_pname(X0,collect_pname(X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X7,X12] : insert_pname(X7,collect_pname(X12)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1899,plain,
! [X2,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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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),X2)))))),
inference(definition_unfolding,[],[f1683,f1384,f1384,f1384,f1384]) ).
fof(f1683,plain,
! [X2,X0,X1] : insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)),
inference(cnf_transformation,[],[f712]) ).
fof(f712,plain,
! [X0,X1,X2] : insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X10,X32,X4] : insert_pname(X10,insert_pname(X32,X4)) = insert_pname(X32,insert_pname(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4750,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))))))
| ~ spl17_340
| ~ spl17_420 ),
inference(resolution,[],[f4683,f3990]) ).
fof(f18444,plain,
( spl17_1094
| ~ spl17_338
| ~ spl17_418 ),
inference(avatar_split_clause,[],[f4741,f4674,f3981,f18442]) ).
fof(f18442,plain,
( spl17_1094
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),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),X2))),cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1094])]) ).
fof(f4741,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),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),X2))),cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))))
| ~ spl17_338
| ~ spl17_418 ),
inference(forward_demodulation,[],[f4738,f2068]) ).
fof(f2068,plain,
! [X2,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))) = 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),X1))),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),X2)))),
inference(forward_demodulation,[],[f1900,f1849]) ).
fof(f1849,plain,
! [X0,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)) = 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),collect_a(X1)))),
inference(definition_unfolding,[],[f1393,f1386]) ).
fof(f1393,plain,
! [X0,X1] : 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,[],[f510]) ).
fof(f510,plain,
! [X0,X1] : 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,[],[f282]) ).
fof(f282,axiom,
! [X7,X12] : 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(f1900,plain,
! [X2,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),X2)))))),
inference(definition_unfolding,[],[f1684,f1386,f1386,f1386,f1386]) ).
fof(f1684,plain,
! [X2,X0,X1] : insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)),
inference(cnf_transformation,[],[f713]) ).
fof(f713,plain,
! [X0,X1,X2] : insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X10,X32,X4] : insert_a(X10,insert_a(X32,X4)) = insert_a(X32,insert_a(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4738,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))))))
| ~ spl17_338
| ~ spl17_418 ),
inference(resolution,[],[f4675,f3982]) ).
fof(f18440,plain,
( spl17_1093
| ~ spl17_248
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f4557,f4546,f3318,f18438]) ).
fof(f18438,plain,
( spl17_1093
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X2,X3))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1093])]) ).
fof(f4546,plain,
( spl17_398
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(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,[spl17_398])]) ).
fof(f4557,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X2,X3))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) )
| ~ spl17_248
| ~ spl17_398 ),
inference(resolution,[],[f4547,f3319]) ).
fof(f4547,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) )
| ~ spl17_398 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f18436,plain,
( spl17_1092
| ~ spl17_353
| ~ spl17_397 ),
inference(avatar_split_clause,[],[f4542,f4516,f4063,f18434]) ).
fof(f18434,plain,
( spl17_1092
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f921600141ol_nat(finite_card_pname,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1092])]) ).
fof(f4542,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f921600141ol_nat(finite_card_pname,X0))) )
| ~ spl17_353
| ~ spl17_397 ),
inference(resolution,[],[f4517,f4064]) ).
fof(f18432,plain,
( spl17_1091
| ~ spl17_353
| ~ spl17_395 ),
inference(avatar_split_clause,[],[f4538,f4508,f4063,f18430]) ).
fof(f18430,plain,
( spl17_1091
<=> ! [X2,X0,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))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_fun_a_bool_nat(finite_card_a,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1091])]) ).
fof(f4538,plain,
( ! [X2,X0,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))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_fun_a_bool_nat(finite_card_a,X0))) )
| ~ spl17_353
| ~ spl17_395 ),
inference(resolution,[],[f4509,f4064]) ).
fof(f18428,plain,
( spl17_1090
| ~ spl17_171
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4536,f4504,f2839,f18426]) ).
fof(f18426,plain,
( spl17_1090
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),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,[spl17_1090])]) ).
fof(f4536,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_394 ),
inference(superposition,[],[f4505,f2840]) ).
fof(f18424,plain,
( spl17_1089
| ~ spl17_353
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4532,f4504,f4063,f18422]) ).
fof(f18422,plain,
( spl17_1089
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1089])]) ).
fof(f4532,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f22106695ol_nat(finite_card_nat,X0))) )
| ~ spl17_353
| ~ spl17_394 ),
inference(resolution,[],[f4505,f4064]) ).
fof(f18420,plain,
( spl17_1088
| ~ spl17_177
| ~ spl17_1081 ),
inference(avatar_split_clause,[],[f18285,f17908,f2876,f18418]) ).
fof(f18418,plain,
( spl17_1088
<=> ! [X0] :
( is_pname(sK16(mgt_call,X0,u))
| hBOOL(hAPP_fun_a_bool_bool(p(X0),g)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1088])]) ).
fof(f17908,plain,
( spl17_1081
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),X0))
| is_pname(sK16(mgt_call,X0,u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1081])]) ).
fof(f18285,plain,
( ! [X0] :
( is_pname(sK16(mgt_call,X0,u))
| hBOOL(hAPP_fun_a_bool_bool(p(X0),g)) )
| ~ spl17_177
| ~ spl17_1081 ),
inference(resolution,[],[f17909,f2877]) ).
fof(f17909,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),X0))
| is_pname(sK16(mgt_call,X0,u)) )
| ~ spl17_1081 ),
inference(avatar_component_clause,[],[f17908]) ).
fof(f18416,plain,
( spl17_1087
| ~ spl17_353
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f4528,f4500,f4063,f18414]) ).
fof(f18414,plain,
( spl17_1087
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1087])]) ).
fof(f4528,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f55526627ol_nat(finite1340463720e_bool,X0))) )
| ~ spl17_353
| ~ spl17_393 ),
inference(resolution,[],[f4501,f4064]) ).
fof(f18412,plain,
( spl17_1086
| ~ spl17_353
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f4524,f4496,f4063,f18410]) ).
fof(f18410,plain,
( spl17_1086
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1086])]) ).
fof(f4524,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0))) )
| ~ spl17_353
| ~ spl17_392 ),
inference(resolution,[],[f4497,f4064]) ).
fof(f18408,plain,
( spl17_1085
| ~ spl17_353
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f4520,f4492,f4063,f18406]) ).
fof(f18406,plain,
( spl17_1085
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1085])]) ).
fof(f4520,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_f696928925ol_nat(finite346522414t_bool,X0))) )
| ~ spl17_353
| ~ spl17_391 ),
inference(resolution,[],[f4493,f4064]) ).
fof(f18404,plain,
( spl17_1084
| ~ spl17_350
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4444,f4297,f4051,f18402]) ).
fof(f18402,plain,
( spl17_1084
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(suc,sK11(X3))))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1084])]) ).
fof(f4444,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(suc,sK11(X3))))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))) )
| ~ spl17_350
| ~ spl17_376 ),
inference(superposition,[],[f4052,f4298]) ).
fof(f18400,plain,
( spl17_1083
| ~ spl17_188
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4156,f4051,f2921,f18398]) ).
fof(f18398,plain,
( spl17_1083
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(cOMBB_bool_bool_nat(X0,X1))))))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1083])]) ).
fof(f2921,plain,
( spl17_188
<=> ! [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,[spl17_188])]) ).
fof(f4156,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(cOMBB_bool_bool_nat(X0,X1))))))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))) )
| ~ spl17_188
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4155,f2922]) ).
fof(f2922,plain,
( ! [X2,X0,X1] : hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))
| ~ spl17_188 ),
inference(avatar_component_clause,[],[f2921]) ).
fof(f4155,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(cOMBB_bool_bool_nat(X0,X1))))))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))))
| ~ hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2)) )
| ~ spl17_188
| ~ spl17_350 ),
inference(forward_demodulation,[],[f4149,f2922]) ).
fof(f4149,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))))
| hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),hAPP_nat_nat(suc,sK11(cOMBB_bool_bool_nat(X0,X1)))))
| ~ hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2)) )
| ~ spl17_188
| ~ spl17_350 ),
inference(superposition,[],[f4052,f2922]) ).
fof(f18384,plain,
( ~ spl17_334
| spl17_1082
| spl17_99
| ~ spl17_185
| ~ spl17_480 ),
inference(avatar_split_clause,[],[f5383,f5309,f2909,f2545,f18381,f3962]) ).
fof(f18381,plain,
( spl17_1082
<=> hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1082])]) ).
fof(f2545,plain,
( spl17_99
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
fof(f5383,plain,
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| spl17_99
| ~ spl17_185
| ~ spl17_480 ),
inference(forward_demodulation,[],[f5380,f2910]) ).
fof(f5380,plain,
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) = hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| spl17_99
| ~ spl17_480 ),
inference(resolution,[],[f5310,f2547]) ).
fof(f2547,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g))
| spl17_99 ),
inference(avatar_component_clause,[],[f2545]) ).
fof(f17910,plain,
( spl17_1081
| ~ spl17_100
| ~ spl17_830 ),
inference(avatar_split_clause,[],[f11245,f10944,f2550,f17908]) ).
fof(f10944,plain,
( spl17_830
<=> ! [X0,X3,X2,X1] :
( 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,X0),image_pname_a(X2,X3)))
| is_pname(sK16(X2,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_830])]) ).
fof(f11245,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),X0))
| is_pname(sK16(mgt_call,X0,u)) )
| ~ spl17_100
| ~ spl17_830 ),
inference(resolution,[],[f10945,f2552]) ).
fof(f2552,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ spl17_100 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f10945,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X2,X3)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_pname(sK16(X2,X1,X3)) )
| ~ spl17_830 ),
inference(avatar_component_clause,[],[f10944]) ).
fof(f17767,plain,
( spl17_1080
| ~ spl17_621
| ~ spl17_653 ),
inference(avatar_split_clause,[],[f8097,f8093,f7187,f17765]) ).
fof(f17765,plain,
( spl17_1080
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(sK9(mgt_call,u,g),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1080])]) ).
fof(f8093,plain,
( spl17_653
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(mgt_call,u,g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_653])]) ).
fof(f8097,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(sK9(mgt_call,u,g),X0)) )
| ~ spl17_621
| ~ spl17_653 ),
inference(resolution,[],[f8095,f7188]) ).
fof(f8095,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(mgt_call,u,g)))
| ~ spl17_653 ),
inference(avatar_component_clause,[],[f8093]) ).
fof(f17471,plain,
( spl17_1079
| ~ spl17_193
| ~ spl17_506 ),
inference(avatar_split_clause,[],[f5983,f5745,f2989,f17469]) ).
fof(f17469,plain,
( spl17_1079
<=> ! [X0] : hAPP_a93125764e_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_pname(hAPP_a93125764e_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1079])]) ).
fof(f2989,plain,
( spl17_193
<=> is_a(sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_193])]) ).
fof(f5745,plain,
( spl17_506
<=> ! [X0,X1] :
( ~ is_a(X0)
| hAPP_a93125764e_bool(X1,X0) = collect_pname(hAPP_a93125764e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_506])]) ).
fof(f5983,plain,
( ! [X0] : hAPP_a93125764e_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_pname(hAPP_a93125764e_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))))
| ~ spl17_193
| ~ spl17_506 ),
inference(resolution,[],[f5746,f2991]) ).
fof(f2991,plain,
( is_a(sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))
| ~ spl17_193 ),
inference(avatar_component_clause,[],[f2989]) ).
fof(f5746,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| hAPP_a93125764e_bool(X1,X0) = collect_pname(hAPP_a93125764e_bool(X1,X0)) )
| ~ spl17_506 ),
inference(avatar_component_clause,[],[f5745]) ).
fof(f17438,plain,
( spl17_1078
| ~ spl17_40
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4936,f4840,f2259,f17436]) ).
fof(f17436,plain,
( spl17_1078
<=> ! [X0,X1] :
( is_fun_a_bool(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)))
| ~ is_fun_a_bool(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),collect_a(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1078])]) ).
fof(f4936,plain,
( ! [X0,X1] :
( is_fun_a_bool(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)))
| ~ is_fun_a_bool(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),collect_a(X1)))) )
| ~ spl17_40
| ~ spl17_434 ),
inference(superposition,[],[f2260,f4841]) ).
fof(f17434,plain,
( spl17_1077
| ~ spl17_41
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4919,f4836,f2263,f17432]) ).
fof(f17432,plain,
( spl17_1077
<=> ! [X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))
| ~ is_fun_pname_bool(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1077])]) ).
fof(f4919,plain,
( ! [X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))
| ~ is_fun_pname_bool(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1)))) )
| ~ spl17_41
| ~ spl17_433 ),
inference(superposition,[],[f2264,f4837]) ).
fof(f17430,plain,
( spl17_1076
| ~ spl17_38
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4896,f4832,f2251,f17428]) ).
fof(f17428,plain,
( spl17_1076
<=> ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))
| ~ is_fun949378684l_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1076])]) ).
fof(f2251,plain,
( spl17_38
<=> ! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f4896,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))
| ~ is_fun949378684l_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))) )
| ~ spl17_38
| ~ spl17_432 ),
inference(superposition,[],[f2252,f4833]) ).
fof(f2252,plain,
( ! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f2251]) ).
fof(f17426,plain,
( spl17_1075
| ~ spl17_37
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4884,f4828,f2247,f17424]) ).
fof(f17424,plain,
( spl17_1075
<=> ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))
| ~ is_fun1661590463l_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1075])]) ).
fof(f2247,plain,
( spl17_37
<=> ! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f4884,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))
| ~ is_fun1661590463l_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))) )
| ~ spl17_37
| ~ spl17_431 ),
inference(superposition,[],[f2248,f4829]) ).
fof(f2248,plain,
( ! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f2247]) ).
fof(f17422,plain,
( spl17_1074
| ~ spl17_185
| ~ spl17_418 ),
inference(avatar_split_clause,[],[f4740,f4674,f2909,f17420]) ).
fof(f17420,plain,
( spl17_1074
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1074])]) ).
fof(f4740,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) )
| ~ spl17_185
| ~ spl17_418 ),
inference(superposition,[],[f4675,f2910]) ).
fof(f17418,plain,
( spl17_1073
| ~ spl17_193
| ~ spl17_460 ),
inference(avatar_split_clause,[],[f5710,f5153,f2989,f17416]) ).
fof(f17416,plain,
( spl17_1073
<=> ! [X0] : hAPP_a85458249l_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1073])]) ).
fof(f5153,plain,
( spl17_460
<=> ! [X0,X1] :
( hAPP_a85458249l_bool(X0,X1) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_460])]) ).
fof(f5710,plain,
( ! [X0] : hAPP_a85458249l_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))))
| ~ spl17_193
| ~ spl17_460 ),
inference(resolution,[],[f5154,f2991]) ).
fof(f5154,plain,
( ! [X0,X1] :
( ~ is_a(X1)
| hAPP_a85458249l_bool(X0,X1) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1)) )
| ~ spl17_460 ),
inference(avatar_component_clause,[],[f5153]) ).
fof(f17414,plain,
( spl17_1072
| ~ spl17_257
| ~ spl17_415 ),
inference(avatar_split_clause,[],[f4734,f4662,f3397,f17412]) ).
fof(f17412,plain,
( spl17_1072
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1072])]) ).
fof(f4734,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))) )
| ~ spl17_257
| ~ spl17_415 ),
inference(resolution,[],[f4663,f3398]) ).
fof(f17410,plain,
( spl17_1071
| ~ spl17_185
| ~ spl17_412 ),
inference(avatar_split_clause,[],[f4726,f4650,f2909,f17408]) ).
fof(f17408,plain,
( spl17_1071
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1071])]) ).
fof(f4726,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) )
| ~ spl17_185
| ~ spl17_412 ),
inference(superposition,[],[f4651,f2910]) ).
fof(f17406,plain,
( spl17_1070
| ~ spl17_256
| ~ spl17_412 ),
inference(avatar_split_clause,[],[f4724,f4650,f3393,f17404]) ).
fof(f17404,plain,
( spl17_1070
<=> ! [X2,X0,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))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1070])]) ).
fof(f4724,plain,
( ! [X2,X0,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))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))) )
| ~ spl17_256
| ~ spl17_412 ),
inference(resolution,[],[f4651,f3394]) ).
fof(f17402,plain,
( spl17_1069
| ~ spl17_185
| ~ spl17_411 ),
inference(avatar_split_clause,[],[f4719,f4646,f2909,f17400]) ).
fof(f17400,plain,
( spl17_1069
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1069])]) ).
fof(f4719,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) )
| ~ spl17_185
| ~ spl17_411 ),
inference(superposition,[],[f4647,f2910]) ).
fof(f17389,plain,
( spl17_1068
| ~ spl17_942
| ~ spl17_1067 ),
inference(avatar_split_clause,[],[f17385,f17382,f12920,f17387]) ).
fof(f17387,plain,
( spl17_1068
<=> ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1068])]) ).
fof(f17382,plain,
( spl17_1067
<=> ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1067])]) ).
fof(f17385,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))))
| ~ spl17_942
| ~ spl17_1067 ),
inference(forward_demodulation,[],[f17383,f12921]) ).
fof(f17383,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))))
| ~ spl17_1067 ),
inference(avatar_component_clause,[],[f17382]) ).
fof(f17384,plain,
( spl17_1067
| ~ spl17_330
| ~ spl17_405 ),
inference(avatar_split_clause,[],[f4628,f4587,f3843,f17382]) ).
fof(f4628,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))))
| ~ spl17_330
| ~ spl17_405 ),
inference(forward_demodulation,[],[f4626,f2066]) ).
fof(f4626,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))))))
| ~ spl17_330
| ~ spl17_405 ),
inference(resolution,[],[f4588,f3844]) ).
fof(f17380,plain,
( spl17_1066
| ~ spl17_328
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f4556,f4546,f3807,f17378]) ).
fof(f17378,plain,
( spl17_1066
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X0,X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1066])]) ).
fof(f4556,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X0,X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) )
| ~ spl17_328
| ~ spl17_398 ),
inference(resolution,[],[f4547,f3808]) ).
fof(f17376,plain,
( spl17_1065
| ~ spl17_359
| ~ spl17_380 ),
inference(avatar_split_clause,[],[f4464,f4314,f4087,f17374]) ).
fof(f17374,plain,
( spl17_1065
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),sK10(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1065])]) ).
fof(f4464,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),sK10(X0,X1,X2))) )
| ~ spl17_359
| ~ spl17_380 ),
inference(resolution,[],[f4315,f4088]) ).
fof(f17372,plain,
( spl17_1064
| ~ spl17_360
| ~ spl17_380 ),
inference(avatar_split_clause,[],[f4463,f4314,f4091,f17370]) ).
fof(f17370,plain,
( spl17_1064
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),sK10(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1064])]) ).
fof(f4463,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),sK10(X0,X1,X2))) )
| ~ spl17_360
| ~ spl17_380 ),
inference(resolution,[],[f4315,f4092]) ).
fof(f17356,plain,
( spl17_1063
| ~ spl17_291
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4442,f4297,f3621,f17354]) ).
fof(f17354,plain,
( spl17_1063
<=> ! [X0,X3,X2,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)),hAPP_nat_nat(suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1063])]) ).
fof(f4442,plain,
( ! [X2,X3,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X3)),hAPP_nat_nat(suc,X2))
| ~ spl17_291
| ~ spl17_376 ),
inference(superposition,[],[f3622,f4298]) ).
fof(f17352,plain,
( spl17_1062
| ~ spl17_335
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4401,f4264,f3969,f17350]) ).
fof(f17350,plain,
( spl17_1062
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK1(X0))),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(sK1(X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1062])]) ).
fof(f4401,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,sK1(X0))),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(sK1(X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_335
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3970]) ).
fof(f17348,plain,
( spl17_1061
| ~ spl17_219
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3942,f3799,f3138,f17346]) ).
fof(f17346,plain,
( spl17_1061
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1061])]) ).
fof(f3942,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1))),X1)) )
| ~ spl17_219
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3941,f3139]) ).
fof(f3941,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2)) )
| ~ spl17_219
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3936,f3139]) ).
fof(f3936,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,sK11(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1))),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2)) )
| ~ spl17_219
| ~ spl17_326 ),
inference(superposition,[],[f3800,f3139]) ).
fof(f17344,plain,
( spl17_1060
| ~ spl17_218
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3940,f3799,f3134,f17342]) ).
fof(f17342,plain,
( spl17_1060
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1060])]) ).
fof(f3940,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1))),X1)) )
| ~ spl17_218
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3939,f3135]) ).
fof(f3939,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,hAPP_nat_nat(minus_minus_nat(X2),X3)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2)) )
| ~ spl17_218
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3935,f3135]) ).
fof(f3935,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,sK11(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1))),X1))
| hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2)) )
| ~ spl17_218
| ~ spl17_326 ),
inference(superposition,[],[f3800,f3135]) ).
fof(f17340,plain,
( spl17_1059
| ~ spl17_288
| ~ spl17_322 ),
inference(avatar_split_clause,[],[f3912,f3783,f3609,f17338]) ).
fof(f17338,plain,
( spl17_1059
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1059])]) ).
fof(f3912,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_322 ),
inference(resolution,[],[f3784,f3610]) ).
fof(f17336,plain,
( spl17_1058
| ~ spl17_289
| ~ spl17_322 ),
inference(avatar_split_clause,[],[f3911,f3783,f3613,f17334]) ).
fof(f17334,plain,
( spl17_1058
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1058])]) ).
fof(f3911,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_322 ),
inference(resolution,[],[f3784,f3614]) ).
fof(f17332,plain,
( spl17_1057
| ~ spl17_288
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f3910,f3779,f3609,f17330]) ).
fof(f17330,plain,
( spl17_1057
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1057])]) ).
fof(f3910,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_321 ),
inference(resolution,[],[f3780,f3610]) ).
fof(f17328,plain,
( spl17_1056
| ~ spl17_289
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f3909,f3779,f3613,f17326]) ).
fof(f17326,plain,
( spl17_1056
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1056])]) ).
fof(f3909,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_321 ),
inference(resolution,[],[f3780,f3614]) ).
fof(f17324,plain,
( spl17_1055
| ~ spl17_288
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f3908,f3775,f3609,f17322]) ).
fof(f17322,plain,
( spl17_1055
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1055])]) ).
fof(f3908,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)))) )
| ~ spl17_288
| ~ spl17_320 ),
inference(resolution,[],[f3776,f3610]) ).
fof(f17320,plain,
( spl17_1054
| ~ spl17_289
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f3907,f3775,f3613,f17318]) ).
fof(f17318,plain,
( spl17_1054
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1054])]) ).
fof(f3907,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X0)))) )
| ~ spl17_289
| ~ spl17_320 ),
inference(resolution,[],[f3776,f3614]) ).
fof(f17314,plain,
( spl17_1053
| ~ spl17_288
| ~ spl17_319 ),
inference(avatar_split_clause,[],[f3906,f3770,f3609,f17312]) ).
fof(f17312,plain,
( spl17_1053
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1053])]) ).
fof(f3906,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_319 ),
inference(resolution,[],[f3771,f3610]) ).
fof(f17310,plain,
( spl17_1052
| ~ spl17_289
| ~ spl17_319 ),
inference(avatar_split_clause,[],[f3905,f3770,f3613,f17308]) ).
fof(f17308,plain,
( spl17_1052
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1052])]) ).
fof(f3905,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_319 ),
inference(resolution,[],[f3771,f3614]) ).
fof(f17306,plain,
( spl17_1051
| ~ spl17_288
| ~ spl17_318 ),
inference(avatar_split_clause,[],[f3904,f3766,f3609,f17304]) ).
fof(f17304,plain,
( spl17_1051
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1051])]) ).
fof(f3904,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_318 ),
inference(resolution,[],[f3767,f3610]) ).
fof(f17302,plain,
( spl17_1050
| ~ spl17_289
| ~ spl17_318 ),
inference(avatar_split_clause,[],[f3903,f3766,f3613,f17300]) ).
fof(f17300,plain,
( spl17_1050
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1050])]) ).
fof(f3903,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_318 ),
inference(resolution,[],[f3767,f3614]) ).
fof(f17298,plain,
( spl17_1049
| ~ spl17_288
| ~ spl17_317 ),
inference(avatar_split_clause,[],[f3902,f3762,f3609,f17296]) ).
fof(f17296,plain,
( spl17_1049
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1049])]) ).
fof(f3902,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_317 ),
inference(resolution,[],[f3763,f3610]) ).
fof(f17294,plain,
( spl17_1048
| ~ spl17_289
| ~ spl17_317 ),
inference(avatar_split_clause,[],[f3901,f3762,f3613,f17292]) ).
fof(f17292,plain,
( spl17_1048
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1048])]) ).
fof(f3901,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hAPP_f921600141ol_nat(finite_card_pname,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_317 ),
inference(resolution,[],[f3763,f3614]) ).
fof(f17290,plain,
( spl17_1047
| ~ spl17_288
| ~ spl17_316 ),
inference(avatar_split_clause,[],[f3900,f3758,f3609,f17288]) ).
fof(f17288,plain,
( spl17_1047
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1047])]) ).
fof(f3900,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_316 ),
inference(resolution,[],[f3759,f3610]) ).
fof(f17286,plain,
( spl17_1046
| ~ spl17_289
| ~ spl17_316 ),
inference(avatar_split_clause,[],[f3899,f3758,f3613,f17284]) ).
fof(f17284,plain,
( spl17_1046
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))
| ~ 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,image_a_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1046])]) ).
fof(f3899,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X0))
| ~ 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,image_a_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_316 ),
inference(resolution,[],[f3759,f3614]) ).
fof(f17282,plain,
( spl17_1045
| ~ spl17_288
| ~ spl17_315 ),
inference(avatar_split_clause,[],[f3898,f3754,f3609,f17280]) ).
fof(f17280,plain,
( spl17_1045
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1045])]) ).
fof(f3898,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_315 ),
inference(resolution,[],[f3755,f3610]) ).
fof(f17278,plain,
( spl17_1044
| ~ spl17_289
| ~ spl17_315 ),
inference(avatar_split_clause,[],[f3897,f3754,f3613,f17276]) ).
fof(f17276,plain,
( spl17_1044
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1044])]) ).
fof(f3897,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_315 ),
inference(resolution,[],[f3755,f3614]) ).
fof(f17274,plain,
( spl17_1043
| ~ spl17_550
| ~ spl17_807 ),
inference(avatar_split_clause,[],[f10480,f10439,f5924,f17272]) ).
fof(f17272,plain,
( spl17_1043
<=> ! [X0,X1] :
( is_pname(sK5(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),u))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1043])]) ).
fof(f5924,plain,
( spl17_550
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_550])]) ).
fof(f10439,plain,
( spl17_807
<=> ! [X0] :
( is_pname(sK5(X0,u))
| hBOOL(hAPP_pname_bool(X0,pn)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_807])]) ).
fof(f10480,plain,
( ! [X0,X1] :
( is_pname(sK5(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),u))
| hBOOL(X0) )
| ~ spl17_550
| ~ spl17_807 ),
inference(resolution,[],[f10440,f5925]) ).
fof(f5925,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_550 ),
inference(avatar_component_clause,[],[f5924]) ).
fof(f10440,plain,
( ! [X0] :
( hBOOL(hAPP_pname_bool(X0,pn))
| is_pname(sK5(X0,u)) )
| ~ spl17_807 ),
inference(avatar_component_clause,[],[f10439]) ).
fof(f17270,plain,
( spl17_1042
| ~ spl17_288
| ~ spl17_314 ),
inference(avatar_split_clause,[],[f3896,f3750,f3609,f17268]) ).
fof(f17268,plain,
( spl17_1042
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1042])]) ).
fof(f3896,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)))) )
| ~ spl17_288
| ~ spl17_314 ),
inference(resolution,[],[f3751,f3610]) ).
fof(f17266,plain,
( spl17_1041
| ~ spl17_289
| ~ spl17_314 ),
inference(avatar_split_clause,[],[f3895,f3750,f3613,f17264]) ).
fof(f17264,plain,
( spl17_1041
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1041])]) ).
fof(f3895,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hAPP_fun_a_bool_nat(finite_card_a,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X0)))) )
| ~ spl17_289
| ~ spl17_314 ),
inference(resolution,[],[f3751,f3614]) ).
fof(f17262,plain,
( spl17_1040
| ~ spl17_288
| ~ spl17_313 ),
inference(avatar_split_clause,[],[f3892,f3746,f3609,f17260]) ).
fof(f17260,plain,
( spl17_1040
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1040])]) ).
fof(f3892,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_313 ),
inference(resolution,[],[f3747,f3610]) ).
fof(f17258,plain,
( spl17_1039
| ~ spl17_289
| ~ spl17_313 ),
inference(avatar_split_clause,[],[f3891,f3746,f3613,f17256]) ).
fof(f17256,plain,
( spl17_1039
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1039])]) ).
fof(f3891,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_313 ),
inference(resolution,[],[f3747,f3614]) ).
fof(f17254,plain,
( spl17_1038
| ~ spl17_288
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f3889,f3742,f3609,f17252]) ).
fof(f17252,plain,
( spl17_1038
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1038])]) ).
fof(f3889,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_312 ),
inference(resolution,[],[f3743,f3610]) ).
fof(f17250,plain,
( spl17_1037
| ~ spl17_289
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f3888,f3742,f3613,f17248]) ).
fof(f17248,plain,
( spl17_1037
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1037])]) ).
fof(f3888,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_312 ),
inference(resolution,[],[f3743,f3614]) ).
fof(f17246,plain,
( spl17_1036
| ~ spl17_288
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f3886,f3738,f3609,f17244]) ).
fof(f17244,plain,
( spl17_1036
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1036])]) ).
fof(f3886,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_311 ),
inference(resolution,[],[f3739,f3610]) ).
fof(f17242,plain,
( spl17_1035
| ~ spl17_289
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f3885,f3738,f3613,f17240]) ).
fof(f17240,plain,
( spl17_1035
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1035])]) ).
fof(f3885,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_311 ),
inference(resolution,[],[f3739,f3614]) ).
fof(f17238,plain,
( spl17_1034
| ~ spl17_288
| ~ spl17_310 ),
inference(avatar_split_clause,[],[f3883,f3734,f3609,f17236]) ).
fof(f17236,plain,
( spl17_1034
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1034])]) ).
fof(f3883,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_310 ),
inference(resolution,[],[f3735,f3610]) ).
fof(f17234,plain,
( spl17_1033
| ~ spl17_289
| ~ spl17_310 ),
inference(avatar_split_clause,[],[f3882,f3734,f3613,f17232]) ).
fof(f17232,plain,
( spl17_1033
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1033])]) ).
fof(f3882,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_310 ),
inference(resolution,[],[f3735,f3614]) ).
fof(f17230,plain,
( spl17_1032
| ~ spl17_545
| ~ spl17_807 ),
inference(avatar_split_clause,[],[f10478,f10439,f5904,f17228]) ).
fof(f17228,plain,
( spl17_1032
<=> ! [X0] :
( is_pname(sK5(cOMBB_647938656_pname(fNot,X0),u))
| ~ hBOOL(hAPP_pname_bool(X0,pn)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1032])]) ).
fof(f5904,plain,
( spl17_545
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(fNot,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_545])]) ).
fof(f10478,plain,
( ! [X0] :
( is_pname(sK5(cOMBB_647938656_pname(fNot,X0),u))
| ~ hBOOL(hAPP_pname_bool(X0,pn)) )
| ~ spl17_545
| ~ spl17_807 ),
inference(resolution,[],[f10440,f5905]) ).
fof(f5905,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(fNot,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_545 ),
inference(avatar_component_clause,[],[f5904]) ).
fof(f17226,plain,
( spl17_1031
| ~ spl17_288
| ~ spl17_308 ),
inference(avatar_split_clause,[],[f3880,f3725,f3609,f17224]) ).
fof(f17224,plain,
( spl17_1031
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1031])]) ).
fof(f3880,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)))) )
| ~ spl17_288
| ~ spl17_308 ),
inference(resolution,[],[f3726,f3610]) ).
fof(f17222,plain,
( spl17_1030
| ~ spl17_289
| ~ spl17_308 ),
inference(avatar_split_clause,[],[f3879,f3725,f3613,f17220]) ).
fof(f17220,plain,
( spl17_1030
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1030])]) ).
fof(f3879,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X0)))) )
| ~ spl17_289
| ~ spl17_308 ),
inference(resolution,[],[f3726,f3614]) ).
fof(f17218,plain,
( spl17_1029
| ~ spl17_288
| ~ spl17_307 ),
inference(avatar_split_clause,[],[f3878,f3721,f3609,f17216]) ).
fof(f17216,plain,
( spl17_1029
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1029])]) ).
fof(f3878,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_307 ),
inference(resolution,[],[f3722,f3610]) ).
fof(f17214,plain,
( spl17_1028
| ~ spl17_289
| ~ spl17_307 ),
inference(avatar_split_clause,[],[f3877,f3721,f3613,f17212]) ).
fof(f17212,plain,
( spl17_1028
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1028])]) ).
fof(f3877,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_307 ),
inference(resolution,[],[f3722,f3614]) ).
fof(f17210,plain,
( spl17_1027
| ~ spl17_288
| ~ spl17_306 ),
inference(avatar_split_clause,[],[f3876,f3717,f3609,f17208]) ).
fof(f17208,plain,
( spl17_1027
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1027])]) ).
fof(f3876,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_306 ),
inference(resolution,[],[f3718,f3610]) ).
fof(f17206,plain,
( spl17_1026
| ~ spl17_289
| ~ spl17_306 ),
inference(avatar_split_clause,[],[f3875,f3717,f3613,f17204]) ).
fof(f17204,plain,
( spl17_1026
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1026])]) ).
fof(f3875,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_306 ),
inference(resolution,[],[f3718,f3614]) ).
fof(f17202,plain,
( spl17_1025
| ~ spl17_288
| ~ spl17_305 ),
inference(avatar_split_clause,[],[f3874,f3713,f3609,f17200]) ).
fof(f17200,plain,
( spl17_1025
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1025])]) ).
fof(f3874,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_305 ),
inference(resolution,[],[f3714,f3610]) ).
fof(f17198,plain,
( spl17_1024
| ~ spl17_289
| ~ spl17_305 ),
inference(avatar_split_clause,[],[f3873,f3713,f3613,f17196]) ).
fof(f17196,plain,
( spl17_1024
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1024])]) ).
fof(f3873,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_305 ),
inference(resolution,[],[f3714,f3614]) ).
fof(f17194,plain,
( spl17_1023
| ~ spl17_288
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f3872,f3709,f3609,f17192]) ).
fof(f17192,plain,
( spl17_1023
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1023])]) ).
fof(f3872,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_304 ),
inference(resolution,[],[f3710,f3610]) ).
fof(f17190,plain,
( spl17_1022
| ~ spl17_289
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f3871,f3709,f3613,f17188]) ).
fof(f17188,plain,
( spl17_1022
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1022])]) ).
fof(f3871,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_304 ),
inference(resolution,[],[f3710,f3614]) ).
fof(f17185,plain,
( spl17_1021
| ~ spl17_288
| ~ spl17_303 ),
inference(avatar_split_clause,[],[f3870,f3705,f3609,f17183]) ).
fof(f17183,plain,
( spl17_1021
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1021])]) ).
fof(f3870,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_303 ),
inference(resolution,[],[f3706,f3610]) ).
fof(f17181,plain,
( spl17_1020
| ~ spl17_289
| ~ spl17_303 ),
inference(avatar_split_clause,[],[f3869,f3705,f3613,f17179]) ).
fof(f17179,plain,
( spl17_1020
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1020])]) ).
fof(f3869,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_303 ),
inference(resolution,[],[f3706,f3614]) ).
fof(f17177,plain,
( spl17_1019
| ~ spl17_288
| ~ spl17_302 ),
inference(avatar_split_clause,[],[f3867,f3701,f3609,f17175]) ).
fof(f17175,plain,
( spl17_1019
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1019])]) ).
fof(f3867,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)))) )
| ~ spl17_288
| ~ spl17_302 ),
inference(resolution,[],[f3702,f3610]) ).
fof(f17173,plain,
( spl17_1018
| ~ spl17_289
| ~ spl17_302 ),
inference(avatar_split_clause,[],[f3866,f3701,f3613,f17171]) ).
fof(f17171,plain,
( spl17_1018
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1018])]) ).
fof(f3866,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X0)))) )
| ~ spl17_289
| ~ spl17_302 ),
inference(resolution,[],[f3702,f3614]) ).
fof(f17169,plain,
( spl17_1017
| ~ spl17_288
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f3865,f3697,f3609,f17167]) ).
fof(f17167,plain,
( spl17_1017
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1017])]) ).
fof(f3865,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)))) )
| ~ spl17_288
| ~ spl17_301 ),
inference(resolution,[],[f3698,f3610]) ).
fof(f17165,plain,
( spl17_1016
| ~ spl17_289
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f3864,f3697,f3613,f17163]) ).
fof(f17163,plain,
( spl17_1016
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1016])]) ).
fof(f3864,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hAPP_f55526627ol_nat(finite1340463720e_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X0)))) )
| ~ spl17_289
| ~ spl17_301 ),
inference(resolution,[],[f3698,f3614]) ).
fof(f17161,plain,
( spl17_1015
| ~ spl17_288
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f3863,f3693,f3609,f17159]) ).
fof(f17159,plain,
( spl17_1015
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1015])]) ).
fof(f3863,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)))) )
| ~ spl17_288
| ~ spl17_300 ),
inference(resolution,[],[f3694,f3610]) ).
fof(f17157,plain,
( spl17_1014
| ~ spl17_289
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f3862,f3693,f3613,f17155]) ).
fof(f17155,plain,
( spl17_1014
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1014])]) ).
fof(f3862,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X0)))) )
| ~ spl17_289
| ~ spl17_300 ),
inference(resolution,[],[f3694,f3614]) ).
fof(f17153,plain,
( spl17_1013
| ~ spl17_288
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f3861,f3689,f3609,f17151]) ).
fof(f17151,plain,
( spl17_1013
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1013])]) ).
fof(f3861,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)))) )
| ~ spl17_288
| ~ spl17_299 ),
inference(resolution,[],[f3690,f3610]) ).
fof(f17149,plain,
( spl17_1012
| ~ spl17_289
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f3860,f3689,f3613,f17147]) ).
fof(f17147,plain,
( spl17_1012
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1012])]) ).
fof(f3860,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hAPP_f696928925ol_nat(finite346522414t_bool,X0) = hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X0)))) )
| ~ spl17_289
| ~ spl17_299 ),
inference(resolution,[],[f3690,f3614]) ).
fof(f17138,plain,
( spl17_1011
| ~ spl17_288
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f3859,f3684,f3609,f17136]) ).
fof(f17136,plain,
( spl17_1011
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1011])]) ).
fof(f3859,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_298 ),
inference(resolution,[],[f3685,f3610]) ).
fof(f17134,plain,
( spl17_1010
| ~ spl17_289
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f3858,f3684,f3613,f17132]) ).
fof(f17132,plain,
( spl17_1010
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
| hAPP_f1253658590ol_nat(finite1659325229l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1010])]) ).
fof(f3858,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
| hAPP_f1253658590ol_nat(finite1659325229l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1253658590ol_nat(finite1659325229l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_298 ),
inference(resolution,[],[f3685,f3614]) ).
fof(f17130,plain,
( spl17_1009
| ~ spl17_288
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f3857,f3680,f3609,f17128]) ).
fof(f17128,plain,
( spl17_1009
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1009])]) ).
fof(f3857,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_297 ),
inference(resolution,[],[f3681,f3610]) ).
fof(f17126,plain,
( spl17_1008
| ~ spl17_289
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f3856,f3680,f3613,f17124]) ).
fof(f17124,plain,
( spl17_1008
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
| hAPP_f98387925ol_nat(finite269641166l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1008])]) ).
fof(f3856,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
| hAPP_f98387925ol_nat(finite269641166l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f98387925ol_nat(finite269641166l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_297 ),
inference(resolution,[],[f3681,f3614]) ).
fof(f17122,plain,
( spl17_1007
| ~ spl17_288
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f3855,f3676,f3609,f17120]) ).
fof(f17120,plain,
( spl17_1007
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1007])]) ).
fof(f3855,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
| hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)) = hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)))) )
| ~ spl17_288
| ~ spl17_296 ),
inference(resolution,[],[f3677,f3610]) ).
fof(f17118,plain,
( spl17_1006
| ~ spl17_289
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f3854,f3676,f3613,f17116]) ).
fof(f17116,plain,
( spl17_1006
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
| hAPP_f1690079119ol_nat(finite1352710292l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1006])]) ).
fof(f3854,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
| hAPP_f1690079119ol_nat(finite1352710292l_bool,X0) = hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1690079119ol_nat(finite1352710292l_bool,X0)),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X0)))) )
| ~ spl17_289
| ~ spl17_296 ),
inference(resolution,[],[f3677,f3614]) ).
fof(f17061,plain,
( spl17_1005
| ~ spl17_220
| ~ spl17_407 ),
inference(avatar_split_clause,[],[f4698,f4606,f3142,f17059]) ).
fof(f17059,plain,
( spl17_1005
<=> ! [X4,X0,X3,X2,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1005])]) ).
fof(f3142,plain,
( spl17_220
<=> ! [X2,X0,X1] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_220])]) ).
fof(f4606,plain,
( spl17_407
<=> ! [X2,X0,X1,X3] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_407])]) ).
fof(f4698,plain,
( ! [X2,X3,X0,X1,X4] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1))))
| ~ spl17_220
| ~ spl17_407 ),
inference(superposition,[],[f4607,f3143]) ).
fof(f3143,plain,
( ! [X2,X0,X1] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1)
| ~ spl17_220 ),
inference(avatar_component_clause,[],[f3142]) ).
fof(f4607,plain,
( ! [X2,X3,X0,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))))
| ~ spl17_407 ),
inference(avatar_component_clause,[],[f4606]) ).
fof(f16491,plain,
( spl17_1004
| ~ spl17_189
| ~ spl17_407 ),
inference(avatar_split_clause,[],[f4697,f4606,f2925,f16489]) ).
fof(f16489,plain,
( spl17_1004
<=> ! [X4,X0,X3,X2,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1004])]) ).
fof(f2925,plain,
( spl17_189
<=> ! [X2,X0,X1] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_189])]) ).
fof(f4697,plain,
( ! [X2,X3,X0,X1,X4] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))))
| ~ spl17_189
| ~ spl17_407 ),
inference(superposition,[],[f4607,f2926]) ).
fof(f2926,plain,
( ! [X2,X0,X1] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))
| ~ spl17_189 ),
inference(avatar_component_clause,[],[f2925]) ).
fof(f16439,plain,
( spl17_1003
| ~ spl17_329
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5587,f5583,f3811,f16437]) ).
fof(f16437,plain,
( spl17_1003
<=> ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1003])]) ).
fof(f5587,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2))))
| ~ spl17_329
| ~ spl17_499 ),
inference(superposition,[],[f3812,f5584]) ).
fof(f16435,plain,
( spl17_1002
| ~ spl17_270
| ~ spl17_486 ),
inference(avatar_split_clause,[],[f5419,f5412,f3449,f16433]) ).
fof(f16433,plain,
( spl17_1002
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK2(X0,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1002])]) ).
fof(f3449,plain,
( spl17_270
<=> ! [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,[spl17_270])]) ).
fof(f5412,plain,
( spl17_486
<=> ! [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,sK2(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,[spl17_486])]) ).
fof(f5419,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))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK2(X0,X1)))))) )
| ~ spl17_270
| ~ spl17_486 ),
inference(resolution,[],[f5413,f3450]) ).
fof(f3450,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))) )
| ~ spl17_270 ),
inference(avatar_component_clause,[],[f3449]) ).
fof(f5413,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,sK2(X0,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_486 ),
inference(avatar_component_clause,[],[f5412]) ).
fof(f16431,plain,
( spl17_1001
| ~ spl17_166
| ~ spl17_452 ),
inference(avatar_split_clause,[],[f5026,f5023,f2819,f16429]) ).
fof(f16429,plain,
( spl17_1001
<=> ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1001])]) ).
fof(f5026,plain,
( ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_166
| ~ spl17_452 ),
inference(resolution,[],[f5024,f2820]) ).
fof(f16427,plain,
( spl17_1000
| ~ spl17_273
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4610,f4575,f3461,f16425]) ).
fof(f16425,plain,
( spl17_1000
<=> ! [X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) = X1
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1000])]) ).
fof(f4610,plain,
( ! [X0,X1] :
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),sK5(X0,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) = X1
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
| ~ spl17_273
| ~ spl17_402 ),
inference(resolution,[],[f4576,f3462]) ).
fof(f16423,plain,
( spl17_999
| ~ spl17_271
| ~ spl17_401 ),
inference(avatar_split_clause,[],[f4600,f4571,f3453,f16421]) ).
fof(f16421,plain,
( spl17_999
<=> ! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) = X1
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_999])]) ).
fof(f4571,plain,
( spl17_401
<=> ! [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))) = 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,[spl17_401])]) ).
fof(f4600,plain,
( ! [X0,X1] :
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),sK4(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) = X1
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) )
| ~ spl17_271
| ~ spl17_401 ),
inference(resolution,[],[f4572,f3454]) ).
fof(f4572,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_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))) = X1
| ~ is_fun_a_bool(X1) )
| ~ spl17_401 ),
inference(avatar_component_clause,[],[f4571]) ).
fof(f16419,plain,
( spl17_998
| ~ spl17_248
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f4461,f4310,f3318,f16417]) ).
fof(f16417,plain,
( spl17_998
<=> ! [X0,X3,X2,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_998])]) ).
fof(f4310,plain,
( spl17_379
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK9(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,[spl17_379])]) ).
fof(f4461,plain,
( ! [X2,X3,X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X3)))
| ~ is_fun_a_bool(image_pname_a(X2,X3))
| is_pname(sK16(X2,image_pname_a(X0,X1),X3)) )
| ~ spl17_248
| ~ spl17_379 ),
inference(resolution,[],[f4311,f3319]) ).
fof(f4311,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| is_fun_pname_bool(sK9(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) )
| ~ spl17_379 ),
inference(avatar_component_clause,[],[f4310]) ).
fof(f16415,plain,
( spl17_997
| ~ spl17_248
| ~ spl17_370 ),
inference(avatar_split_clause,[],[f4422,f4273,f3318,f16413]) ).
fof(f16413,plain,
( spl17_997
<=> ! [X2,X0,X1] :
( image_pname_a(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(image_pname_a(X1,X2))
| ~ is_fun_a_bool(X0)
| is_pname(sK16(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_997])]) ).
fof(f4422,plain,
( ! [X2,X0,X1] :
( image_pname_a(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(image_pname_a(X1,X2))
| ~ is_fun_a_bool(X0)
| is_pname(sK16(X1,X0,X2)) )
| ~ spl17_248
| ~ spl17_370 ),
inference(resolution,[],[f4274,f3319]) ).
fof(f16411,plain,
( spl17_996
| ~ spl17_352
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4222,f4063,f4059,f16409]) ).
fof(f16409,plain,
( spl17_996
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_996])]) ).
fof(f4222,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) )
| ~ spl17_352
| ~ spl17_353 ),
inference(resolution,[],[f4064,f4060]) ).
fof(f16407,plain,
( spl17_995
| ~ spl17_351
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4221,f4063,f4055,f16405]) ).
fof(f16405,plain,
( spl17_995
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_995])]) ).
fof(f4221,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
| ~ spl17_351
| ~ spl17_353 ),
inference(resolution,[],[f4064,f4056]) ).
fof(f16397,plain,
( spl17_994
| ~ spl17_291
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4185,f4059,f3621,f16395]) ).
fof(f16395,plain,
( spl17_994
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_994])]) ).
fof(f4185,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(X0),X1))) )
| ~ spl17_291
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3622]) ).
fof(f16393,plain,
( spl17_993
| ~ spl17_291
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4181,f4059,f3621,f16391]) ).
fof(f16391,plain,
( spl17_993
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_993])]) ).
fof(f4181,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)) )
| ~ spl17_291
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3622]) ).
fof(f16389,plain,
( spl17_992
| ~ spl17_291
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4175,f4055,f3621,f16387]) ).
fof(f16387,plain,
( spl17_992
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_992])]) ).
fof(f4175,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
| ~ spl17_291
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3622]) ).
fof(f16385,plain,
( spl17_991
| ~ spl17_291
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4171,f4055,f3621,f16383]) ).
fof(f16383,plain,
( spl17_991
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_991])]) ).
fof(f4171,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
| ~ spl17_291
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3622]) ).
fof(f16381,plain,
( spl17_990
| ~ spl17_291
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4147,f4051,f3621,f16379]) ).
fof(f16379,plain,
( spl17_990
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(suc,sK11(X3))))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_990])]) ).
fof(f4147,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(suc,sK11(X3))))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(minus_minus_nat(X0),X1))) )
| ~ spl17_291
| ~ spl17_350 ),
inference(superposition,[],[f4052,f3622]) ).
fof(f16377,plain,
( spl17_989
| ~ spl17_188
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3938,f3799,f2921,f16375]) ).
fof(f16375,plain,
( spl17_989
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))))
| ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,sK11(cOMBB_bool_bool_nat(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_989])]) ).
fof(f3938,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))))
| ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,sK11(cOMBB_bool_bool_nat(X0,X1))))) )
| ~ spl17_188
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3937,f2922]) ).
fof(f3937,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))))
| ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,sK11(cOMBB_bool_bool_nat(X0,X1)))))
| ~ hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2)) )
| ~ spl17_188
| ~ spl17_326 ),
inference(forward_demodulation,[],[f3934,f2922]) ).
fof(f3934,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(X0,hAPP_nat_bool(X1,sK11(cOMBB_bool_bool_nat(X0,X1)))))
| hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2)) )
| ~ spl17_188
| ~ spl17_326 ),
inference(superposition,[],[f3800,f2922]) ).
fof(f16352,plain,
( spl17_988
| ~ spl17_188
| ~ spl17_396 ),
inference(avatar_split_clause,[],[f4558,f4512,f2921,f16350]) ).
fof(f16350,plain,
( spl17_988
<=> ! [X4,X0,X3,X2,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_988])]) ).
fof(f4512,plain,
( spl17_396
<=> ! [X2,X0,X1,X3] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_396])]) ).
fof(f4558,plain,
( ! [X2,X3,X0,X1,X4] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X4,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))))
| ~ spl17_188
| ~ spl17_396 ),
inference(superposition,[],[f4513,f2922]) ).
fof(f4513,plain,
( ! [X2,X3,X0,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))))
| ~ spl17_396 ),
inference(avatar_component_clause,[],[f4512]) ).
fof(f15898,plain,
( spl17_987
| ~ spl17_11
| ~ spl17_255
| ~ spl17_404
| ~ spl17_423 ),
inference(avatar_split_clause,[],[f6526,f4694,f4583,f3389,f2141,f15896]) ).
fof(f15896,plain,
( spl17_987
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_987])]) ).
fof(f6526,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_11
| ~ spl17_255
| ~ spl17_404
| ~ spl17_423 ),
inference(forward_demodulation,[],[f4624,f4760]) ).
fof(f4624,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) )
| ~ spl17_255
| ~ spl17_404 ),
inference(resolution,[],[f4584,f3390]) ).
fof(f15766,plain,
( spl17_986
| ~ spl17_640
| ~ spl17_973 ),
inference(avatar_split_clause,[],[f15577,f14056,f7266,f15763]) ).
fof(f15763,plain,
( spl17_986
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),undefined_pname(pname)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_986])]) ).
fof(f7266,plain,
( spl17_640
<=> ! [X1] : hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_640])]) ).
fof(f14056,plain,
( spl17_973
<=> ! [X0] : hAPP_p61793385e_bool(X0,undefined_pname(pname)) = collect_pname(hAPP_p61793385e_bool(X0,undefined_pname(pname))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_973])]) ).
fof(f15577,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),undefined_pname(pname))))
| ~ spl17_640
| ~ spl17_973 ),
inference(superposition,[],[f7267,f14057]) ).
fof(f14057,plain,
( ! [X0] : hAPP_p61793385e_bool(X0,undefined_pname(pname)) = collect_pname(hAPP_p61793385e_bool(X0,undefined_pname(pname)))
| ~ spl17_973 ),
inference(avatar_component_clause,[],[f14056]) ).
fof(f7267,plain,
( ! [X1] : hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))))
| ~ spl17_640 ),
inference(avatar_component_clause,[],[f7266]) ).
fof(f14583,plain,
( spl17_985
| ~ spl17_3
| ~ spl17_917 ),
inference(avatar_split_clause,[],[f14444,f12820,f2103,f14580]) ).
fof(f14580,plain,
( spl17_985
<=> p(collect_a(g)) = collect_fun_a_bool(p(collect_a(g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_985])]) ).
fof(f2103,plain,
( spl17_3
<=> is_fun_a_bool(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f12820,plain,
( spl17_917
<=> ! [X0] :
( p(collect_a(X0)) = collect_fun_a_bool(p(collect_a(X0)))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_917])]) ).
fof(f14444,plain,
( p(collect_a(g)) = collect_fun_a_bool(p(collect_a(g)))
| ~ spl17_3
| ~ spl17_917 ),
inference(resolution,[],[f12821,f2105]) ).
fof(f2105,plain,
( is_fun_a_bool(g)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f2103]) ).
fof(f12821,plain,
( ! [X0] :
( ~ is_fun_a_bool(X0)
| p(collect_a(X0)) = collect_fun_a_bool(p(collect_a(X0))) )
| ~ spl17_917 ),
inference(avatar_component_clause,[],[f12820]) ).
fof(f14110,plain,
( ~ spl17_334
| ~ spl17_637 ),
inference(avatar_contradiction_clause,[],[f14109]) ).
fof(f14109,plain,
( $false
| ~ spl17_334
| ~ spl17_637 ),
inference(resolution,[],[f7253,f3964]) ).
fof(f3964,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ spl17_334 ),
inference(avatar_component_clause,[],[f3962]) ).
fof(f7253,plain,
( ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ spl17_637 ),
inference(avatar_component_clause,[],[f7252]) ).
fof(f7252,plain,
( spl17_637
<=> ! [X0] : ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_637])]) ).
fof(f14102,plain,
( spl17_984
| ~ spl17_185
| ~ spl17_636 ),
inference(avatar_split_clause,[],[f7260,f7249,f2909,f14100]) ).
fof(f14100,plain,
( spl17_984
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_984])]) ).
fof(f7249,plain,
( spl17_636
<=> ! [X1] : hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_636])]) ).
fof(f7260,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1))))
| ~ spl17_185
| ~ spl17_636 ),
inference(superposition,[],[f7250,f2910]) ).
fof(f7250,plain,
( ! [X1] : hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))))
| ~ spl17_636 ),
inference(avatar_component_clause,[],[f7249]) ).
fof(f14098,plain,
( spl17_983
| ~ spl17_284
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4934,f4840,f3518,f14096]) ).
fof(f14096,plain,
( spl17_983
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_983])]) ).
fof(f4934,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(X1))))) )
| ~ spl17_284
| ~ spl17_434 ),
inference(superposition,[],[f3519,f4841]) ).
fof(f14094,plain,
( spl17_982
| ~ spl17_418
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4931,f4840,f4674,f14092]) ).
fof(f14092,plain,
( spl17_982
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_982])]) ).
fof(f4931,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(X1)),X2)) )
| ~ spl17_418
| ~ spl17_434 ),
inference(superposition,[],[f4675,f4841]) ).
fof(f14090,plain,
( spl17_981
| ~ spl17_416
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4930,f4840,f4666,f14088]) ).
fof(f14088,plain,
( spl17_981
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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)),X2))
| ~ hBOOL(hAPP_a_bool(collect_a(X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_981])]) ).
fof(f4930,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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)),X2))
| ~ hBOOL(hAPP_a_bool(collect_a(X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) )
| ~ spl17_416
| ~ spl17_434 ),
inference(superposition,[],[f4667,f4841]) ).
fof(f14086,plain,
( spl17_980
| ~ spl17_412
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4929,f4840,f4650,f14084]) ).
fof(f14084,plain,
( spl17_980
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_980])]) ).
fof(f4929,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(X1))) )
| ~ spl17_412
| ~ spl17_434 ),
inference(superposition,[],[f4651,f4841]) ).
fof(f14082,plain,
( spl17_979
| ~ spl17_411
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4928,f4840,f4646,f14080]) ).
fof(f14080,plain,
( spl17_979
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_979])]) ).
fof(f4928,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),collect_a(X1))) )
| ~ spl17_411
| ~ spl17_434 ),
inference(superposition,[],[f4647,f4841]) ).
fof(f14078,plain,
( spl17_978
| ~ spl17_286
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4917,f4836,f3526,f14076]) ).
fof(f14076,plain,
( spl17_978
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_978])]) ).
fof(f3526,plain,
( spl17_286
<=> ! [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,[spl17_286])]) ).
fof(f4917,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(X1))))) )
| ~ spl17_286
| ~ spl17_433 ),
inference(superposition,[],[f3527,f4837]) ).
fof(f3527,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))) )
| ~ spl17_286 ),
inference(avatar_component_clause,[],[f3526]) ).
fof(f14074,plain,
( spl17_977
| ~ spl17_420
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4914,f4836,f4682,f14072]) ).
fof(f14072,plain,
( spl17_977
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_977])]) ).
fof(f4914,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),X2)) )
| ~ spl17_420
| ~ spl17_433 ),
inference(superposition,[],[f4683,f4837]) ).
fof(f14070,plain,
( spl17_976
| ~ spl17_417
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4913,f4836,f4670,f14068]) ).
fof(f14068,plain,
( spl17_976
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),X2))
| ~ hBOOL(hAPP_pname_bool(collect_pname(X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_976])]) ).
fof(f4670,plain,
( spl17_417
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(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))),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_417])]) ).
fof(f4913,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)),X2))
| ~ hBOOL(hAPP_pname_bool(collect_pname(X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) )
| ~ spl17_417
| ~ spl17_433 ),
inference(superposition,[],[f4671,f4837]) ).
fof(f4671,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(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))),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_pname(X0) )
| ~ spl17_417 ),
inference(avatar_component_clause,[],[f4670]) ).
fof(f14066,plain,
( spl17_975
| ~ spl17_415
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4912,f4836,f4662,f14064]) ).
fof(f14064,plain,
( spl17_975
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_975])]) ).
fof(f4912,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),collect_pname(X1))) )
| ~ spl17_415
| ~ spl17_433 ),
inference(superposition,[],[f4663,f4837]) ).
fof(f14062,plain,
( spl17_974
| ~ spl17_414
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4911,f4836,f4658,f14060]) ).
fof(f14060,plain,
( spl17_974
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_974])]) ).
fof(f4911,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),collect_pname(X1))) )
| ~ spl17_414
| ~ spl17_433 ),
inference(superposition,[],[f4659,f4837]) ).
fof(f14058,plain,
( spl17_973
| ~ spl17_7
| ~ spl17_507 ),
inference(avatar_split_clause,[],[f5985,f5749,f2123,f14056]) ).
fof(f2123,plain,
( spl17_7
<=> is_pname(undefined_pname(pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f5749,plain,
( spl17_507
<=> ! [X0,X1] :
( ~ is_pname(X0)
| hAPP_p61793385e_bool(X1,X0) = collect_pname(hAPP_p61793385e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_507])]) ).
fof(f5985,plain,
( ! [X0] : hAPP_p61793385e_bool(X0,undefined_pname(pname)) = collect_pname(hAPP_p61793385e_bool(X0,undefined_pname(pname)))
| ~ spl17_7
| ~ spl17_507 ),
inference(resolution,[],[f5750,f2125]) ).
fof(f2125,plain,
( is_pname(undefined_pname(pname))
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f2123]) ).
fof(f5750,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| hAPP_p61793385e_bool(X1,X0) = collect_pname(hAPP_p61793385e_bool(X1,X0)) )
| ~ spl17_507 ),
inference(avatar_component_clause,[],[f5749]) ).
fof(f14054,plain,
( spl17_972
| ~ spl17_282
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4894,f4832,f3510,f14052]) ).
fof(f14052,plain,
( spl17_972
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_972])]) ).
fof(f3510,plain,
( spl17_282
<=> ! [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,[spl17_282])]) ).
fof(f4894,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1))))) )
| ~ spl17_282
| ~ spl17_432 ),
inference(superposition,[],[f3511,f4833]) ).
fof(f3511,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))) )
| ~ spl17_282 ),
inference(avatar_component_clause,[],[f3510]) ).
fof(f14050,plain,
( spl17_971
| ~ spl17_280
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4882,f4828,f3502,f14048]) ).
fof(f14048,plain,
( spl17_971
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_971])]) ).
fof(f3502,plain,
( spl17_280
<=> ! [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,[spl17_280])]) ).
fof(f4882,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1))))) )
| ~ spl17_280
| ~ spl17_431 ),
inference(superposition,[],[f3503,f4829]) ).
fof(f3503,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))) )
| ~ spl17_280 ),
inference(avatar_component_clause,[],[f3502]) ).
fof(f14046,plain,
( spl17_970
| ~ spl17_391
| ~ spl17_408 ),
inference(avatar_split_clause,[],[f4701,f4634,f4492,f14044]) ).
fof(f14044,plain,
( spl17_970
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_970])]) ).
fof(f4701,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_391
| ~ spl17_408 ),
inference(resolution,[],[f4635,f4493]) ).
fof(f14042,plain,
( spl17_969
| ~ spl17_171
| ~ spl17_394 ),
inference(avatar_split_clause,[],[f4535,f4504,f2839,f14040]) ).
fof(f14040,plain,
( spl17_969
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_969])]) ).
fof(f4535,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_171
| ~ spl17_394 ),
inference(superposition,[],[f4505,f2840]) ).
fof(f14038,plain,
( spl17_968
| ~ spl17_328
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f4460,f4310,f3807,f14036]) ).
fof(f14036,plain,
( spl17_968
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_968])]) ).
fof(f4460,plain,
( ! [X2,X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X2)))
| ~ is_fun_a_bool(image_pname_a(X0,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) )
| ~ spl17_328
| ~ spl17_379 ),
inference(resolution,[],[f4311,f3808]) ).
fof(f14034,plain,
( spl17_967
| ~ spl17_277
| ~ spl17_369 ),
inference(avatar_split_clause,[],[f4416,f4269,f3477,f14032]) ).
fof(f14032,plain,
( spl17_967
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_967])]) ).
fof(f4416,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) )
| ~ spl17_277
| ~ spl17_369 ),
inference(resolution,[],[f4270,f3478]) ).
fof(f14030,plain,
( spl17_966
| ~ spl17_259
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4396,f4264,f3405,f14028]) ).
fof(f14028,plain,
( spl17_966
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_966])]) ).
fof(f4396,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) )
| ~ spl17_259
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3406]) ).
fof(f14026,plain,
( spl17_965
| ~ spl17_335
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4223,f4063,f3969,f14024]) ).
fof(f14024,plain,
( spl17_965
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK1(X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_965])]) ).
fof(f4223,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK1(X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_335
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3970]) ).
fof(f14022,plain,
( spl17_964
| ~ spl17_114
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4144,f4051,f2609,f14020]) ).
fof(f14020,plain,
( spl17_964
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(fequal_nat,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_964])]) ).
fof(f2609,plain,
( spl17_114
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
fof(f4144,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),hAPP_nat_nat(minus_minus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(fequal_nat,X0))) = X0 )
| ~ spl17_114
| ~ spl17_350 ),
inference(resolution,[],[f4052,f2610]) ).
fof(f2610,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| X0 = X1 )
| ~ spl17_114 ),
inference(avatar_component_clause,[],[f2609]) ).
fof(f14018,plain,
( spl17_963
| ~ spl17_114
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4137,f4051,f2609,f14016]) ).
fof(f14016,plain,
( spl17_963
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(fequal_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_963])]) ).
fof(f4137,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),hAPP_nat_nat(suc,sK11(hAPP_n1699378549t_bool(fequal_nat,X0)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = X0 )
| ~ spl17_114
| ~ spl17_350 ),
inference(resolution,[],[f4052,f2610]) ).
fof(f14014,plain,
( spl17_962
| ~ spl17_6
| ~ spl17_506 ),
inference(avatar_split_clause,[],[f5981,f5745,f2118,f14012]) ).
fof(f14012,plain,
( spl17_962
<=> ! [X0] : hAPP_a93125764e_bool(X0,undefined_a(x_a)) = collect_pname(hAPP_a93125764e_bool(X0,undefined_a(x_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_962])]) ).
fof(f2118,plain,
( spl17_6
<=> is_a(undefined_a(x_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f5981,plain,
( ! [X0] : hAPP_a93125764e_bool(X0,undefined_a(x_a)) = collect_pname(hAPP_a93125764e_bool(X0,undefined_a(x_a)))
| ~ spl17_6
| ~ spl17_506 ),
inference(resolution,[],[f5746,f2120]) ).
fof(f2120,plain,
( is_a(undefined_a(x_a))
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f14010,plain,
( spl17_961
| ~ spl17_248
| ~ spl17_349 ),
inference(avatar_split_clause,[],[f4129,f4047,f3318,f14008]) ).
fof(f14008,plain,
( spl17_961
<=> ! [X0,X3,X2,X1] :
( image_pname_a(X1,X2) = image_pname_a(X0,sK10(image_pname_a(X1,X2),X0,X3))
| ~ is_fun_a_bool(image_pname_a(X1,X2))
| is_pname(sK16(X1,image_pname_a(X0,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_961])]) ).
fof(f4047,plain,
( spl17_349
<=> ! [X2,X0,X1] :
( image_pname_a(X1,sK10(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,[spl17_349])]) ).
fof(f4129,plain,
( ! [X2,X3,X0,X1] :
( image_pname_a(X1,X2) = image_pname_a(X0,sK10(image_pname_a(X1,X2),X0,X3))
| ~ is_fun_a_bool(image_pname_a(X1,X2))
| is_pname(sK16(X1,image_pname_a(X0,X3),X2)) )
| ~ spl17_248
| ~ spl17_349 ),
inference(resolution,[],[f4048,f3319]) ).
fof(f4048,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| image_pname_a(X1,sK10(X0,X1,X2)) = X0
| ~ is_fun_a_bool(X0) )
| ~ spl17_349 ),
inference(avatar_component_clause,[],[f4047]) ).
fof(f14006,plain,
( spl17_960
| ~ spl17_289
| ~ spl17_324 ),
inference(avatar_split_clause,[],[f3924,f3791,f3613,f14004]) ).
fof(f14004,plain,
( spl17_960
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_960])]) ).
fof(f3924,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0))) )
| ~ spl17_289
| ~ spl17_324 ),
inference(resolution,[],[f3792,f3614]) ).
fof(f14002,plain,
( spl17_959
| ~ spl17_271
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f3670,f3629,f3453,f14000]) ).
fof(f14000,plain,
( spl17_959
<=> ! [X2,X0,X1] :
( is_pname(sK8(sK4(X0,image_pname_a(X1,X2)),X1,X2))
| ~ is_a(sK4(X0,image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_959])]) ).
fof(f3670,plain,
( ! [X2,X0,X1] :
( is_pname(sK8(sK4(X0,image_pname_a(X1,X2)),X1,X2))
| ~ is_a(sK4(X0,image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) )
| ~ spl17_271
| ~ spl17_293 ),
inference(resolution,[],[f3630,f3454]) ).
fof(f13998,plain,
( spl17_958
| ~ spl17_271
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f3668,f3625,f3453,f13996]) ).
fof(f13996,plain,
( spl17_958
<=> ! [X2,X0,X1] :
( is_pname(sK7(sK4(X0,image_pname_a(X1,X2)),X1,X2))
| ~ is_a(sK4(X0,image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_958])]) ).
fof(f3668,plain,
( ! [X2,X0,X1] :
( is_pname(sK7(sK4(X0,image_pname_a(X1,X2)),X1,X2))
| ~ is_a(sK4(X0,image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X0)) )
| ~ spl17_271
| ~ spl17_292 ),
inference(resolution,[],[f3626,f3454]) ).
fof(f13875,plain,
( spl17_957
| ~ spl17_250
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4184,f4059,f3367,f13873]) ).
fof(f13873,plain,
( spl17_957
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))),hAPP_fun_a_bool_nat(finite_card_a,g)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_957])]) ).
fof(f4184,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))),hAPP_fun_a_bool_nat(finite_card_a,g)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) )
| ~ spl17_250
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3369]) ).
fof(f13871,plain,
( spl17_956
| ~ spl17_250
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4180,f4059,f3367,f13869]) ).
fof(f13869,plain,
( spl17_956
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_956])]) ).
fof(f4180,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,na))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)) )
| ~ spl17_250
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3369]) ).
fof(f13867,plain,
( spl17_955
| ~ spl17_260
| ~ spl17_355 ),
inference(avatar_split_clause,[],[f4352,f4071,f3409,f13865]) ).
fof(f13865,plain,
( spl17_955
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_955])]) ).
fof(f4352,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))))
| ~ spl17_260
| ~ spl17_355 ),
inference(resolution,[],[f4072,f3410]) ).
fof(f13863,plain,
( spl17_954
| ~ spl17_250
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4174,f4055,f3367,f13861]) ).
fof(f13861,plain,
( spl17_954
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_fun_a_bool_nat(finite_card_a,g)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_954])]) ).
fof(f4174,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_fun_a_bool_nat(finite_card_a,g)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),X0)) )
| ~ spl17_250
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3369]) ).
fof(f13859,plain,
( spl17_953
| ~ spl17_250
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4170,f4055,f3367,f13857]) ).
fof(f13857,plain,
( spl17_953
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,na))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_953])]) ).
fof(f4170,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,na))) )
| ~ spl17_250
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3369]) ).
fof(f13776,plain,
( spl17_952
| ~ spl17_41
| ~ spl17_172 ),
inference(avatar_split_clause,[],[f3817,f2847,f2263,f13774]) ).
fof(f13774,plain,
( spl17_952
<=> ! [X0] :
( collect_pname(collect_pname(X0)) = collect_pname(collect_pname(collect_pname(X0)))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_952])]) ).
fof(f2847,plain,
( spl17_172
<=> ! [X0] :
( collect_pname(X0) = collect_pname(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_172])]) ).
fof(f3817,plain,
( ! [X0] :
( collect_pname(collect_pname(X0)) = collect_pname(collect_pname(collect_pname(X0)))
| ~ is_fun_pname_bool(X0) )
| ~ spl17_41
| ~ spl17_172 ),
inference(resolution,[],[f2848,f2264]) ).
fof(f2848,plain,
( ! [X0] :
( ~ is_fun_pname_bool(X0)
| collect_pname(X0) = collect_pname(collect_pname(X0)) )
| ~ spl17_172 ),
inference(avatar_component_clause,[],[f2847]) ).
fof(f13617,plain,
( spl17_951
| ~ spl17_27
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3605,f2807,f2205,f13615]) ).
fof(f13615,plain,
( spl17_951
<=> ! [X0,X1] : p(hAPP_nat_fun_a_bool(X0,X1)) = collect_fun_a_bool(p(hAPP_nat_fun_a_bool(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_951])]) ).
fof(f2205,plain,
( spl17_27
<=> ! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f3605,plain,
( ! [X0,X1] : p(hAPP_nat_fun_a_bool(X0,X1)) = collect_fun_a_bool(p(hAPP_nat_fun_a_bool(X0,X1)))
| ~ spl17_27
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2206]) ).
fof(f2206,plain,
( ! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1))
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f2205]) ).
fof(f13438,plain,
( spl17_950
| ~ spl17_23
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3602,f2807,f2189,f13436]) ).
fof(f13436,plain,
( spl17_950
<=> ! [X0,X1] : p(image_526090948bool_a(X0,X1)) = collect_fun_a_bool(p(image_526090948bool_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_950])]) ).
fof(f2189,plain,
( spl17_23
<=> ! [X0,X1] : is_fun_a_bool(image_526090948bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f3602,plain,
( ! [X0,X1] : p(image_526090948bool_a(X0,X1)) = collect_fun_a_bool(p(image_526090948bool_a(X0,X1)))
| ~ spl17_23
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2190]) ).
fof(f2190,plain,
( ! [X0,X1] : is_fun_a_bool(image_526090948bool_a(X0,X1))
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f2189]) ).
fof(f13258,plain,
( spl17_949
| ~ spl17_24
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3601,f2807,f2193,f13256]) ).
fof(f13256,plain,
( spl17_949
<=> ! [X0,X1] : p(image_349102846bool_a(X0,X1)) = collect_fun_a_bool(p(image_349102846bool_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_949])]) ).
fof(f2193,plain,
( spl17_24
<=> ! [X0,X1] : is_fun_a_bool(image_349102846bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f3601,plain,
( ! [X0,X1] : p(image_349102846bool_a(X0,X1)) = collect_fun_a_bool(p(image_349102846bool_a(X0,X1)))
| ~ spl17_24
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2194]) ).
fof(f2194,plain,
( ! [X0,X1] : is_fun_a_bool(image_349102846bool_a(X0,X1))
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f2193]) ).
fof(f12976,plain,
( spl17_948
| ~ spl17_22
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3600,f2807,f2185,f12974]) ).
fof(f12974,plain,
( spl17_948
<=> ! [X0,X1] : p(image_573985017bool_a(X0,X1)) = collect_fun_a_bool(p(image_573985017bool_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_948])]) ).
fof(f2185,plain,
( spl17_22
<=> ! [X0,X1] : is_fun_a_bool(image_573985017bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f3600,plain,
( ! [X0,X1] : p(image_573985017bool_a(X0,X1)) = collect_fun_a_bool(p(image_573985017bool_a(X0,X1)))
| ~ spl17_22
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2186]) ).
fof(f2186,plain,
( ! [X0,X1] : is_fun_a_bool(image_573985017bool_a(X0,X1))
| ~ spl17_22 ),
inference(avatar_component_clause,[],[f2185]) ).
fof(f12942,plain,
( spl17_947
| ~ spl17_287
| ~ spl17_499 ),
inference(avatar_split_clause,[],[f5586,f5583,f3530,f12940]) ).
fof(f12940,plain,
( spl17_947
<=> ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_947])]) ).
fof(f3530,plain,
( spl17_287
<=> ! [X2,X1] : hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_287])]) ).
fof(f5586,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)),X0))
| ~ spl17_287
| ~ spl17_499 ),
inference(superposition,[],[f3531,f5584]) ).
fof(f3531,plain,
( ! [X2,X1] : hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),X2))
| ~ spl17_287 ),
inference(avatar_component_clause,[],[f3530]) ).
fof(f12938,plain,
( spl17_946
| ~ spl17_419
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4932,f4840,f4678,f12936]) ).
fof(f12936,plain,
( spl17_946
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_946])]) ).
fof(f4932,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl17_419
| ~ spl17_434 ),
inference(superposition,[],[f4679,f4841]) ).
fof(f12934,plain,
( spl17_945
| ~ spl17_421
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4915,f4836,f4686,f12932]) ).
fof(f12932,plain,
( spl17_945
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_945])]) ).
fof(f4915,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ spl17_421
| ~ spl17_433 ),
inference(superposition,[],[f4687,f4837]) ).
fof(f12930,plain,
( spl17_944
| ~ spl17_166
| ~ spl17_441 ),
inference(avatar_split_clause,[],[f4872,f4869,f2819,f12928]) ).
fof(f12928,plain,
( spl17_944
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_944])]) ).
fof(f4869,plain,
( spl17_441
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_441])]) ).
fof(f4872,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2))),X1),X0)) )
| ~ spl17_166
| ~ spl17_441 ),
inference(resolution,[],[f4870,f2820]) ).
fof(f4870,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 )
| ~ spl17_441 ),
inference(avatar_component_clause,[],[f4869]) ).
fof(f12926,plain,
( spl17_943
| ~ spl17_170
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4817,f4802,f2835,f12924]) ).
fof(f12924,plain,
( spl17_943
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_943])]) ).
fof(f4817,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_170
| ~ spl17_430 ),
inference(resolution,[],[f4803,f2836]) ).
fof(f12922,plain,
( spl17_942
| ~ spl17_11
| ~ spl17_423 ),
inference(avatar_split_clause,[],[f4760,f4694,f2141,f12920]) ).
fof(f12918,plain,
( spl17_941
| ~ spl17_10
| ~ spl17_422 ),
inference(avatar_split_clause,[],[f4758,f4690,f2137,f12916]) ).
fof(f12916,plain,
( spl17_941
<=> ! [X0,X1] : cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_941])]) ).
fof(f2137,plain,
( spl17_10
<=> ! [X0] : collect_fun_nat_bool(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f4690,plain,
( spl17_422
<=> ! [X0,X1] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_422])]) ).
fof(f4758,plain,
( ! [X0,X1] : cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)
| ~ spl17_10
| ~ spl17_422 ),
inference(superposition,[],[f4691,f2138]) ).
fof(f2138,plain,
( ! [X0] : collect_fun_nat_bool(X0) = X0
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f4691,plain,
( ! [X0,X1] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)
| ~ spl17_422 ),
inference(avatar_component_clause,[],[f4690]) ).
fof(f12914,plain,
( spl17_940
| ~ spl17_177
| ~ spl17_412 ),
inference(avatar_split_clause,[],[f4725,f4650,f2876,f12912]) ).
fof(f12912,plain,
( spl17_940
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_940])]) ).
fof(f4725,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),X0)) )
| ~ spl17_177
| ~ spl17_412 ),
inference(resolution,[],[f4651,f2877]) ).
fof(f12910,plain,
( spl17_939
| ~ spl17_25
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3599,f2807,f2197,f12908]) ).
fof(f12908,plain,
( spl17_939
<=> ! [X0,X1] : p(image_fun_nat_bool_a(X0,X1)) = collect_fun_a_bool(p(image_fun_nat_bool_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_939])]) ).
fof(f2197,plain,
( spl17_25
<=> ! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f3599,plain,
( ! [X0,X1] : p(image_fun_nat_bool_a(X0,X1)) = collect_fun_a_bool(p(image_fun_nat_bool_a(X0,X1)))
| ~ spl17_25
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2198]) ).
fof(f2198,plain,
( ! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1))
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f2197]) ).
fof(f12906,plain,
( spl17_938
| ~ spl17_52
| ~ spl17_400 ),
inference(avatar_split_clause,[],[f4594,f4567,f2311,f12904]) ).
fof(f2311,plain,
( spl17_52
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f4594,plain,
( ! [X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK9(X0,X1,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_52
| ~ spl17_400 ),
inference(resolution,[],[f4568,f2312]) ).
fof(f2312,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0))
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f12902,plain,
( spl17_937
| ~ spl17_328
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f4247,f4083,f3807,f12900]) ).
fof(f12900,plain,
( spl17_937
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_937])]) ).
fof(f4247,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) )
| ~ spl17_328
| ~ spl17_358 ),
inference(resolution,[],[f4084,f3808]) ).
fof(f12898,plain,
( spl17_936
| ~ spl17_328
| ~ spl17_357 ),
inference(avatar_split_clause,[],[f4241,f4079,f3807,f12896]) ).
fof(f12896,plain,
( spl17_936
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_936])]) ).
fof(f4241,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) )
| ~ spl17_328
| ~ spl17_357 ),
inference(resolution,[],[f4080,f3808]) ).
fof(f12894,plain,
( spl17_935
| ~ spl17_324
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4220,f4063,f3791,f12892]) ).
fof(f12892,plain,
( spl17_935
<=> ! [X2,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),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_935])]) ).
fof(f4220,plain,
( ! [X2,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),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) )
| ~ spl17_324
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3792]) ).
fof(f12890,plain,
( spl17_934
| ~ spl17_298
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4218,f4063,f3684,f12888]) ).
fof(f12888,plain,
( spl17_934
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X2,X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_934])]) ).
fof(f4218,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X2,X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) )
| ~ spl17_298
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3685]) ).
fof(f12886,plain,
( spl17_933
| ~ spl17_297
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4217,f4063,f3680,f12884]) ).
fof(f12884,plain,
( spl17_933
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X2,X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_933])]) ).
fof(f4217,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X2,X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) )
| ~ spl17_297
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3681]) ).
fof(f12882,plain,
( spl17_932
| ~ spl17_296
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4216,f4063,f3676,f12880]) ).
fof(f12880,plain,
( spl17_932
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X2,X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_932])]) ).
fof(f4216,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X2,X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) )
| ~ spl17_296
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3677]) ).
fof(f12878,plain,
( spl17_931
| ~ spl17_305
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4215,f4063,f3713,f12876]) ).
fof(f12876,plain,
( spl17_931
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_931])]) ).
fof(f4215,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_305
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3714]) ).
fof(f12874,plain,
( spl17_930
| ~ spl17_304
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4214,f4063,f3709,f12872]) ).
fof(f12872,plain,
( spl17_930
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_930])]) ).
fof(f4214,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_304
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3710]) ).
fof(f12870,plain,
( spl17_929
| ~ spl17_300
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4213,f4063,f3693,f12868]) ).
fof(f12868,plain,
( spl17_929
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_929])]) ).
fof(f4213,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_300
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3694]) ).
fof(f12866,plain,
( spl17_928
| ~ spl17_26
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3596,f2807,f2201,f12864]) ).
fof(f12864,plain,
( spl17_928
<=> ! [X0,X1] : p(image_nat_a(X0,X1)) = collect_fun_a_bool(p(image_nat_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_928])]) ).
fof(f2201,plain,
( spl17_26
<=> ! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f3596,plain,
( ! [X0,X1] : p(image_nat_a(X0,X1)) = collect_fun_a_bool(p(image_nat_a(X0,X1)))
| ~ spl17_26
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2202]) ).
fof(f2202,plain,
( ! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1))
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f12862,plain,
( spl17_927
| ~ spl17_306
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4212,f4063,f3717,f12860]) ).
fof(f12860,plain,
( spl17_927
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_927])]) ).
fof(f4212,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_306
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3718]) ).
fof(f12858,plain,
( spl17_926
| ~ spl17_302
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4211,f4063,f3701,f12856]) ).
fof(f12856,plain,
( spl17_926
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_926])]) ).
fof(f4211,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_302
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3702]) ).
fof(f12854,plain,
( spl17_925
| ~ spl17_301
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4210,f4063,f3697,f12852]) ).
fof(f12852,plain,
( spl17_925
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_925])]) ).
fof(f4210,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_301
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3698]) ).
fof(f12850,plain,
( spl17_924
| ~ spl17_307
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4209,f4063,f3721,f12848]) ).
fof(f12848,plain,
( spl17_924
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_924])]) ).
fof(f4209,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_307
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3722]) ).
fof(f12846,plain,
( spl17_923
| ~ spl17_303
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4208,f4063,f3705,f12844]) ).
fof(f12844,plain,
( spl17_923
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_923])]) ).
fof(f4208,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_303
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3706]) ).
fof(f12842,plain,
( spl17_922
| ~ spl17_299
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4207,f4063,f3689,f12840]) ).
fof(f12840,plain,
( spl17_922
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_922])]) ).
fof(f4207,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_299
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3690]) ).
fof(f12838,plain,
( spl17_921
| ~ spl17_316
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4205,f4063,f3758,f12836]) ).
fof(f12836,plain,
( spl17_921
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_921])]) ).
fof(f4205,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_316
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3759]) ).
fof(f12834,plain,
( spl17_920
| ~ spl17_315
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4204,f4063,f3754,f12832]) ).
fof(f12832,plain,
( spl17_920
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_920])]) ).
fof(f4204,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_315
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3755]) ).
fof(f12830,plain,
( spl17_919
| ~ spl17_314
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4203,f4063,f3750,f12828]) ).
fof(f12828,plain,
( spl17_919
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_919])]) ).
fof(f4203,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
| ~ spl17_314
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3751]) ).
fof(f12826,plain,
( spl17_918
| ~ spl17_319
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4202,f4063,f3770,f12824]) ).
fof(f12824,plain,
( spl17_918
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_918])]) ).
fof(f4202,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_319
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3771]) ).
fof(f12822,plain,
( spl17_917
| ~ spl17_40
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3593,f2807,f2259,f12820]) ).
fof(f3593,plain,
( ! [X0] :
( p(collect_a(X0)) = collect_fun_a_bool(p(collect_a(X0)))
| ~ is_fun_a_bool(X0) )
| ~ spl17_40
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2260]) ).
fof(f12818,plain,
( spl17_916
| ~ spl17_318
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4201,f4063,f3766,f12816]) ).
fof(f12816,plain,
( spl17_916
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_916])]) ).
fof(f4201,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_318
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3767]) ).
fof(f12814,plain,
( spl17_915
| ~ spl17_317
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4200,f4063,f3762,f12812]) ).
fof(f12812,plain,
( spl17_915
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_915])]) ).
fof(f4200,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_317
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3763]) ).
fof(f12810,plain,
( spl17_914
| ~ spl17_322
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4199,f4063,f3783,f12808]) ).
fof(f12808,plain,
( spl17_914
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_914])]) ).
fof(f4199,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_322
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3784]) ).
fof(f12806,plain,
( spl17_913
| ~ spl17_321
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4198,f4063,f3779,f12804]) ).
fof(f12804,plain,
( spl17_913
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_913])]) ).
fof(f4198,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_321
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3780]) ).
fof(f12802,plain,
( spl17_912
| ~ spl17_320
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4197,f4063,f3775,f12800]) ).
fof(f12800,plain,
( spl17_912
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_912])]) ).
fof(f4197,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_320
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3776]) ).
fof(f12798,plain,
( spl17_911
| ~ spl17_311
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4196,f4063,f3738,f12796]) ).
fof(f12796,plain,
( spl17_911
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_911])]) ).
fof(f4196,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_311
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3739]) ).
fof(f12794,plain,
( spl17_910
| ~ spl17_310
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4195,f4063,f3734,f12792]) ).
fof(f12792,plain,
( spl17_910
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_910])]) ).
fof(f4195,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_310
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3735]) ).
fof(f12790,plain,
( spl17_909
| ~ spl17_308
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4194,f4063,f3725,f12788]) ).
fof(f12788,plain,
( spl17_909
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_909])]) ).
fof(f4194,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_308
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3726]) ).
fof(f12786,plain,
( spl17_908
| ~ spl17_313
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4193,f4063,f3746,f12784]) ).
fof(f12784,plain,
( spl17_908
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_908])]) ).
fof(f4193,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_313
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3747]) ).
fof(f12782,plain,
( spl17_907
| ~ spl17_312
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4192,f4063,f3742,f12780]) ).
fof(f12780,plain,
( spl17_907
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_907])]) ).
fof(f4192,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_312
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3743]) ).
fof(f12778,plain,
( spl17_906
| ~ spl17_39
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f3564,f2719,f2255,f12776]) ).
fof(f12776,plain,
( spl17_906
<=> ! [X0] :
( collect_fun_a_bool(p(X0)) = collect_fun_a_bool(collect_fun_a_bool(p(X0)))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_906])]) ).
fof(f2255,plain,
( spl17_39
<=> ! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f3564,plain,
( ! [X0] :
( collect_fun_a_bool(p(X0)) = collect_fun_a_bool(collect_fun_a_bool(p(X0)))
| ~ is_fun_a_bool(X0) )
| ~ spl17_39
| ~ spl17_141 ),
inference(resolution,[],[f2720,f2256]) ).
fof(f2256,plain,
( ! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) )
| ~ spl17_39 ),
inference(avatar_component_clause,[],[f2255]) ).
fof(f12774,plain,
( spl17_905
| ~ spl17_237
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4183,f4059,f3271,f12772]) ).
fof(f12772,plain,
( spl17_905
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_905])]) ).
fof(f4183,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,X0))) )
| ~ spl17_237
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3272]) ).
fof(f12770,plain,
( spl17_904
| ~ spl17_237
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f4179,f4059,f3271,f12768]) ).
fof(f12768,plain,
( spl17_904
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_904])]) ).
fof(f4179,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(suc,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X2)) )
| ~ spl17_237
| ~ spl17_352 ),
inference(superposition,[],[f4060,f3272]) ).
fof(f12766,plain,
( spl17_903
| ~ spl17_237
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4173,f4055,f3271,f12764]) ).
fof(f12764,plain,
( spl17_903
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_903])]) ).
fof(f4173,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) )
| ~ spl17_237
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3272]) ).
fof(f12762,plain,
( spl17_902
| ~ spl17_237
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f4169,f4055,f3271,f12760]) ).
fof(f12760,plain,
( spl17_902
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_902])]) ).
fof(f4169,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(suc,X1))) )
| ~ spl17_237
| ~ spl17_351 ),
inference(superposition,[],[f4056,f3272]) ).
fof(f12758,plain,
( spl17_901
| ~ spl17_328
| ~ spl17_349 ),
inference(avatar_split_clause,[],[f4128,f4047,f3807,f12756]) ).
fof(f12756,plain,
( spl17_901
<=> ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK10(image_pname_a(X0,X1),X0,X2))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_901])]) ).
fof(f4128,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK10(image_pname_a(X0,X1),X0,X2))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) )
| ~ spl17_328
| ~ spl17_349 ),
inference(resolution,[],[f4048,f3808]) ).
fof(f12754,plain,
( spl17_900
| ~ spl17_327
| ~ spl17_348 ),
inference(avatar_split_clause,[],[f4122,f4043,f3803,f12752]) ).
fof(f12752,plain,
( spl17_900
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X0,X1) = hAPP_pname_a(X0,sK8(hAPP_pname_a(X0,X1),X0,X2))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_900])]) ).
fof(f4122,plain,
( ! [X2,X0,X1] :
( hAPP_pname_a(X0,X1) = hAPP_pname_a(X0,sK8(hAPP_pname_a(X0,X1),X0,X2))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl17_327
| ~ spl17_348 ),
inference(resolution,[],[f4044,f3804]) ).
fof(f12750,plain,
( spl17_899
| ~ spl17_327
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f4119,f4039,f3803,f12748]) ).
fof(f12748,plain,
( spl17_899
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X0,X1) = hAPP_pname_a(X0,sK7(hAPP_pname_a(X0,X1),X0,X2))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_899])]) ).
fof(f4119,plain,
( ! [X2,X0,X1] :
( hAPP_pname_a(X0,X1) = hAPP_pname_a(X0,sK7(hAPP_pname_a(X0,X1),X0,X2))
| ~ is_a(hAPP_pname_a(X0,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl17_327
| ~ spl17_347 ),
inference(resolution,[],[f4040,f3804]) ).
fof(f12746,plain,
( spl17_898
| ~ spl17_171
| ~ spl17_313 ),
inference(avatar_split_clause,[],[f3893,f3746,f2839,f12744]) ).
fof(f12744,plain,
( spl17_898
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,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,[spl17_898])]) ).
fof(f3893,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_313 ),
inference(superposition,[],[f3747,f2840]) ).
fof(f12742,plain,
( spl17_897
| ~ spl17_171
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f3890,f3742,f2839,f12740]) ).
fof(f12740,plain,
( spl17_897
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,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,[spl17_897])]) ).
fof(f3890,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_312 ),
inference(superposition,[],[f3743,f2840]) ).
fof(f12738,plain,
( spl17_896
| ~ spl17_171
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f3887,f3738,f2839,f12736]) ).
fof(f12736,plain,
( spl17_896
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,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,[spl17_896])]) ).
fof(f3887,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_311 ),
inference(superposition,[],[f3739,f2840]) ).
fof(f12734,plain,
( spl17_895
| ~ spl17_38
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f3558,f2719,f2251,f12732]) ).
fof(f12732,plain,
( spl17_895
<=> ! [X0] :
( collect_fun_a_bool(collect_fun_a_bool(X0)) = collect_fun_a_bool(collect_fun_a_bool(collect_fun_a_bool(X0)))
| ~ is_fun949378684l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_895])]) ).
fof(f3558,plain,
( ! [X0] :
( collect_fun_a_bool(collect_fun_a_bool(X0)) = collect_fun_a_bool(collect_fun_a_bool(collect_fun_a_bool(X0)))
| ~ is_fun949378684l_bool(X0) )
| ~ spl17_38
| ~ spl17_141 ),
inference(resolution,[],[f2720,f2252]) ).
fof(f12730,plain,
( spl17_894
| ~ spl17_171
| ~ spl17_310 ),
inference(avatar_split_clause,[],[f3884,f3734,f2839,f12728]) ).
fof(f12728,plain,
( spl17_894
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,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,[spl17_894])]) ).
fof(f3884,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_310 ),
inference(superposition,[],[f3735,f2840]) ).
fof(f12726,plain,
( spl17_893
| ~ spl17_171
| ~ spl17_308 ),
inference(avatar_split_clause,[],[f3881,f3725,f2839,f12724]) ).
fof(f12724,plain,
( spl17_893
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,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,[spl17_893])]) ).
fof(f3881,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),hAPP_nat_nat(suc,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) )
| ~ spl17_171
| ~ spl17_308 ),
inference(superposition,[],[f3726,f2840]) ).
fof(f12315,plain,
( spl17_892
| ~ spl17_50
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f5069,f5005,f2303,f12313]) ).
fof(f12313,plain,
( spl17_892
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_892])]) ).
fof(f2303,plain,
( spl17_50
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f5069,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X0)),hAPP_nat_nat(minus_minus_nat(X1),X0)) )
| ~ spl17_50
| ~ spl17_448 ),
inference(resolution,[],[f5006,f2304]) ).
fof(f2304,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0))
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f2303]) ).
fof(f12311,plain,
( spl17_891
| ~ spl17_163
| ~ spl17_817 ),
inference(avatar_split_clause,[],[f10835,f10818,f2807,f12308]) ).
fof(f12308,plain,
( spl17_891
<=> p(image_pname_a(mgt_call,u)) = collect_fun_a_bool(p(image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_891])]) ).
fof(f10835,plain,
( p(image_pname_a(mgt_call,u)) = collect_fun_a_bool(p(image_pname_a(mgt_call,u)))
| ~ spl17_163
| ~ spl17_817 ),
inference(resolution,[],[f10819,f2808]) ).
fof(f10819,plain,
( is_fun_a_bool(image_pname_a(mgt_call,u))
| ~ spl17_817 ),
inference(avatar_component_clause,[],[f10818]) ).
fof(f12306,plain,
( spl17_890
| ~ spl17_164
| ~ spl17_421 ),
inference(avatar_split_clause,[],[f4754,f4686,f2811,f12304]) ).
fof(f12304,plain,
( spl17_890
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK5(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),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_890])]) ).
fof(f4754,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK5(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),X2))))) )
| ~ spl17_164
| ~ spl17_421 ),
inference(resolution,[],[f4687,f2812]) ).
fof(f12302,plain,
( spl17_889
| ~ spl17_164
| ~ spl17_420 ),
inference(avatar_split_clause,[],[f4749,f4682,f2811,f12300]) ).
fof(f12300,plain,
( spl17_889
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| is_pname(sK5(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_889])]) ).
fof(f4749,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| is_pname(sK5(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))) )
| ~ spl17_164
| ~ spl17_420 ),
inference(resolution,[],[f4683,f2812]) ).
fof(f12298,plain,
( spl17_888
| ~ spl17_162
| ~ spl17_419 ),
inference(avatar_split_clause,[],[f4743,f4678,f2803,f12296]) ).
fof(f12296,plain,
( spl17_888
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| is_a(sK4(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),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_888])]) ).
fof(f4743,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| is_a(sK4(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),X2))))) )
| ~ spl17_162
| ~ spl17_419 ),
inference(resolution,[],[f4679,f2804]) ).
fof(f12294,plain,
( spl17_887
| ~ spl17_162
| ~ spl17_418 ),
inference(avatar_split_clause,[],[f4737,f4674,f2803,f12292]) ).
fof(f12292,plain,
( spl17_887
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK4(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_887])]) ).
fof(f4737,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| is_a(sK4(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))) )
| ~ spl17_162
| ~ spl17_418 ),
inference(resolution,[],[f4675,f2804]) ).
fof(f12290,plain,
( spl17_886
| ~ spl17_169
| ~ spl17_414 ),
inference(avatar_split_clause,[],[f4728,f4658,f2831,f12288]) ).
fof(f12288,plain,
( spl17_886
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_886])]) ).
fof(f4728,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X0)) )
| ~ spl17_169
| ~ spl17_414 ),
inference(resolution,[],[f4659,f2832]) ).
fof(f12286,plain,
( spl17_885
| ~ spl17_167
| ~ spl17_411 ),
inference(avatar_split_clause,[],[f4717,f4646,f2823,f12284]) ).
fof(f12284,plain,
( spl17_885
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_885])]) ).
fof(f4717,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X0)) )
| ~ spl17_167
| ~ spl17_411 ),
inference(resolution,[],[f4647,f2824]) ).
fof(f12281,plain,
( spl17_884
| ~ spl17_275
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f4488,f4361,f3469,f12279]) ).
fof(f12279,plain,
( spl17_884
<=> ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X0,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_884])]) ).
fof(f4488,plain,
( ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK6(X0,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)) = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) )
| ~ spl17_275
| ~ spl17_390 ),
inference(resolution,[],[f4362,f3470]) ).
fof(f12277,plain,
( spl17_883
| ~ spl17_185
| ~ spl17_388 ),
inference(avatar_split_clause,[],[f4484,f4346,f2909,f12275]) ).
fof(f12275,plain,
( spl17_883
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_883])]) ).
fof(f4484,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) )
| ~ spl17_185
| ~ spl17_388 ),
inference(superposition,[],[f4347,f2910]) ).
fof(f12273,plain,
( spl17_882
| ~ spl17_185
| ~ spl17_384 ),
inference(avatar_split_clause,[],[f4474,f4330,f2909,f12271]) ).
fof(f12271,plain,
( spl17_882
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_882])]) ).
fof(f4474,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) )
| ~ spl17_185
| ~ spl17_384 ),
inference(superposition,[],[f4331,f2910]) ).
fof(f12269,plain,
( spl17_881
| ~ spl17_327
| ~ spl17_381 ),
inference(avatar_split_clause,[],[f4467,f4318,f3803,f12267]) ).
fof(f12267,plain,
( spl17_881
<=> ! [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_p338031245l_bool(member_pname,sK16(X0,image_pname_a(X0,X2),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_881])]) ).
fof(f4467,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_p338031245l_bool(member_pname,sK16(X0,image_pname_a(X0,X2),X1)),X2)) )
| ~ spl17_327
| ~ spl17_381 ),
inference(resolution,[],[f4319,f3804]) ).
fof(f12254,plain,
( spl17_880
| ~ spl17_257
| ~ spl17_380 ),
inference(avatar_split_clause,[],[f4465,f4314,f3397,f12252]) ).
fof(f12252,plain,
( spl17_880
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK10(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_880])]) ).
fof(f4465,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ is_fun_a_bool(X0)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK10(X0,X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
| ~ spl17_257
| ~ spl17_380 ),
inference(resolution,[],[f4315,f3398]) ).
fof(f12250,plain,
( spl17_879
| ~ spl17_113
| ~ spl17_369 ),
inference(avatar_split_clause,[],[f4413,f4269,f2605,f12248]) ).
fof(f12248,plain,
( spl17_879
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X0))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_879])]) ).
fof(f4413,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),X0))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1) )
| ~ spl17_113
| ~ spl17_369 ),
inference(resolution,[],[f4270,f2606]) ).
fof(f12246,plain,
( spl17_878
| ~ spl17_324
| ~ spl17_369 ),
inference(avatar_split_clause,[],[f4410,f4269,f3791,f12244]) ).
fof(f12244,plain,
( spl17_878
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,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,[spl17_878])]) ).
fof(f4410,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_324
| ~ spl17_369 ),
inference(resolution,[],[f4270,f3792]) ).
fof(f12242,plain,
( spl17_877
| ~ spl17_185
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f4021,f3977,f2909,f12240]) ).
fof(f12240,plain,
( spl17_877
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_877])]) ).
fof(f4021,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ spl17_185
| ~ spl17_337 ),
inference(superposition,[],[f3978,f2910]) ).
fof(f12238,plain,
( spl17_876
| ~ spl17_288
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4018,f3969,f3609,f12236]) ).
fof(f12236,plain,
( spl17_876
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_nat_nat(minus_minus_nat(sK1(X1)),hAPP_nat_nat(minus_minus_nat(sK1(X1)),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_876])]) ).
fof(f4018,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_nat_nat(minus_minus_nat(sK1(X1)),hAPP_nat_nat(minus_minus_nat(sK1(X1)),X0)) = X0 )
| ~ spl17_288
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3610]) ).
fof(f12234,plain,
( spl17_875
| ~ spl17_289
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4017,f3969,f3613,f12232]) ).
fof(f12232,plain,
( spl17_875
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| sK1(X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK1(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_875])]) ).
fof(f4017,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| sK1(X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK1(X1)),X0)) )
| ~ spl17_289
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3614]) ).
fof(f12230,plain,
( spl17_874
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f3659,f3621,f12228]) ).
fof(f12228,plain,
( spl17_874
<=> ! [X0,X3,X2,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_874])]) ).
fof(f3659,plain,
( ! [X2,X3,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X3)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),X3)
| ~ spl17_291 ),
inference(superposition,[],[f3622,f3622]) ).
fof(f12187,plain,
( spl17_873
| ~ spl17_250
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4146,f4051,f3367,f12185]) ).
fof(f12185,plain,
( spl17_873
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(X0,hAPP_fun_a_bool_nat(finite_card_a,g)))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK11(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_873])]) ).
fof(f4146,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(X0,hAPP_fun_a_bool_nat(finite_card_a,g)))
| hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK11(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) )
| ~ spl17_250
| ~ spl17_350 ),
inference(superposition,[],[f4052,f3369]) ).
fof(f12180,plain,
( spl17_872
| ~ spl17_185
| ~ spl17_333 ),
inference(avatar_split_clause,[],[f3967,f3958,f2909,f12178]) ).
fof(f12178,plain,
( spl17_872
<=> ! [X2,X0,X1] :
( is_fun_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))
| ~ is_fun_a_bool(X2)
| ~ is_a(hAPP_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_872])]) ).
fof(f3967,plain,
( ! [X2,X0,X1] :
( is_fun_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))
| ~ is_fun_a_bool(X2)
| ~ is_a(hAPP_pname_a(X0,X1)) )
| ~ spl17_185
| ~ spl17_333 ),
inference(superposition,[],[f3959,f2910]) ).
fof(f12162,plain,
( ~ spl17_870
| spl17_871
| ~ spl17_194
| ~ spl17_289 ),
inference(avatar_split_clause,[],[f3654,f3613,f3037,f12159,f12155]) ).
fof(f12155,plain,
( spl17_870
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_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,[spl17_870])]) ).
fof(f12159,plain,
( spl17_871
<=> 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,[spl17_871])]) ).
fof(f3654,plain,
( hAPP_nat_nat(suc,na) = hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)))
| ~ spl17_194
| ~ spl17_289 ),
inference(resolution,[],[f3614,f3039]) ).
fof(f11914,plain,
( spl17_869
| ~ spl17_170
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4609,f4575,f2835,f11912]) ).
fof(f11912,plain,
( spl17_869
<=> ! [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))) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_869])]) ).
fof(f4609,plain,
( ! [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))) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_170
| ~ spl17_402 ),
inference(resolution,[],[f4576,f2836]) ).
fof(f11910,plain,
( spl17_868
| ~ spl17_168
| ~ spl17_401 ),
inference(avatar_split_clause,[],[f4599,f4571,f2827,f11908]) ).
fof(f11908,plain,
( spl17_868
<=> ! [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))) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_868])]) ).
fof(f4599,plain,
( ! [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))) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
| ~ spl17_168
| ~ spl17_401 ),
inference(resolution,[],[f4572,f2828]) ).
fof(f11906,plain,
( spl17_867
| ~ spl17_162
| ~ spl17_400 ),
inference(avatar_split_clause,[],[f4595,f4567,f2803,f11904]) ).
fof(f11904,plain,
( spl17_867
<=> ! [X2,X0,X1] :
( image_pname_a(X0,sK9(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_867])]) ).
fof(f4595,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,sK9(X0,X1,X2)) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) )
| ~ spl17_162
| ~ spl17_400 ),
inference(resolution,[],[f4568,f2804]) ).
fof(f11899,plain,
( ~ spl17_640
| ~ spl17_865 ),
inference(avatar_contradiction_clause,[],[f11896]) ).
fof(f11896,plain,
( $false
| ~ spl17_640
| ~ spl17_865 ),
inference(resolution,[],[f11891,f7267]) ).
fof(f11891,plain,
( ! [X1] : ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))))
| ~ spl17_865 ),
inference(avatar_component_clause,[],[f11890]) ).
fof(f11890,plain,
( spl17_865
<=> ! [X1] : ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_865])]) ).
fof(f11895,plain,
( spl17_865
| spl17_866
| ~ spl17_375
| ~ spl17_389 ),
inference(avatar_split_clause,[],[f4486,f4357,f4293,f11893,f11890]) ).
fof(f11893,plain,
( spl17_866
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_866])]) ).
fof(f4486,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)))) )
| ~ spl17_375
| ~ spl17_389 ),
inference(resolution,[],[f4358,f4294]) ).
fof(f11884,plain,
( spl17_864
| ~ spl17_819
| ~ spl17_848 ),
inference(avatar_split_clause,[],[f11769,f11479,f10826,f11881]) ).
fof(f11881,plain,
( spl17_864
<=> is_a(sK4(g,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_864])]) ).
fof(f10826,plain,
( spl17_819
<=> g = image_pname_a(mgt_call,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_819])]) ).
fof(f11479,plain,
( spl17_848
<=> is_a(sK4(g,image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_848])]) ).
fof(f11769,plain,
( is_a(sK4(g,g))
| ~ spl17_819
| ~ spl17_848 ),
inference(superposition,[],[f11481,f10828]) ).
fof(f10828,plain,
( g = image_pname_a(mgt_call,u)
| ~ spl17_819 ),
inference(avatar_component_clause,[],[f10826]) ).
fof(f11481,plain,
( is_a(sK4(g,image_pname_a(mgt_call,u)))
| ~ spl17_848 ),
inference(avatar_component_clause,[],[f11479]) ).
fof(f11877,plain,
( ~ spl17_636
| ~ spl17_862 ),
inference(avatar_contradiction_clause,[],[f11874]) ).
fof(f11874,plain,
( $false
| ~ spl17_636
| ~ spl17_862 ),
inference(resolution,[],[f11869,f7250]) ).
fof(f11869,plain,
( ! [X1] : ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))))
| ~ spl17_862 ),
inference(avatar_component_clause,[],[f11868]) ).
fof(f11868,plain,
( spl17_862
<=> ! [X1] : ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_862])]) ).
fof(f11873,plain,
( spl17_862
| spl17_863
| ~ spl17_374
| ~ spl17_388 ),
inference(avatar_split_clause,[],[f4483,f4346,f4289,f11871,f11868]) ).
fof(f11871,plain,
( spl17_863
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_863])]) ).
fof(f4483,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)))) )
| ~ spl17_374
| ~ spl17_388 ),
inference(resolution,[],[f4347,f4290]) ).
fof(f11864,plain,
( ~ spl17_630
| ~ spl17_860 ),
inference(avatar_contradiction_clause,[],[f11862]) ).
fof(f11862,plain,
( $false
| ~ spl17_630
| ~ spl17_860 ),
inference(resolution,[],[f11857,f7226]) ).
fof(f7226,plain,
( ! [X1] : hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))))
| ~ spl17_630 ),
inference(avatar_component_clause,[],[f7225]) ).
fof(f7225,plain,
( spl17_630
<=> ! [X1] : hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_630])]) ).
fof(f11857,plain,
( ! [X1] : ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))))
| ~ spl17_860 ),
inference(avatar_component_clause,[],[f11856]) ).
fof(f11856,plain,
( spl17_860
<=> ! [X1] : ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_860])]) ).
fof(f11861,plain,
( spl17_860
| spl17_861
| ~ spl17_373
| ~ spl17_387 ),
inference(avatar_split_clause,[],[f4481,f4342,f4285,f11859,f11856]) ).
fof(f11859,plain,
( spl17_861
<=> ! [X0] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_861])]) ).
fof(f4342,plain,
( spl17_387
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_387])]) ).
fof(f4481,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)))) )
| ~ spl17_373
| ~ spl17_387 ),
inference(resolution,[],[f4343,f4286]) ).
fof(f4343,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_387 ),
inference(avatar_component_clause,[],[f4342]) ).
fof(f11820,plain,
( ~ spl17_633
| ~ spl17_857 ),
inference(avatar_contradiction_clause,[],[f11818]) ).
fof(f11818,plain,
( $false
| ~ spl17_633
| ~ spl17_857 ),
inference(resolution,[],[f11735,f7238]) ).
fof(f7238,plain,
( ! [X1] : hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))))
| ~ spl17_633 ),
inference(avatar_component_clause,[],[f7237]) ).
fof(f7237,plain,
( spl17_633
<=> ! [X1] : hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_633])]) ).
fof(f11735,plain,
( ! [X1] : ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))))
| ~ spl17_857 ),
inference(avatar_component_clause,[],[f11734]) ).
fof(f11734,plain,
( spl17_857
<=> ! [X1] : ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_857])]) ).
fof(f11744,plain,
( spl17_859
| ~ spl17_716
| spl17_818 ),
inference(avatar_split_clause,[],[f10836,f10822,f8694,f11741]) ).
fof(f11741,plain,
( spl17_859
<=> hBOOL(hAPP_pname_bool(u,sK16(mgt_call,g,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_859])]) ).
fof(f8694,plain,
( spl17_716
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| hBOOL(hAPP_pname_bool(X1,sK16(X0,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_716])]) ).
fof(f10822,plain,
( spl17_818
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,u)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_818])]) ).
fof(f10836,plain,
( hBOOL(hAPP_pname_bool(u,sK16(mgt_call,g,u)))
| ~ spl17_716
| spl17_818 ),
inference(resolution,[],[f10824,f8695]) ).
fof(f8695,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| hBOOL(hAPP_pname_bool(X1,sK16(X0,X2,X1))) )
| ~ spl17_716 ),
inference(avatar_component_clause,[],[f8694]) ).
fof(f10824,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,u)),g))
| spl17_818 ),
inference(avatar_component_clause,[],[f10822]) ).
fof(f11739,plain,
( spl17_857
| spl17_858
| ~ spl17_372
| ~ spl17_386 ),
inference(avatar_split_clause,[],[f4479,f4338,f4281,f11737,f11734]) ).
fof(f11737,plain,
( spl17_858
<=> ! [X0] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_858])]) ).
fof(f4338,plain,
( spl17_386
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_386])]) ).
fof(f4479,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)))) )
| ~ spl17_372
| ~ spl17_386 ),
inference(resolution,[],[f4339,f4282]) ).
fof(f4339,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_386 ),
inference(avatar_component_clause,[],[f4338]) ).
fof(f11732,plain,
( spl17_856
| ~ spl17_275
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f4227,f4067,f3469,f11730]) ).
fof(f11730,plain,
( spl17_856
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X2,X0)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_856])]) ).
fof(f4227,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X2,X0)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2)) )
| ~ spl17_275
| ~ spl17_354 ),
inference(resolution,[],[f4068,f3470]) ).
fof(f11728,plain,
( spl17_855
| ~ spl17_259
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4219,f4063,f3405,f11726]) ).
fof(f11726,plain,
( spl17_855
<=> ! [X2,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),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_855])]) ).
fof(f4219,plain,
( ! [X2,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),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) )
| ~ spl17_259
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3406]) ).
fof(f11724,plain,
( spl17_854
| ~ spl17_277
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4191,f4063,f3477,f11722]) ).
fof(f11722,plain,
( spl17_854
<=> ! [X2,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,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_854])]) ).
fof(f4191,plain,
( ! [X2,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,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_277
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3478]) ).
fof(f11720,plain,
( spl17_853
| ~ spl17_237
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f4145,f4051,f3271,f11718]) ).
fof(f11718,plain,
( spl17_853
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(minus_minus_nat(X0),X1)))
| hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(suc,sK11(X2))))
| ~ hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_853])]) ).
fof(f4145,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(minus_minus_nat(X0),X1)))
| hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(suc,sK11(X2))))
| ~ hBOOL(hAPP_nat_bool(X2,hAPP_nat_nat(suc,X0))) )
| ~ spl17_237
| ~ spl17_350 ),
inference(superposition,[],[f4052,f3272]) ).
fof(f11716,plain,
( spl17_852
| ~ spl17_261
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4014,f3969,f3413,f11714]) ).
fof(f11714,plain,
( spl17_852
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| sK1(X1) = hAPP_nat_nat(suc,sK3(sK1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_852])]) ).
fof(f4014,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| sK1(X1) = hAPP_nat_nat(suc,sK3(sK1(X1))) )
| ~ spl17_261
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3414]) ).
fof(f11661,plain,
( ~ spl17_8
| spl17_851
| ~ spl17_4
| ~ spl17_44
| ~ spl17_95
| ~ spl17_433
| ~ spl17_457
| ~ spl17_524 ),
inference(avatar_split_clause,[],[f6512,f5817,f5140,f4836,f2513,f2278,f2108,f11658,f2128]) ).
fof(f11658,plain,
( spl17_851
<=> hAPP_f921600141ol_nat(finite_card_pname,u) = hAPP_f921600141ol_nat(finite_card_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_851])]) ).
fof(f2108,plain,
( spl17_4
<=> is_fun_pname_bool(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f2513,plain,
( spl17_95
<=> u = collect_pname(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
fof(f5817,plain,
( spl17_524
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBS_568398431l_bool(X1,X0) = collect_pname(cOMBS_568398431l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_524])]) ).
fof(f6512,plain,
( hAPP_f921600141ol_nat(finite_card_pname,u) = hAPP_f921600141ol_nat(finite_card_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_4
| ~ spl17_44
| ~ spl17_95
| ~ spl17_433
| ~ spl17_457
| ~ spl17_524 ),
inference(forward_demodulation,[],[f5188,f6243]) ).
fof(f6243,plain,
( ! [X0] : cOMBS_568398431l_bool(X0,u) = collect_pname(cOMBS_568398431l_bool(X0,u))
| ~ spl17_4
| ~ spl17_524 ),
inference(resolution,[],[f5818,f2110]) ).
fof(f2110,plain,
( is_fun_pname_bool(u)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f2108]) ).
fof(f5818,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBS_568398431l_bool(X1,X0) = collect_pname(cOMBS_568398431l_bool(X1,X0)) )
| ~ spl17_524 ),
inference(avatar_component_clause,[],[f5817]) ).
fof(f5188,plain,
( hAPP_f921600141ol_nat(finite_card_pname,u) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_44
| ~ spl17_95
| ~ spl17_433
| ~ spl17_457 ),
inference(forward_demodulation,[],[f5186,f4905]) ).
fof(f4905,plain,
( ! [X0] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),u)) = 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),u)))
| ~ spl17_95
| ~ spl17_433 ),
inference(superposition,[],[f4837,f2515]) ).
fof(f2515,plain,
( u = collect_pname(u)
| ~ spl17_95 ),
inference(avatar_component_clause,[],[f2513]) ).
fof(f5186,plain,
( hAPP_f921600141ol_nat(finite_card_pname,u) = hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_44
| ~ spl17_457 ),
inference(resolution,[],[f5141,f2280]) ).
fof(f2280,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl17_44 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f11650,plain,
( spl17_850
| ~ spl17_819
| ~ spl17_849 ),
inference(avatar_split_clause,[],[f11646,f11643,f10826,f11648]) ).
fof(f11648,plain,
( spl17_850
<=> ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0)),hAPP_nat_nat(suc,na)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_850])]) ).
fof(f11643,plain,
( spl17_849
<=> ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_849])]) ).
fof(f11646,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0)),hAPP_nat_nat(suc,na))
| ~ spl17_819
| ~ spl17_849 ),
inference(forward_demodulation,[],[f11644,f10828]) ).
fof(f11644,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0)
| ~ spl17_849 ),
inference(avatar_component_clause,[],[f11643]) ).
fof(f11645,plain,
( spl17_849
| ~ spl17_250
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f3658,f3621,f3367,f11643]) ).
fof(f3658,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),X0)),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,g)),X0)
| ~ spl17_250
| ~ spl17_291 ),
inference(superposition,[],[f3622,f3369]) ).
fof(f11482,plain,
( spl17_848
| ~ spl17_162
| spl17_818 ),
inference(avatar_split_clause,[],[f10839,f10822,f2803,f11479]) ).
fof(f10839,plain,
( is_a(sK4(g,image_pname_a(mgt_call,u)))
| ~ spl17_162
| spl17_818 ),
inference(resolution,[],[f10824,f2804]) ).
fof(f11192,plain,
( spl17_847
| ~ spl17_113
| ~ spl17_368
| ~ spl17_824 ),
inference(avatar_split_clause,[],[f10860,f10857,f4264,f2605,f11190]) ).
fof(f11190,plain,
( spl17_847
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),hAPP_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,[spl17_847])]) ).
fof(f10857,plain,
( spl17_824
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_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,[spl17_824])]) ).
fof(f10860,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_113
| ~ spl17_368
| ~ spl17_824 ),
inference(forward_demodulation,[],[f10858,f4365]) ).
fof(f4365,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ spl17_113
| ~ spl17_368 ),
inference(resolution,[],[f4265,f2606]) ).
fof(f10858,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_824 ),
inference(avatar_component_clause,[],[f10857]) ).
fof(f11016,plain,
( spl17_846
| ~ spl17_472
| ~ spl17_819 ),
inference(avatar_split_clause,[],[f10881,f10826,f5252,f11013]) ).
fof(f11013,plain,
( spl17_846
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_846])]) ).
fof(f5252,plain,
( spl17_472
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_472])]) ).
fof(f10881,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,g)))
| ~ spl17_472
| ~ spl17_819 ),
inference(superposition,[],[f5254,f10828]) ).
fof(f5254,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl17_472 ),
inference(avatar_component_clause,[],[f5252]) ).
fof(f11008,plain,
( spl17_845
| ~ spl17_388
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4927,f4840,f4346,f11006]) ).
fof(f11006,plain,
( spl17_845
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_845])]) ).
fof(f4927,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
| ~ spl17_388
| ~ spl17_434 ),
inference(superposition,[],[f4347,f4841]) ).
fof(f11004,plain,
( spl17_844
| ~ spl17_384
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4926,f4840,f4330,f11002]) ).
fof(f11002,plain,
( spl17_844
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_844])]) ).
fof(f4926,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
| ~ spl17_384
| ~ spl17_434 ),
inference(superposition,[],[f4331,f4841]) ).
fof(f11000,plain,
( spl17_843
| ~ spl17_389
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4910,f4836,f4357,f10998]) ).
fof(f10998,plain,
( spl17_843
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_843])]) ).
fof(f4910,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
| ~ spl17_389
| ~ spl17_433 ),
inference(superposition,[],[f4358,f4837]) ).
fof(f10996,plain,
( spl17_842
| ~ spl17_385
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4909,f4836,f4334,f10994]) ).
fof(f10994,plain,
( spl17_842
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_842])]) ).
fof(f4909,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
| ~ spl17_385
| ~ spl17_433 ),
inference(superposition,[],[f4335,f4837]) ).
fof(f10992,plain,
( spl17_841
| ~ spl17_382
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4891,f4832,f4322,f10990]) ).
fof(f10990,plain,
( spl17_841
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_841])]) ).
fof(f4322,plain,
( spl17_382
<=> ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_382])]) ).
fof(f4891,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
| ~ spl17_382
| ~ spl17_432 ),
inference(superposition,[],[f4323,f4833]) ).
fof(f4323,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
| ~ spl17_382 ),
inference(avatar_component_clause,[],[f4322]) ).
fof(f10988,plain,
( spl17_840
| ~ spl17_387
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4890,f4832,f4342,f10986]) ).
fof(f10986,plain,
( spl17_840
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_840])]) ).
fof(f4890,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
| ~ spl17_387
| ~ spl17_432 ),
inference(superposition,[],[f4343,f4833]) ).
fof(f10984,plain,
( spl17_839
| ~ spl17_383
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4879,f4828,f4326,f10982]) ).
fof(f10982,plain,
( spl17_839
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_839])]) ).
fof(f4326,plain,
( spl17_383
<=> ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_383])]) ).
fof(f4879,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
| ~ spl17_383
| ~ spl17_431 ),
inference(superposition,[],[f4327,f4829]) ).
fof(f4327,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
| ~ spl17_383 ),
inference(avatar_component_clause,[],[f4326]) ).
fof(f10980,plain,
( spl17_838
| ~ spl17_386
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4878,f4828,f4338,f10978]) ).
fof(f10978,plain,
( spl17_838
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_838])]) ).
fof(f4878,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
| ~ spl17_386
| ~ spl17_431 ),
inference(superposition,[],[f4339,f4829]) ).
fof(f10976,plain,
( spl17_837
| ~ spl17_162
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f4554,f4546,f2803,f10974]) ).
fof(f10974,plain,
( spl17_837
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_837])]) ).
fof(f4554,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) )
| ~ spl17_162
| ~ spl17_398 ),
inference(resolution,[],[f4547,f2804]) ).
fof(f10971,plain,
( spl17_836
| ~ spl17_52
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f4553,f4546,f2311,f10969]) ).
fof(f10969,plain,
( spl17_836
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_836])]) ).
fof(f4553,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,image_pname_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_52
| ~ spl17_398 ),
inference(resolution,[],[f4547,f2312]) ).
fof(f10966,plain,
( spl17_835
| ~ spl17_203
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f4489,f4361,f3074,f10964]) ).
fof(f10964,plain,
( spl17_835
<=> ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK0(X0,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) = X0
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_835])]) ).
fof(f3074,plain,
( spl17_203
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_203])]) ).
fof(f4489,plain,
( ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),sK0(X0,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) = X0
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_203
| ~ spl17_390 ),
inference(resolution,[],[f4362,f3075]) ).
fof(f3075,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_203 ),
inference(avatar_component_clause,[],[f3074]) ).
fof(f10962,plain,
( spl17_834
| ~ spl17_237
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4438,f4297,f3271,f10960]) ).
fof(f10960,plain,
( spl17_834
<=> ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,X1))),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_834])]) ).
fof(f10958,plain,
( spl17_833
| ~ spl17_237
| ~ spl17_277
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4404,f4264,f3477,f3271,f10956]) ).
fof(f10956,plain,
( spl17_833
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_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,[spl17_833])]) ).
fof(f4404,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_237
| ~ spl17_277
| ~ spl17_368 ),
inference(forward_demodulation,[],[f4368,f3272]) ).
fof(f4368,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_277
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3478]) ).
fof(f10954,plain,
( spl17_832
| ~ spl17_206
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4366,f4264,f3086,f10952]) ).
fof(f10952,plain,
( spl17_832
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(suc,hAPP_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,[spl17_832])]) ).
fof(f4366,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_206
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3087]) ).
fof(f10950,plain,
( spl17_831
| ~ spl17_113
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4365,f4264,f2605,f10948]) ).
fof(f10948,plain,
( spl17_831
<=> ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(X0),X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_831])]) ).
fof(f10946,plain,
( spl17_830
| ~ spl17_248
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f4246,f4083,f3318,f10944]) ).
fof(f4246,plain,
( ! [X2,X3,X0,X1] :
( 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,X0),image_pname_a(X2,X3)))
| is_pname(sK16(X2,X1,X3)) )
| ~ spl17_248
| ~ spl17_358 ),
inference(resolution,[],[f4084,f3319]) ).
fof(f10942,plain,
( spl17_829
| ~ spl17_248
| ~ spl17_357 ),
inference(avatar_split_clause,[],[f4240,f4079,f3318,f10940]) ).
fof(f10940,plain,
( spl17_829
<=> ! [X0,X3,X2,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),image_pname_a(X2,X3)))
| is_pname(sK16(X2,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_829])]) ).
fof(f4240,plain,
( ! [X2,X3,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),image_pname_a(X2,X3)))
| is_pname(sK16(X2,X1,X3)) )
| ~ spl17_248
| ~ spl17_357 ),
inference(resolution,[],[f4080,f3319]) ).
fof(f10938,plain,
( spl17_828
| ~ spl17_185
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f4024,f3981,f2909,f10936]) ).
fof(f10936,plain,
( spl17_828
<=> ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_828])]) ).
fof(f4024,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ spl17_185
| ~ spl17_338 ),
inference(superposition,[],[f3982,f2910]) ).
fof(f10873,plain,
( spl17_827
| ~ spl17_248
| spl17_818 ),
inference(avatar_split_clause,[],[f10837,f10822,f3318,f10870]) ).
fof(f10870,plain,
( spl17_827
<=> is_pname(sK16(mgt_call,g,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_827])]) ).
fof(f10837,plain,
( is_pname(sK16(mgt_call,g,u))
| ~ spl17_248
| spl17_818 ),
inference(resolution,[],[f10824,f3319]) ).
fof(f10868,plain,
( spl17_826
| ~ spl17_260
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4015,f3969,f3409,f10866]) ).
fof(f10866,plain,
( spl17_826
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_826])]) ).
fof(f4015,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),sK1(X1))) )
| ~ spl17_260
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3410]) ).
fof(f10864,plain,
( spl17_825
| ~ spl17_278
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4013,f3969,f3481,f10862]) ).
fof(f10862,plain,
( spl17_825
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK1(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_825])]) ).
fof(f4013,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK1(X1)),X0)) )
| ~ spl17_278
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3482]) ).
fof(f10859,plain,
( spl17_824
| ~ spl17_237
| ~ spl17_288
| ~ spl17_324 ),
inference(avatar_split_clause,[],[f3926,f3791,f3609,f3271,f10857]) ).
fof(f3926,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_237
| ~ spl17_288
| ~ spl17_324 ),
inference(forward_demodulation,[],[f3925,f3272]) ).
fof(f3925,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X0))) )
| ~ spl17_288
| ~ spl17_324 ),
inference(resolution,[],[f3792,f3610]) ).
fof(f10855,plain,
( spl17_823
| ~ spl17_237
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f3657,f3621,f3271,f10853]) ).
fof(f10853,plain,
( spl17_823
<=> ! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X2)),hAPP_nat_nat(suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_823])]) ).
fof(f10851,plain,
( spl17_822
| ~ spl17_259
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3647,f3609,f3405,f10849]) ).
fof(f10849,plain,
( spl17_822
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_822])]) ).
fof(f3647,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) )
| ~ spl17_259
| ~ spl17_288 ),
inference(resolution,[],[f3610,f3406]) ).
fof(f10847,plain,
( spl17_821
| ~ spl17_277
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3645,f3609,f3477,f10845]) ).
fof(f10845,plain,
( spl17_821
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,X1) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_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,[spl17_821])]) ).
fof(f3645,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,X1) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(suc,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_277
| ~ spl17_288 ),
inference(resolution,[],[f3610,f3478]) ).
fof(f10843,plain,
( spl17_820
| ~ spl17_185
| ~ spl17_238 ),
inference(avatar_split_clause,[],[f3328,f3275,f2909,f10841]) ).
fof(f10841,plain,
( spl17_820
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(fequal_a,X0),X1),X2))
| hAPP_pname_a(X0,X1) = X2
| ~ is_a(X2)
| ~ is_a(hAPP_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_820])]) ).
fof(f3275,plain,
( spl17_238
<=> ! [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,[spl17_238])]) ).
fof(f3328,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(fequal_a,X0),X1),X2))
| hAPP_pname_a(X0,X1) = X2
| ~ is_a(X2)
| ~ is_a(hAPP_pname_a(X0,X1)) )
| ~ spl17_185
| ~ spl17_238 ),
inference(superposition,[],[f3276,f2910]) ).
fof(f3276,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| X0 = X1
| ~ is_a(X1)
| ~ is_a(X0) )
| ~ spl17_238 ),
inference(avatar_component_clause,[],[f3275]) ).
fof(f10831,plain,
( ~ spl17_4
| ~ spl17_49
| spl17_817 ),
inference(avatar_split_clause,[],[f10830,f10818,f2299,f2108]) ).
fof(f10830,plain,
( ~ is_fun_pname_bool(u)
| ~ spl17_49
| spl17_817 ),
inference(resolution,[],[f10820,f2300]) ).
fof(f10820,plain,
( ~ is_fun_a_bool(image_pname_a(mgt_call,u))
| spl17_817 ),
inference(avatar_component_clause,[],[f10818]) ).
fof(f10829,plain,
( ~ spl17_817
| ~ spl17_3
| ~ spl17_818
| spl17_819
| ~ spl17_100
| ~ spl17_370 ),
inference(avatar_split_clause,[],[f4421,f4273,f2550,f10826,f10822,f2103,f10818]) ).
fof(f4421,plain,
( g = image_pname_a(mgt_call,u)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,u)),g))
| ~ is_fun_a_bool(g)
| ~ is_fun_a_bool(image_pname_a(mgt_call,u))
| ~ spl17_100
| ~ spl17_370 ),
inference(resolution,[],[f4274,f2552]) ).
fof(f10666,plain,
( spl17_816
| ~ spl17_37
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f3492,f2631,f2247,f10664]) ).
fof(f10664,plain,
( spl17_816
<=> ! [X0] :
( collec1974731493e_bool(collec1974731493e_bool(X0)) = collec1974731493e_bool(collec1974731493e_bool(collec1974731493e_bool(X0)))
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_816])]) ).
fof(f3492,plain,
( ! [X0] :
( collec1974731493e_bool(collec1974731493e_bool(X0)) = collec1974731493e_bool(collec1974731493e_bool(collec1974731493e_bool(X0)))
| ~ is_fun1661590463l_bool(X0) )
| ~ spl17_37
| ~ spl17_119 ),
inference(resolution,[],[f2632,f2248]) ).
fof(f10477,plain,
( spl17_815
| ~ spl17_268
| ~ spl17_486 ),
inference(avatar_split_clause,[],[f5420,f5412,f3441,f10475]) ).
fof(f10475,plain,
( spl17_815
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_815])]) ).
fof(f3441,plain,
( spl17_268
<=> ! [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,[spl17_268])]) ).
fof(f5420,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))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) )
| ~ spl17_268
| ~ spl17_486 ),
inference(resolution,[],[f5413,f3442]) ).
fof(f3442,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))) )
| ~ spl17_268 ),
inference(avatar_component_clause,[],[f3441]) ).
fof(f10472,plain,
( ~ spl17_595
| ~ spl17_813 ),
inference(avatar_contradiction_clause,[],[f10471]) ).
fof(f10471,plain,
( $false
| ~ spl17_595
| ~ spl17_813 ),
inference(resolution,[],[f10466,f7078]) ).
fof(f7078,plain,
( ! [X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)))
| ~ spl17_595 ),
inference(avatar_component_clause,[],[f7077]) ).
fof(f7077,plain,
( spl17_595
<=> ! [X1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_595])]) ).
fof(f10466,plain,
( ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)))
| ~ spl17_813 ),
inference(avatar_component_clause,[],[f10465]) ).
fof(f10465,plain,
( spl17_813
<=> ! [X1] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_813])]) ).
fof(f10470,plain,
( spl17_813
| spl17_814
| ~ spl17_332
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f4261,f4107,f3851,f10468,f10465]) ).
fof(f10468,plain,
( spl17_814
<=> ! [X0] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_814])]) ).
fof(f3851,plain,
( spl17_332
<=> ! [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,[spl17_332])]) ).
fof(f4261,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))) )
| ~ spl17_332
| ~ spl17_364 ),
inference(resolution,[],[f4108,f3852]) ).
fof(f3852,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))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_332 ),
inference(avatar_component_clause,[],[f3851]) ).
fof(f10462,plain,
( ~ spl17_572
| ~ spl17_811 ),
inference(avatar_contradiction_clause,[],[f10461]) ).
fof(f10461,plain,
( $false
| ~ spl17_572
| ~ spl17_811 ),
inference(resolution,[],[f10456,f6427]) ).
fof(f6427,plain,
( ! [X1] : hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)))
| ~ spl17_572 ),
inference(avatar_component_clause,[],[f6426]) ).
fof(f6426,plain,
( spl17_572
<=> ! [X1] : hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_572])]) ).
fof(f10456,plain,
( ! [X1] : ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)))
| ~ spl17_811 ),
inference(avatar_component_clause,[],[f10455]) ).
fof(f10455,plain,
( spl17_811
<=> ! [X1] : ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_811])]) ).
fof(f10460,plain,
( spl17_811
| spl17_812
| ~ spl17_331
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f4259,f4103,f3847,f10458,f10455]) ).
fof(f10458,plain,
( spl17_812
<=> ! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_812])]) ).
fof(f3847,plain,
( spl17_331
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_331])]) ).
fof(f4103,plain,
( spl17_363
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_363])]) ).
fof(f4259,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))) )
| ~ spl17_331
| ~ spl17_363 ),
inference(resolution,[],[f4104,f3848]) ).
fof(f3848,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_331 ),
inference(avatar_component_clause,[],[f3847]) ).
fof(f4104,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_363 ),
inference(avatar_component_clause,[],[f4103]) ).
fof(f10453,plain,
( spl17_810
| ~ spl17_203
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f4228,f4067,f3074,f10451]) ).
fof(f10451,plain,
( spl17_810
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_810])]) ).
fof(f4228,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_203
| ~ spl17_354 ),
inference(resolution,[],[f4068,f3075]) ).
fof(f10449,plain,
( spl17_809
| ~ spl17_206
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4189,f4063,f3086,f10447]) ).
fof(f10447,plain,
( spl17_809
<=> ! [X2,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),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_809])]) ).
fof(f4189,plain,
( ! [X2,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),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) )
| ~ spl17_206
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3087]) ).
fof(f10445,plain,
( spl17_808
| ~ spl17_256
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3948,f3807,f3393,f10443]) ).
fof(f10443,plain,
( spl17_808
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_808])]) ).
fof(f3948,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) )
| ~ spl17_256
| ~ spl17_328 ),
inference(resolution,[],[f3808,f3394]) ).
fof(f10441,plain,
( spl17_807
| ~ spl17_169
| ~ spl17_789 ),
inference(avatar_split_clause,[],[f10396,f10265,f2831,f10439]) ).
fof(f10265,plain,
( spl17_789
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),X0))
| is_pname(sK5(X0,u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_789])]) ).
fof(f10396,plain,
( ! [X0] :
( is_pname(sK5(X0,u))
| hBOOL(hAPP_pname_bool(X0,pn)) )
| ~ spl17_169
| ~ spl17_789 ),
inference(resolution,[],[f10266,f2832]) ).
fof(f10266,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),X0))
| is_pname(sK5(X0,u)) )
| ~ spl17_789 ),
inference(avatar_component_clause,[],[f10265]) ).
fof(f10437,plain,
( spl17_806
| ~ spl17_248
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f3674,f3633,f3318,f10435]) ).
fof(f10435,plain,
( spl17_806
<=> ! [X0,X3,X2,X1] :
( is_fun_pname_bool(sK10(image_pname_a(X0,X1),X2,X3))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| is_pname(sK16(X0,image_pname_a(X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_806])]) ).
fof(f3633,plain,
( spl17_294
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK10(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,[spl17_294])]) ).
fof(f3674,plain,
( ! [X2,X3,X0,X1] :
( is_fun_pname_bool(sK10(image_pname_a(X0,X1),X2,X3))
| ~ is_fun_a_bool(image_pname_a(X0,X1))
| is_pname(sK16(X0,image_pname_a(X2,X3),X1)) )
| ~ spl17_248
| ~ spl17_294 ),
inference(resolution,[],[f3634,f3319]) ).
fof(f3634,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| is_fun_pname_bool(sK10(X0,X1,X2))
| ~ is_fun_a_bool(X0) )
| ~ spl17_294 ),
inference(avatar_component_clause,[],[f3633]) ).
fof(f10433,plain,
( spl17_805
| ~ spl17_226
| ~ spl17_247 ),
inference(avatar_split_clause,[],[f3363,f3314,f3167,f10431]) ).
fof(f10431,plain,
( spl17_805
<=> ! [X0,X3,X2,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_805])]) ).
fof(f3167,plain,
( spl17_226
<=> ! [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,[spl17_226])]) ).
fof(f3314,plain,
( spl17_247
<=> ! [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,[spl17_247])]) ).
fof(f3363,plain,
( ! [X2,X3,X0,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1))
| ~ spl17_226
| ~ spl17_247 ),
inference(superposition,[],[f3315,f3168]) ).
fof(f3168,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)
| ~ spl17_226 ),
inference(avatar_component_clause,[],[f3167]) ).
fof(f3315,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))
| ~ spl17_247 ),
inference(avatar_component_clause,[],[f3314]) ).
fof(f10429,plain,
( spl17_804
| ~ spl17_224
| ~ spl17_247 ),
inference(avatar_split_clause,[],[f3362,f3314,f3158,f10427]) ).
fof(f10427,plain,
( spl17_804
<=> ! [X0,X3,X2,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_804])]) ).
fof(f3158,plain,
( spl17_224
<=> ! [X2,X0,X1] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_224])]) ).
fof(f3362,plain,
( ! [X2,X3,X0,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1))
| ~ spl17_224
| ~ spl17_247 ),
inference(superposition,[],[f3315,f3159]) ).
fof(f3159,plain,
( ! [X2,X0,X1] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1)
| ~ spl17_224 ),
inference(avatar_component_clause,[],[f3158]) ).
fof(f10425,plain,
( spl17_803
| ~ spl17_223
| ~ spl17_246 ),
inference(avatar_split_clause,[],[f3359,f3310,f3154,f10423]) ).
fof(f10423,plain,
( spl17_803
<=> ! [X0,X3,X2,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_803])]) ).
fof(f3154,plain,
( spl17_223
<=> ! [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,[spl17_223])]) ).
fof(f3310,plain,
( spl17_246
<=> ! [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,[spl17_246])]) ).
fof(f3359,plain,
( ! [X2,X3,X0,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1))
| ~ spl17_223
| ~ spl17_246 ),
inference(superposition,[],[f3311,f3155]) ).
fof(f3155,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)
| ~ spl17_223 ),
inference(avatar_component_clause,[],[f3154]) ).
fof(f3311,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))
| ~ spl17_246 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f10421,plain,
( spl17_802
| ~ spl17_222
| ~ spl17_246 ),
inference(avatar_split_clause,[],[f3358,f3310,f3150,f10419]) ).
fof(f10419,plain,
( spl17_802
<=> ! [X0,X3,X2,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_802])]) ).
fof(f3150,plain,
( spl17_222
<=> ! [X2,X0,X1] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_222])]) ).
fof(f3358,plain,
( ! [X2,X3,X0,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1))
| ~ spl17_222
| ~ spl17_246 ),
inference(superposition,[],[f3311,f3151]) ).
fof(f3151,plain,
( ! [X2,X0,X1] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1)
| ~ spl17_222 ),
inference(avatar_component_clause,[],[f3150]) ).
fof(f10417,plain,
( spl17_801
| ~ spl17_221
| ~ spl17_245 ),
inference(avatar_split_clause,[],[f3354,f3306,f3146,f10415]) ).
fof(f10415,plain,
( spl17_801
<=> ! [X0,X3,X2,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_801])]) ).
fof(f3146,plain,
( spl17_221
<=> ! [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,[spl17_221])]) ).
fof(f3306,plain,
( spl17_245
<=> ! [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,[spl17_245])]) ).
fof(f3354,plain,
( ! [X2,X3,X0,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1))
| ~ spl17_221
| ~ spl17_245 ),
inference(superposition,[],[f3307,f3147]) ).
fof(f3147,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)
| ~ spl17_221 ),
inference(avatar_component_clause,[],[f3146]) ).
fof(f3307,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))
| ~ spl17_245 ),
inference(avatar_component_clause,[],[f3306]) ).
fof(f10413,plain,
( spl17_800
| ~ spl17_220
| ~ spl17_245 ),
inference(avatar_split_clause,[],[f3353,f3306,f3142,f10411]) ).
fof(f10411,plain,
( spl17_800
<=> ! [X0,X3,X2,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_800])]) ).
fof(f3353,plain,
( ! [X2,X3,X0,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1))
| ~ spl17_220
| ~ spl17_245 ),
inference(superposition,[],[f3307,f3143]) ).
fof(f10409,plain,
( spl17_799
| ~ spl17_219
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3349,f3302,f3138,f10407]) ).
fof(f10407,plain,
( spl17_799
<=> ! [X0,X3,X2,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_799])]) ).
fof(f3302,plain,
( spl17_244
<=> ! [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,[spl17_244])]) ).
fof(f3349,plain,
( ! [X2,X3,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| ~ spl17_219
| ~ spl17_244 ),
inference(superposition,[],[f3303,f3139]) ).
fof(f3303,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))
| ~ spl17_244 ),
inference(avatar_component_clause,[],[f3302]) ).
fof(f10405,plain,
( spl17_798
| ~ spl17_218
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3348,f3302,f3134,f10403]) ).
fof(f10403,plain,
( spl17_798
<=> ! [X0,X3,X2,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_798])]) ).
fof(f3348,plain,
( ! [X2,X3,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| ~ spl17_218
| ~ spl17_244 ),
inference(superposition,[],[f3303,f3135]) ).
fof(f10401,plain,
( spl17_797
| ~ spl17_213
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3343,f3298,f3114,f10399]) ).
fof(f10399,plain,
( spl17_797
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_797])]) ).
fof(f3114,plain,
( spl17_213
<=> ! [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,[spl17_213])]) ).
fof(f3298,plain,
( spl17_243
<=> ! [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,[spl17_243])]) ).
fof(f3343,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1))
| ~ spl17_213
| ~ spl17_243 ),
inference(superposition,[],[f3299,f3115]) ).
fof(f3115,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)
| ~ spl17_213 ),
inference(avatar_component_clause,[],[f3114]) ).
fof(f3299,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))
| ~ spl17_243 ),
inference(avatar_component_clause,[],[f3298]) ).
fof(f10391,plain,
( spl17_796
| ~ spl17_212
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3342,f3298,f3110,f10389]) ).
fof(f10389,plain,
( spl17_796
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_796])]) ).
fof(f3110,plain,
( spl17_212
<=> ! [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,[spl17_212])]) ).
fof(f3342,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1))
| ~ spl17_212
| ~ spl17_243 ),
inference(superposition,[],[f3299,f3111]) ).
fof(f3111,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)
| ~ spl17_212 ),
inference(avatar_component_clause,[],[f3110]) ).
fof(f10387,plain,
( spl17_795
| ~ spl17_210
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3341,f3298,f3102,f10385]) ).
fof(f10385,plain,
( spl17_795
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_795])]) ).
fof(f3102,plain,
( spl17_210
<=> ! [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,[spl17_210])]) ).
fof(f3341,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X3,X2),hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1))
| ~ spl17_210
| ~ spl17_243 ),
inference(superposition,[],[f3299,f3103]) ).
fof(f3103,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)
| ~ spl17_210 ),
inference(avatar_component_clause,[],[f3102]) ).
fof(f10383,plain,
( spl17_794
| ~ spl17_214
| ~ spl17_242 ),
inference(avatar_split_clause,[],[f3337,f3294,f3118,f10381]) ).
fof(f10381,plain,
( spl17_794
<=> ! [X0,X3,X2,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X3,X2),hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_794])]) ).
fof(f3118,plain,
( spl17_214
<=> ! [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,[spl17_214])]) ).
fof(f3294,plain,
( spl17_242
<=> ! [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,[spl17_242])]) ).
fof(f3337,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X3,X2),hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1))
| ~ spl17_214
| ~ spl17_242 ),
inference(superposition,[],[f3295,f3119]) ).
fof(f3119,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)
| ~ spl17_214 ),
inference(avatar_component_clause,[],[f3118]) ).
fof(f3295,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))
| ~ spl17_242 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f10379,plain,
( spl17_793
| ~ spl17_211
| ~ spl17_242 ),
inference(avatar_split_clause,[],[f3336,f3294,f3106,f10377]) ).
fof(f10377,plain,
( spl17_793
<=> ! [X0,X3,X2,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X3,X2),hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_793])]) ).
fof(f3106,plain,
( spl17_211
<=> ! [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,[spl17_211])]) ).
fof(f3336,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X3,X2),hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1))
| ~ spl17_211
| ~ spl17_242 ),
inference(superposition,[],[f3295,f3107]) ).
fof(f3107,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)
| ~ spl17_211 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f10282,plain,
( spl17_792
| ~ spl17_95
| ~ spl17_433
| ~ spl17_589
| ~ spl17_791 ),
inference(avatar_split_clause,[],[f10278,f10274,f6721,f4836,f2513,f10280]) ).
fof(f10280,plain,
( spl17_792
<=> ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_792])]) ).
fof(f6721,plain,
( spl17_589
<=> ! [X0] : cOMBS_568398431l_bool(X0,u) = collect_pname(cOMBS_568398431l_bool(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_589])]) ).
fof(f10274,plain,
( spl17_791
<=> ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_791])]) ).
fof(f10278,plain,
( ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u))
| ~ spl17_95
| ~ spl17_433
| ~ spl17_589
| ~ spl17_791 ),
inference(forward_demodulation,[],[f10277,f6722]) ).
fof(f6722,plain,
( ! [X0] : cOMBS_568398431l_bool(X0,u) = collect_pname(cOMBS_568398431l_bool(X0,u))
| ~ spl17_589 ),
inference(avatar_component_clause,[],[f6721]) ).
fof(f10277,plain,
( ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn))),u)))
| ~ spl17_95
| ~ spl17_433
| ~ spl17_791 ),
inference(forward_demodulation,[],[f10275,f4905]) ).
fof(f10275,plain,
( ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u))))
| ~ spl17_791 ),
inference(avatar_component_clause,[],[f10274]) ).
fof(f10276,plain,
( spl17_791
| ~ spl17_44
| ~ spl17_430 ),
inference(avatar_split_clause,[],[f4825,f4802,f2278,f10274]) ).
fof(f4825,plain,
( ! [X0] : image_pname_a(X0,u) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u))))
| ~ spl17_44
| ~ spl17_430 ),
inference(resolution,[],[f4803,f2280]) ).
fof(f10272,plain,
( spl17_790
| ~ spl17_194
| ~ spl17_250
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4405,f4264,f3367,f3037,f10269]) ).
fof(f10269,plain,
( spl17_790
<=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_790])]) ).
fof(f4405,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,g))
| ~ spl17_194
| ~ spl17_250
| ~ spl17_368 ),
inference(forward_demodulation,[],[f4383,f3369]) ).
fof(f4383,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),hAPP_nat_nat(suc,na)) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)))
| ~ spl17_194
| ~ spl17_368 ),
inference(resolution,[],[f4265,f3039]) ).
fof(f10267,plain,
( spl17_789
| ~ spl17_44
| ~ spl17_757 ),
inference(avatar_split_clause,[],[f9748,f9200,f2278,f10265]) ).
fof(f9200,plain,
( spl17_757
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| is_pname(sK5(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_757])]) ).
fof(f9748,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),X0))
| is_pname(sK5(X0,u)) )
| ~ spl17_44
| ~ spl17_757 ),
inference(resolution,[],[f9201,f2280]) ).
fof(f9201,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))
| is_pname(sK5(X1,X2)) )
| ~ spl17_757 ),
inference(avatar_component_clause,[],[f9200]) ).
fof(f10263,plain,
( spl17_788
| ~ spl17_194
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4206,f4063,f3037,f10261]) ).
fof(f10261,plain,
( spl17_788
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,na))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_788])]) ).
fof(f4206,plain,
( ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,na))) )
| ~ spl17_194
| ~ spl17_353 ),
inference(resolution,[],[f4064,f3039]) ).
fof(f9959,plain,
( spl17_787
| ~ spl17_338
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4925,f4840,f3981,f9957]) ).
fof(f9957,plain,
( spl17_787
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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,[spl17_787])]) ).
fof(f4925,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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))))
| ~ spl17_338
| ~ spl17_434 ),
inference(superposition,[],[f3982,f4841]) ).
fof(f9955,plain,
( spl17_786
| ~ spl17_341
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4908,f4836,f3993,f9953]) ).
fof(f9953,plain,
( spl17_786
<=> ! [X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))
| ~ is_fun_pname_bool(collect_pname(X1))
| ~ is_pname(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_786])]) ).
fof(f4908,plain,
( ! [X0,X1] :
( is_fun_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))
| ~ is_fun_pname_bool(collect_pname(X1))
| ~ is_pname(X0) )
| ~ spl17_341
| ~ spl17_433 ),
inference(superposition,[],[f3994,f4837]) ).
fof(f9951,plain,
( spl17_785
| ~ spl17_340
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4907,f4836,f3989,f9949]) ).
fof(f9949,plain,
( spl17_785
<=> ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_785])]) ).
fof(f4907,plain,
( ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(X1)),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ spl17_340
| ~ spl17_433 ),
inference(superposition,[],[f3990,f4837]) ).
fof(f9947,plain,
( spl17_784
| ~ spl17_342
| ~ spl17_432 ),
inference(avatar_split_clause,[],[f4892,f4832,f3997,f9945]) ).
fof(f9945,plain,
( spl17_784
<=> ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))
| ~ is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_784])]) ).
fof(f4892,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)))
| ~ is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun_a_bool(X0) )
| ~ spl17_342
| ~ spl17_432 ),
inference(superposition,[],[f3998,f4833]) ).
fof(f9943,plain,
( spl17_783
| ~ spl17_343
| ~ spl17_431 ),
inference(avatar_split_clause,[],[f4880,f4828,f4001,f9941]) ).
fof(f9941,plain,
( spl17_783
<=> ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))
| ~ is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_783])]) ).
fof(f4880,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)))
| ~ is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun_pname_bool(X0) )
| ~ spl17_343
| ~ spl17_431 ),
inference(superposition,[],[f4002,f4829]) ).
fof(f9868,plain,
( spl17_782
| ~ spl17_11
| ~ spl17_423
| ~ spl17_781 ),
inference(avatar_split_clause,[],[f9862,f9859,f4694,f2141,f9866]) ).
fof(f9866,plain,
( spl17_782
<=> ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = X1
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_782])]) ).
fof(f9859,plain,
( spl17_781
<=> ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_781])]) ).
fof(f9862,plain,
( ! [X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1) = X1
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_781 ),
inference(forward_demodulation,[],[f9860,f4760]) ).
fof(f9860,plain,
( ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_781 ),
inference(avatar_component_clause,[],[f9859]) ).
fof(f9861,plain,
( spl17_781
| ~ spl17_166
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f4487,f4361,f2819,f9859]) ).
fof(f4487,plain,
( ! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_166
| ~ spl17_390 ),
inference(resolution,[],[f4362,f2820]) ).
fof(f9857,plain,
( spl17_780
| ~ spl17_168
| ~ spl17_381 ),
inference(avatar_split_clause,[],[f4466,f4318,f2827,f9855]) ).
fof(f9855,plain,
( spl17_780
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| ~ hBOOL(hAPP_a_bool(X2,hAPP_pname_a(X0,sK16(X0,X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_780])]) ).
fof(f4466,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| ~ hBOOL(hAPP_a_bool(X2,hAPP_pname_a(X0,sK16(X0,X2,X1)))) )
| ~ spl17_168
| ~ spl17_381 ),
inference(resolution,[],[f4319,f2828]) ).
fof(f9853,plain,
( spl17_779
| ~ spl17_162
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f4458,f4310,f2803,f9851]) ).
fof(f9851,plain,
( spl17_779
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_779])]) ).
fof(f4458,plain,
( ! [X2,X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| is_a(sK4(image_pname_a(X0,X1),X2)) )
| ~ spl17_162
| ~ spl17_379 ),
inference(resolution,[],[f4311,f2804]) ).
fof(f9849,plain,
( spl17_778
| ~ spl17_52
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f4457,f4310,f2311,f9847]) ).
fof(f9847,plain,
( spl17_778
<=> ! [X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_778])]) ).
fof(f4457,plain,
( ! [X0,X1] :
( is_fun_pname_bool(sK9(X0,X1,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_52
| ~ spl17_379 ),
inference(resolution,[],[f4311,f2312]) ).
fof(f9845,plain,
( spl17_777
| ~ spl17_169
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f4456,f4305,f2831,f9843]) ).
fof(f9843,plain,
( spl17_777
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0)
| hBOOL(hAPP_pname_bool(X2,sK8(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_777])]) ).
fof(f4456,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0)
| hBOOL(hAPP_pname_bool(X2,sK8(X0,X1,X2))) )
| ~ spl17_169
| ~ spl17_378 ),
inference(resolution,[],[f4306,f2832]) ).
fof(f9841,plain,
( spl17_776
| ~ spl17_169
| ~ spl17_377 ),
inference(avatar_split_clause,[],[f4455,f4301,f2831,f9839]) ).
fof(f9839,plain,
( spl17_776
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0)
| hBOOL(hAPP_pname_bool(X2,sK7(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_776])]) ).
fof(f4455,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ~ is_a(X0)
| hBOOL(hAPP_pname_bool(X2,sK7(X0,X1,X2))) )
| ~ spl17_169
| ~ spl17_377 ),
inference(resolution,[],[f4302,f2832]) ).
fof(f9837,plain,
( spl17_775
| ~ spl17_113
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f4441,f4297,f2605,f9835]) ).
fof(f9835,plain,
( spl17_775
<=> ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_775])]) ).
fof(f4441,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2)),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)))
| ~ spl17_113
| ~ spl17_376 ),
inference(superposition,[],[f2606,f4298]) ).
fof(f9833,plain,
( spl17_774
| ~ spl17_164
| ~ spl17_371 ),
inference(avatar_split_clause,[],[f4426,f4277,f2811,f9831]) ).
fof(f9831,plain,
( spl17_774
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0)
| is_pname(sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_774])]) ).
fof(f4426,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0)
| is_pname(sK5(X0,X1)) )
| ~ spl17_164
| ~ spl17_371 ),
inference(resolution,[],[f4278,f2812]) ).
fof(f9829,plain,
( spl17_773
| ~ spl17_162
| ~ spl17_370 ),
inference(avatar_split_clause,[],[f4419,f4273,f2803,f9827]) ).
fof(f9827,plain,
( spl17_773
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0)
| is_a(sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_773])]) ).
fof(f4419,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0)
| is_a(sK4(X0,X1)) )
| ~ spl17_162
| ~ spl17_370 ),
inference(resolution,[],[f4274,f2804]) ).
fof(f9825,plain,
( spl17_772
| ~ spl17_205
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4016,f3969,f3082,f9823]) ).
fof(f9823,plain,
( spl17_772
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,sK1(X1))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_772])]) ).
fof(f3082,plain,
( spl17_205
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_205])]) ).
fof(f4016,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,sK1(X1))),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_205
| ~ spl17_335 ),
inference(resolution,[],[f3970,f3083]) ).
fof(f3083,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_205 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f9818,plain,
( spl17_771
| ~ spl17_294
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3947,f3807,f3633,f9816]) ).
fof(f9816,plain,
( spl17_771
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| is_fun_pname_bool(sK10(image_pname_a(X2,X0),X2,X1))
| ~ is_fun_a_bool(image_pname_a(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_771])]) ).
fof(f3947,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| is_fun_pname_bool(sK10(image_pname_a(X2,X0),X2,X1))
| ~ is_fun_a_bool(image_pname_a(X2,X0)) )
| ~ spl17_294
| ~ spl17_328 ),
inference(resolution,[],[f3808,f3634]) ).
fof(f9814,plain,
( spl17_770
| ~ spl17_292
| ~ spl17_327 ),
inference(avatar_split_clause,[],[f3944,f3803,f3625,f9812]) ).
fof(f9812,plain,
( spl17_770
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK7(hAPP_pname_a(X2,X0),X2,X1))
| ~ is_a(hAPP_pname_a(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_770])]) ).
fof(f3944,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK7(hAPP_pname_a(X2,X0),X2,X1))
| ~ is_a(hAPP_pname_a(X2,X0)) )
| ~ spl17_292
| ~ spl17_327 ),
inference(resolution,[],[f3804,f3626]) ).
fof(f9810,plain,
( spl17_769
| ~ spl17_293
| ~ spl17_327 ),
inference(avatar_split_clause,[],[f3943,f3803,f3629,f9808]) ).
fof(f9808,plain,
( spl17_769
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK8(hAPP_pname_a(X2,X0),X2,X1))
| ~ is_a(hAPP_pname_a(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_769])]) ).
fof(f3943,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| is_pname(sK8(hAPP_pname_a(X2,X0),X2,X1))
| ~ is_a(hAPP_pname_a(X2,X0)) )
| ~ spl17_293
| ~ spl17_327 ),
inference(resolution,[],[f3804,f3630]) ).
fof(f9806,plain,
( spl17_768
| ~ spl17_248
| ~ spl17_325 ),
inference(avatar_split_clause,[],[f3930,f3795,f3318,f9804]) ).
fof(f9804,plain,
( spl17_768
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| is_pname(sK16(X0,image_pname_a(X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_768])]) ).
fof(f3930,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| is_pname(sK16(X0,image_pname_a(X3,X2),X1)) )
| ~ spl17_248
| ~ spl17_325 ),
inference(resolution,[],[f3796,f3319]) ).
fof(f9802,plain,
( spl17_767
| ~ spl17_191
| ~ spl17_247 ),
inference(avatar_split_clause,[],[f3361,f3314,f2933,f9800]) ).
fof(f9800,plain,
( spl17_767
<=> ! [X0,X3,X2,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,cOMBB_307249310e_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_767])]) ).
fof(f2933,plain,
( spl17_191
<=> ! [X2,X0,X1] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_191])]) ).
fof(f3361,plain,
( ! [X2,X3,X0,X1] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X3,cOMBB_307249310e_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)))
| ~ spl17_191
| ~ spl17_247 ),
inference(superposition,[],[f3315,f2934]) ).
fof(f2934,plain,
( ! [X2,X0,X1] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2))
| ~ spl17_191 ),
inference(avatar_component_clause,[],[f2933]) ).
fof(f9798,plain,
( spl17_766
| ~ spl17_190
| ~ spl17_246 ),
inference(avatar_split_clause,[],[f3357,f3310,f2929,f9796]) ).
fof(f9796,plain,
( spl17_766
<=> ! [X0,X3,X2,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,cOMBB_2140588453a_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_766])]) ).
fof(f2929,plain,
( spl17_190
<=> ! [X2,X0,X1] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_190])]) ).
fof(f3357,plain,
( ! [X2,X3,X0,X1] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X3,cOMBB_2140588453a_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)))
| ~ spl17_190
| ~ spl17_246 ),
inference(superposition,[],[f3311,f2930]) ).
fof(f2930,plain,
( ! [X2,X0,X1] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2))
| ~ spl17_190 ),
inference(avatar_component_clause,[],[f2929]) ).
fof(f9794,plain,
( spl17_765
| ~ spl17_189
| ~ spl17_245 ),
inference(avatar_split_clause,[],[f3352,f3306,f2925,f9792]) ).
fof(f9792,plain,
( spl17_765
<=> ! [X0,X3,X2,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,cOMBB_238756964t_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_765])]) ).
fof(f3352,plain,
( ! [X2,X3,X0,X1] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X3,cOMBB_238756964t_bool(X0,X1)),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))
| ~ spl17_189
| ~ spl17_245 ),
inference(superposition,[],[f3307,f2926]) ).
fof(f9790,plain,
( spl17_764
| ~ spl17_188
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3347,f3302,f2921,f9788]) ).
fof(f9788,plain,
( spl17_764
<=> ! [X0,X3,X2,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,cOMBB_bool_bool_nat(X0,X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_764])]) ).
fof(f3347,plain,
( ! [X2,X3,X0,X1] : hAPP_nat_bool(cOMBS_nat_bool_bool(X3,cOMBB_bool_bool_nat(X0,X1)),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X3,X2),hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl17_188
| ~ spl17_244 ),
inference(superposition,[],[f3303,f2922]) ).
fof(f9782,plain,
( spl17_763
| ~ spl17_333
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4923,f4840,f3958,f9780]) ).
fof(f9780,plain,
( spl17_763
<=> ! [X0,X1] :
( is_fun_a_bool(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)))
| ~ is_fun_a_bool(collect_a(X1))
| ~ is_a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_763])]) ).
fof(f4923,plain,
( ! [X0,X1] :
( is_fun_a_bool(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)))
| ~ is_fun_a_bool(collect_a(X1))
| ~ is_a(X0) )
| ~ spl17_333
| ~ spl17_434 ),
inference(superposition,[],[f3959,f4841]) ).
fof(f9700,plain,
( ~ spl17_3
| spl17_762
| ~ spl17_571
| ~ spl17_671 ),
inference(avatar_split_clause,[],[f8260,f8237,f6422,f9697,f2103]) ).
fof(f9697,plain,
( spl17_762
<=> is_fun_pname_bool(sK10(g,mgt_call,sK9(mgt_call,u,g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_762])]) ).
fof(f8237,plain,
( spl17_671
<=> g = image_pname_a(mgt_call,sK9(mgt_call,u,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_671])]) ).
fof(f8260,plain,
( is_fun_pname_bool(sK10(g,mgt_call,sK9(mgt_call,u,g)))
| ~ is_fun_a_bool(g)
| ~ spl17_571
| ~ spl17_671 ),
inference(superposition,[],[f6423,f8239]) ).
fof(f8239,plain,
( g = image_pname_a(mgt_call,sK9(mgt_call,u,g))
| ~ spl17_671 ),
inference(avatar_component_clause,[],[f8237]) ).
fof(f9363,plain,
( ~ spl17_3
| spl17_761
| ~ spl17_485
| ~ spl17_571 ),
inference(avatar_split_clause,[],[f6465,f6422,f5367,f9360,f2103]) ).
fof(f9360,plain,
( spl17_761
<=> is_fun_pname_bool(sK10(g,mgt_call,sK10(g,mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_761])]) ).
fof(f5367,plain,
( spl17_485
<=> g = image_pname_a(mgt_call,sK10(g,mgt_call,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_485])]) ).
fof(f6465,plain,
( is_fun_pname_bool(sK10(g,mgt_call,sK10(g,mgt_call,u)))
| ~ is_fun_a_bool(g)
| ~ spl17_485
| ~ spl17_571 ),
inference(superposition,[],[f6423,f5369]) ).
fof(f5369,plain,
( g = image_pname_a(mgt_call,sK10(g,mgt_call,u))
| ~ spl17_485 ),
inference(avatar_component_clause,[],[f5367]) ).
fof(f9214,plain,
( spl17_760
| ~ spl17_337
| ~ spl17_434 ),
inference(avatar_split_clause,[],[f4924,f4840,f3977,f9212]) ).
fof(f9212,plain,
( spl17_760
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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,[spl17_760])]) ).
fof(f4924,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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))))
| ~ spl17_337
| ~ spl17_434 ),
inference(superposition,[],[f3978,f4841]) ).
fof(f9210,plain,
( spl17_759
| ~ spl17_339
| ~ spl17_433 ),
inference(avatar_split_clause,[],[f4906,f4836,f3985,f9208]) ).
fof(f9208,plain,
( spl17_759
<=> ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_759])]) ).
fof(f4906,plain,
( ! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1))))
| ~ spl17_339
| ~ spl17_433 ),
inference(superposition,[],[f3986,f4837]) ).
fof(f9206,plain,
( spl17_758
| ~ spl17_164
| ~ spl17_360 ),
inference(avatar_split_clause,[],[f4252,f4091,f2811,f9204]) ).
fof(f9204,plain,
( spl17_758
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| is_pname(sK5(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_758])]) ).
fof(f4252,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
| is_pname(sK5(X1,X2)) )
| ~ spl17_164
| ~ spl17_360 ),
inference(resolution,[],[f4092,f2812]) ).
fof(f9202,plain,
( spl17_757
| ~ spl17_164
| ~ spl17_359 ),
inference(avatar_split_clause,[],[f4249,f4087,f2811,f9200]) ).
fof(f4249,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),X2))
| is_pname(sK5(X1,X2)) )
| ~ spl17_164
| ~ spl17_359 ),
inference(resolution,[],[f4088,f2812]) ).
fof(f9198,plain,
( spl17_756
| ~ spl17_58
| ~ spl17_569 ),
inference(avatar_split_clause,[],[f6407,f6403,f2335,f9195]) ).
fof(f9195,plain,
( spl17_756
<=> sK9(mgt_call,u,g) = collect_pname(sK9(mgt_call,u,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_756])]) ).
fof(f6403,plain,
( spl17_569
<=> is_fun_pname_bool(sK9(mgt_call,u,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_569])]) ).
fof(f6407,plain,
( sK9(mgt_call,u,g) = collect_pname(sK9(mgt_call,u,g))
| ~ spl17_58
| ~ spl17_569 ),
inference(resolution,[],[f6405,f2336]) ).
fof(f6405,plain,
( is_fun_pname_bool(sK9(mgt_call,u,g))
| ~ spl17_569 ),
inference(avatar_component_clause,[],[f6403]) ).
fof(f9193,plain,
( spl17_755
| ~ spl17_162
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f4243,f4083,f2803,f9191]) ).
fof(f9191,plain,
( spl17_755
<=> ! [X2,X0,X1] :
( 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,X0),X2))
| is_a(sK4(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_755])]) ).
fof(f4243,plain,
( ! [X2,X0,X1] :
( 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,X0),X2))
| is_a(sK4(X1,X2)) )
| ~ spl17_162
| ~ spl17_358 ),
inference(resolution,[],[f4084,f2804]) ).
fof(f9189,plain,
( spl17_754
| ~ spl17_162
| ~ spl17_357 ),
inference(avatar_split_clause,[],[f4237,f4079,f2803,f9187]) ).
fof(f9187,plain,
( spl17_754
<=> ! [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),X2))
| is_a(sK4(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_754])]) ).
fof(f4237,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),X2))
| is_a(sK4(X1,X2)) )
| ~ spl17_162
| ~ spl17_357 ),
inference(resolution,[],[f4080,f2804]) ).
fof(f9185,plain,
( spl17_753
| ~ spl17_166
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f4226,f4067,f2819,f9183]) ).
fof(f9183,plain,
( spl17_753
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_753])]) ).
fof(f4226,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(X0,X2)) )
| ~ spl17_166
| ~ spl17_354 ),
inference(resolution,[],[f4068,f2820]) ).
fof(f9181,plain,
( spl17_752
| ~ spl17_162
| ~ spl17_349 ),
inference(avatar_split_clause,[],[f4126,f4047,f2803,f9179]) ).
fof(f9179,plain,
( spl17_752
<=> ! [X2,X0,X1] :
( image_pname_a(X0,sK10(X1,X0,X2)) = X1
| ~ is_fun_a_bool(X1)
| is_a(sK4(image_pname_a(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_752])]) ).
fof(f4126,plain,
( ! [X2,X0,X1] :
( image_pname_a(X0,sK10(X1,X0,X2)) = X1
| ~ is_fun_a_bool(X1)
| is_a(sK4(image_pname_a(X0,X2),X1)) )
| ~ spl17_162
| ~ spl17_349 ),
inference(resolution,[],[f4048,f2804]) ).
fof(f9177,plain,
( spl17_751
| ~ spl17_52
| ~ spl17_349 ),
inference(avatar_split_clause,[],[f4125,f4047,f2311,f9175]) ).
fof(f9175,plain,
( spl17_751
<=> ! [X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK10(image_pname_a(X0,X1),X0,X1))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_751])]) ).
fof(f4125,plain,
( ! [X0,X1] :
( image_pname_a(X0,X1) = image_pname_a(X0,sK10(image_pname_a(X0,X1),X0,X1))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_52
| ~ spl17_349 ),
inference(resolution,[],[f4048,f2312]) ).
fof(f9173,plain,
( spl17_750
| ~ spl17_168
| ~ spl17_348 ),
inference(avatar_split_clause,[],[f4123,f4043,f2827,f9171]) ).
fof(f9171,plain,
( spl17_750
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X0,sK8(X1,X0,X2)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_750])]) ).
fof(f4123,plain,
( ! [X2,X0,X1] :
( hAPP_pname_a(X0,sK8(X1,X0,X2)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X0,X2),X1)) )
| ~ spl17_168
| ~ spl17_348 ),
inference(resolution,[],[f4044,f2828]) ).
fof(f9169,plain,
( spl17_749
| ~ spl17_168
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f4120,f4039,f2827,f9167]) ).
fof(f9167,plain,
( spl17_749
<=> ! [X2,X0,X1] :
( hAPP_pname_a(X0,sK7(X1,X0,X2)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_749])]) ).
fof(f4120,plain,
( ! [X2,X0,X1] :
( hAPP_pname_a(X0,sK7(X1,X0,X2)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X0,X2),X1)) )
| ~ spl17_168
| ~ spl17_347 ),
inference(resolution,[],[f4040,f2828]) ).
fof(f9165,plain,
( spl17_748
| ~ spl17_169
| ~ spl17_346 ),
inference(avatar_split_clause,[],[f4118,f4035,f2831,f9163]) ).
fof(f9163,plain,
( spl17_748
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_pname_bool(X1,sK2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_748])]) ).
fof(f4118,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))
| hBOOL(hAPP_pname_bool(X1,sK2(X0,X1))) )
| ~ spl17_169
| ~ spl17_346 ),
inference(resolution,[],[f4036,f2832]) ).
fof(f9161,plain,
( spl17_747
| ~ spl17_177
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f4023,f3981,f2876,f9159]) ).
fof(f9159,plain,
( spl17_747
<=> ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(p(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)))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_747])]) ).
fof(f4023,plain,
( ! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(p(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)))),X1))
| ~ spl17_177
| ~ spl17_338 ),
inference(resolution,[],[f3982,f2877]) ).
fof(f9157,plain,
( spl17_746
| ~ spl17_325
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3946,f3807,f3795,f9155]) ).
fof(f9155,plain,
( spl17_746
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_746])]) ).
fof(f3946,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_325
| ~ spl17_328 ),
inference(resolution,[],[f3808,f3796]) ).
fof(f9153,plain,
( spl17_745
| ~ spl17_6
| ~ spl17_460 ),
inference(avatar_split_clause,[],[f5708,f5153,f2118,f9151]) ).
fof(f9151,plain,
( spl17_745
<=> ! [X0] : hAPP_a85458249l_bool(X0,undefined_a(x_a)) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,undefined_a(x_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_745])]) ).
fof(f5708,plain,
( ! [X0] : hAPP_a85458249l_bool(X0,undefined_a(x_a)) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,undefined_a(x_a)))
| ~ spl17_6
| ~ spl17_460 ),
inference(resolution,[],[f5154,f2120]) ).
fof(f9149,plain,
( spl17_744
| ~ spl17_206
| ~ spl17_323 ),
inference(avatar_split_clause,[],[f3916,f3787,f3086,f9147]) ).
fof(f9147,plain,
( spl17_744
<=> ! [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)),hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_744])]) ).
fof(f3916,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)),hAPP_nat_nat(suc,X0))) )
| ~ spl17_206
| ~ spl17_323 ),
inference(resolution,[],[f3788,f3087]) ).
fof(f9145,plain,
( spl17_743
| ~ spl17_259
| ~ spl17_278 ),
inference(avatar_split_clause,[],[f3589,f3481,f3405,f9143]) ).
fof(f9143,plain,
( spl17_743
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_743])]) ).
fof(f3589,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) )
| ~ spl17_259
| ~ spl17_278 ),
inference(resolution,[],[f3482,f3406]) ).
fof(f9141,plain,
( spl17_742
| ~ spl17_259
| ~ spl17_260 ),
inference(avatar_split_clause,[],[f3548,f3409,f3405,f9139]) ).
fof(f9139,plain,
( spl17_742
<=> ! [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,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_742])]) ).
fof(f3548,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,hAPP_nat_nat(suc,X0)),X1)) )
| ~ spl17_259
| ~ spl17_260 ),
inference(resolution,[],[f3410,f3406]) ).
fof(f9137,plain,
( spl17_741
| ~ spl17_183
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f3265,f3167,f2901,f9135]) ).
fof(f9135,plain,
( spl17_741
<=> ! [X0,X3,X2,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)),X2) = hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f434788991l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_741])]) ).
fof(f2901,plain,
( spl17_183
<=> ! [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,[spl17_183])]) ).
fof(f3265,plain,
( ! [X2,X3,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)),X2) = hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f434788991l_bool(X0,X2)),X1)
| ~ spl17_183
| ~ spl17_226 ),
inference(forward_demodulation,[],[f3263,f2902]) ).
fof(f2902,plain,
( ! [X2,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2))
| ~ spl17_183 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f3263,plain,
( ! [X2,X3,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1))
| ~ spl17_183
| ~ spl17_226 ),
inference(superposition,[],[f2902,f3168]) ).
fof(f9133,plain,
( spl17_740
| ~ spl17_183
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f3261,f3158,f2901,f9131]) ).
fof(f9131,plain,
( spl17_740
<=> ! [X0,X3,X2,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_740])]) ).
fof(f3261,plain,
( ! [X2,X3,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1))
| ~ spl17_183
| ~ spl17_224 ),
inference(superposition,[],[f2902,f3159]) ).
fof(f9129,plain,
( spl17_739
| ~ spl17_182
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f3260,f3154,f2897,f9127]) ).
fof(f9127,plain,
( spl17_739
<=> ! [X0,X3,X2,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)),X2) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f1631501043l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_739])]) ).
fof(f2897,plain,
( spl17_182
<=> ! [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,[spl17_182])]) ).
fof(f3260,plain,
( ! [X2,X3,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)),X2) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f1631501043l_bool(X0,X2)),X1)
| ~ spl17_182
| ~ spl17_223 ),
inference(forward_demodulation,[],[f3258,f2898]) ).
fof(f2898,plain,
( ! [X2,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2))
| ~ spl17_182 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f3258,plain,
( ! [X2,X3,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1))
| ~ spl17_182
| ~ spl17_223 ),
inference(superposition,[],[f2898,f3155]) ).
fof(f9125,plain,
( spl17_738
| ~ spl17_182
| ~ spl17_222 ),
inference(avatar_split_clause,[],[f3256,f3150,f2897,f9123]) ).
fof(f9123,plain,
( spl17_738
<=> ! [X0,X3,X2,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_738])]) ).
fof(f3256,plain,
( ! [X2,X3,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1))
| ~ spl17_182
| ~ spl17_222 ),
inference(superposition,[],[f2898,f3151]) ).
fof(f9121,plain,
( spl17_737
| ~ spl17_181
| ~ spl17_221 ),
inference(avatar_split_clause,[],[f3255,f3146,f2893,f9119]) ).
fof(f9119,plain,
( spl17_737
<=> ! [X0,X3,X2,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1)),X2) = hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f103356543l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_737])]) ).
fof(f2893,plain,
( spl17_181
<=> ! [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,[spl17_181])]) ).
fof(f3255,plain,
( ! [X2,X3,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1)),X2) = hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f103356543l_bool(X0,X2)),X1)
| ~ spl17_181
| ~ spl17_221 ),
inference(forward_demodulation,[],[f3253,f2894]) ).
fof(f2894,plain,
( ! [X2,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2))
| ~ spl17_181 ),
inference(avatar_component_clause,[],[f2893]) ).
fof(f3253,plain,
( ! [X2,X3,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1))
| ~ spl17_181
| ~ spl17_221 ),
inference(superposition,[],[f2894,f3147]) ).
fof(f9117,plain,
( spl17_736
| ~ spl17_181
| ~ spl17_220 ),
inference(avatar_split_clause,[],[f3251,f3142,f2893,f9115]) ).
fof(f9115,plain,
( spl17_736
<=> ! [X0,X3,X2,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_736])]) ).
fof(f3251,plain,
( ! [X2,X3,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1))
| ~ spl17_181
| ~ spl17_220 ),
inference(superposition,[],[f2894,f3143]) ).
fof(f9113,plain,
( spl17_735
| ~ spl17_180
| ~ spl17_219 ),
inference(avatar_split_clause,[],[f3250,f3138,f2889,f9111]) ).
fof(f9111,plain,
( spl17_735
<=> ! [X0,X3,X2,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)),X2) = hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_n1699378549t_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_735])]) ).
fof(f2889,plain,
( spl17_180
<=> ! [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,[spl17_180])]) ).
fof(f3250,plain,
( ! [X2,X3,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)),X2) = hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_n1699378549t_bool(X0,X2)),X1)
| ~ spl17_180
| ~ spl17_219 ),
inference(forward_demodulation,[],[f3248,f2890]) ).
fof(f2890,plain,
( ! [X2,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2))
| ~ spl17_180 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f3248,plain,
( ! [X2,X3,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
| ~ spl17_180
| ~ spl17_219 ),
inference(superposition,[],[f2890,f3139]) ).
fof(f9109,plain,
( spl17_734
| ~ spl17_7
| ~ spl17_453 ),
inference(avatar_split_clause,[],[f5508,f5043,f2123,f9107]) ).
fof(f9107,plain,
( spl17_734
<=> ! [X0] : hAPP_p338031245l_bool(X0,undefined_pname(pname)) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,undefined_pname(pname))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_734])]) ).
fof(f5043,plain,
( spl17_453
<=> ! [X0,X1] :
( hAPP_p338031245l_bool(X0,X1) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_453])]) ).
fof(f5508,plain,
( ! [X0] : hAPP_p338031245l_bool(X0,undefined_pname(pname)) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,undefined_pname(pname)))
| ~ spl17_7
| ~ spl17_453 ),
inference(resolution,[],[f5044,f2125]) ).
fof(f5044,plain,
( ! [X0,X1] :
( ~ is_pname(X1)
| hAPP_p338031245l_bool(X0,X1) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1)) )
| ~ spl17_453 ),
inference(avatar_component_clause,[],[f5043]) ).
fof(f9105,plain,
( spl17_733
| ~ spl17_180
| ~ spl17_181
| ~ spl17_218 ),
inference(avatar_split_clause,[],[f3246,f3134,f2893,f2889,f9103]) ).
fof(f9103,plain,
( spl17_733
<=> ! [X0,X3,X2,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)),X2) = hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_n215258509l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_733])]) ).
fof(f3246,plain,
( ! [X2,X3,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)),X2) = hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,hAPP_n215258509l_bool(X0,X2)),X1)
| ~ spl17_180
| ~ spl17_181
| ~ spl17_218 ),
inference(forward_demodulation,[],[f3244,f2894]) ).
fof(f3244,plain,
( ! [X2,X3,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1))
| ~ spl17_180
| ~ spl17_218 ),
inference(superposition,[],[f2890,f3135]) ).
fof(f9101,plain,
( spl17_732
| ~ spl17_179
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f3238,f3118,f2885,f9099]) ).
fof(f9099,plain,
( spl17_732
<=> ! [X0,X3,X2,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_a_fun_a_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_732])]) ).
fof(f2885,plain,
( spl17_179
<=> ! [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,[spl17_179])]) ).
fof(f3238,plain,
( ! [X2,X3,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_a_fun_a_bool(X0,X2)),X1)
| ~ spl17_179
| ~ spl17_214 ),
inference(forward_demodulation,[],[f3235,f2886]) ).
fof(f2886,plain,
( ! [X2,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2))
| ~ spl17_179 ),
inference(avatar_component_clause,[],[f2885]) ).
fof(f3235,plain,
( ! [X2,X3,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1))
| ~ spl17_179
| ~ spl17_214 ),
inference(superposition,[],[f2886,f3119]) ).
fof(f9097,plain,
( spl17_731
| ~ spl17_187
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f3237,f3118,f2917,f9095]) ).
fof(f9095,plain,
( spl17_731
<=> ! [X0,X3,X2,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_a_fun_a_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_731])]) ).
fof(f2917,plain,
( spl17_187
<=> ! [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,[spl17_187])]) ).
fof(f3237,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_a_fun_a_bool(X0,X2)),X1)
| ~ spl17_187
| ~ spl17_214 ),
inference(forward_demodulation,[],[f3234,f2918]) ).
fof(f2918,plain,
( ! [X2,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2))
| ~ spl17_187 ),
inference(avatar_component_clause,[],[f2917]) ).
fof(f3234,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1))
| ~ spl17_187
| ~ spl17_214 ),
inference(superposition,[],[f2918,f3119]) ).
fof(f9093,plain,
( spl17_730
| ~ spl17_185
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f3233,f3118,f2909,f9091]) ).
fof(f9091,plain,
( spl17_730
<=> ! [X0,X3,X2,X1] : hAPP_a_bool(hAPP_a_fun_a_bool(X0,X3),hAPP_pname_a(X1,X2)) = hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(X0),X1),X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_730])]) ).
fof(f3233,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(hAPP_a_fun_a_bool(X0,X3),hAPP_pname_a(X1,X2)) = hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(X0),X1),X2),X3)
| ~ spl17_185
| ~ spl17_214 ),
inference(superposition,[],[f3119,f2910]) ).
fof(f9089,plain,
( spl17_729
| ~ spl17_184
| ~ spl17_213 ),
inference(avatar_split_clause,[],[f3232,f3114,f2905,f9087]) ).
fof(f9087,plain,
( spl17_729
<=> ! [X0,X3,X2,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_p61793385e_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_729])]) ).
fof(f2905,plain,
( spl17_184
<=> ! [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,[spl17_184])]) ).
fof(f3232,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_p61793385e_bool(X0,X2)),X1)
| ~ spl17_184
| ~ spl17_213 ),
inference(forward_demodulation,[],[f3229,f2906]) ).
fof(f2906,plain,
( ! [X2,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2))
| ~ spl17_184 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f3229,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1))
| ~ spl17_184
| ~ spl17_213 ),
inference(superposition,[],[f2906,f3115]) ).
fof(f9085,plain,
( spl17_728
| ~ spl17_186
| ~ spl17_213 ),
inference(avatar_split_clause,[],[f3231,f3114,f2913,f9083]) ).
fof(f9083,plain,
( spl17_728
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_p61793385e_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_728])]) ).
fof(f2913,plain,
( spl17_186
<=> ! [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,[spl17_186])]) ).
fof(f3231,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_p61793385e_bool(X0,X2)),X1)
| ~ spl17_186
| ~ spl17_213 ),
inference(forward_demodulation,[],[f3228,f2914]) ).
fof(f2914,plain,
( ! [X2,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2))
| ~ spl17_186 ),
inference(avatar_component_clause,[],[f2913]) ).
fof(f3228,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1))
| ~ spl17_186
| ~ spl17_213 ),
inference(superposition,[],[f2914,f3115]) ).
fof(f9081,plain,
( spl17_727
| ~ spl17_183
| ~ spl17_184
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f3227,f3110,f2905,f2901,f9079]) ).
fof(f9079,plain,
( spl17_727
<=> ! [X0,X3,X2,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_p338031245l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_727])]) ).
fof(f3227,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,hAPP_p338031245l_bool(X0,X2)),X1)
| ~ spl17_183
| ~ spl17_184
| ~ spl17_212 ),
inference(forward_demodulation,[],[f3225,f2902]) ).
fof(f3225,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1))
| ~ spl17_184
| ~ spl17_212 ),
inference(superposition,[],[f2906,f3111]) ).
fof(f9077,plain,
( spl17_726
| ~ spl17_186
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f3224,f3110,f2913,f9075]) ).
fof(f9075,plain,
( spl17_726
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_726])]) ).
fof(f3224,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1))
| ~ spl17_186
| ~ spl17_212 ),
inference(superposition,[],[f2914,f3111]) ).
fof(f9073,plain,
( spl17_725
| ~ spl17_179
| ~ spl17_182
| ~ spl17_211 ),
inference(avatar_split_clause,[],[f3223,f3106,f2897,f2885,f9071]) ).
fof(f9071,plain,
( spl17_725
<=> ! [X0,X3,X2,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_a85458249l_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_725])]) ).
fof(f3223,plain,
( ! [X2,X3,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,hAPP_a85458249l_bool(X0,X2)),X1)
| ~ spl17_179
| ~ spl17_182
| ~ spl17_211 ),
inference(forward_demodulation,[],[f3221,f2898]) ).
fof(f3221,plain,
( ! [X2,X3,X0,X1] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1))
| ~ spl17_179
| ~ spl17_211 ),
inference(superposition,[],[f2886,f3107]) ).
fof(f9069,plain,
( spl17_724
| ~ spl17_187
| ~ spl17_211 ),
inference(avatar_split_clause,[],[f3220,f3106,f2917,f9067]) ).
fof(f9067,plain,
( spl17_724
<=> ! [X0,X3,X2,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_724])]) ).
fof(f3220,plain,
( ! [X2,X3,X0,X1] : hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1))
| ~ spl17_187
| ~ spl17_211 ),
inference(superposition,[],[f2918,f3107]) ).
fof(f9065,plain,
( spl17_723
| ~ spl17_58
| ~ spl17_309 ),
inference(avatar_split_clause,[],[f3773,f3729,f2335,f9062]) ).
fof(f9062,plain,
( spl17_723
<=> sK10(g,mgt_call,u) = collect_pname(sK10(g,mgt_call,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_723])]) ).
fof(f3729,plain,
( spl17_309
<=> is_fun_pname_bool(sK10(g,mgt_call,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_309])]) ).
fof(f3773,plain,
( sK10(g,mgt_call,u) = collect_pname(sK10(g,mgt_call,u))
| ~ spl17_58
| ~ spl17_309 ),
inference(resolution,[],[f3731,f2336]) ).
fof(f3731,plain,
( is_fun_pname_bool(sK10(g,mgt_call,u))
| ~ spl17_309 ),
inference(avatar_component_clause,[],[f3729]) ).
fof(f9060,plain,
( spl17_722
| ~ spl17_179
| ~ spl17_184
| ~ spl17_210 ),
inference(avatar_split_clause,[],[f3219,f3102,f2905,f2885,f9058]) ).
fof(f9058,plain,
( spl17_722
<=> ! [X0,X3,X2,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_p1534023578a_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_722])]) ).
fof(f3219,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X3,hAPP_p1534023578a_bool(X0,X2)),X1)
| ~ spl17_179
| ~ spl17_184
| ~ spl17_210 ),
inference(forward_demodulation,[],[f3216,f2886]) ).
fof(f3216,plain,
( ! [X2,X3,X0,X1] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1))
| ~ spl17_184
| ~ spl17_210 ),
inference(superposition,[],[f2906,f3103]) ).
fof(f9056,plain,
( spl17_721
| ~ spl17_186
| ~ spl17_187
| ~ spl17_210 ),
inference(avatar_split_clause,[],[f3218,f3102,f2917,f2913,f9054]) ).
fof(f9054,plain,
( spl17_721
<=> ! [X0,X3,X2,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_p1534023578a_bool(X0,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_721])]) ).
fof(f3218,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_a_bool(cOMBB_bool_bool_a(X3,hAPP_p1534023578a_bool(X0,X2)),X1)
| ~ spl17_186
| ~ spl17_187
| ~ spl17_210 ),
inference(forward_demodulation,[],[f3215,f2918]) ).
fof(f3215,plain,
( ! [X2,X3,X0,X1] : hAPP_pname_bool(cOMBB_647938656_pname(X3,hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)),X2) = hAPP_bool_bool(X3,hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1))
| ~ spl17_186
| ~ spl17_210 ),
inference(superposition,[],[f2914,f3103]) ).
fof(f9021,plain,
( ~ spl17_4
| spl17_720
| ~ spl17_44
| ~ spl17_402 ),
inference(avatar_split_clause,[],[f4616,f4575,f2278,f9018,f2108]) ).
fof(f9018,plain,
( spl17_720
<=> u = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_720])]) ).
fof(f4616,plain,
( u = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),u)))
| ~ is_fun_pname_bool(u)
| ~ spl17_44
| ~ spl17_402 ),
inference(resolution,[],[f4576,f2280]) ).
fof(f8710,plain,
( spl17_719
| ~ spl17_113
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f4188,f4063,f2605,f8708]) ).
fof(f8708,plain,
( spl17_719
<=> ! [X2,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(minus_minus_nat(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_719])]) ).
fof(f4188,plain,
( ! [X2,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(minus_minus_nat(X1),X2))) )
| ~ spl17_113
| ~ spl17_353 ),
inference(resolution,[],[f4064,f2606]) ).
fof(f8706,plain,
( spl17_718
| ~ spl17_169
| ~ spl17_339 ),
inference(avatar_split_clause,[],[f4025,f3985,f2831,f8704]) ).
fof(f8704,plain,
( spl17_718
<=> ! [X0,X1] : hBOOL(hAPP_pname_bool(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))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_718])]) ).
fof(f4025,plain,
( ! [X0,X1] : hBOOL(hAPP_pname_bool(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))),X0))
| ~ spl17_169
| ~ spl17_339 ),
inference(resolution,[],[f3986,f2832]) ).
fof(f8700,plain,
( spl17_717
| ~ spl17_167
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f4020,f3977,f2823,f8698]) ).
fof(f8698,plain,
( spl17_717
<=> ! [X0,X1] : hBOOL(hAPP_a_bool(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))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_717])]) ).
fof(f4020,plain,
( ! [X0,X1] : hBOOL(hAPP_a_bool(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))),X0))
| ~ spl17_167
| ~ spl17_337 ),
inference(resolution,[],[f3978,f2824]) ).
fof(f8696,plain,
( spl17_716
| ~ spl17_169
| ~ spl17_336 ),
inference(avatar_split_clause,[],[f4019,f3973,f2831,f8694]) ).
fof(f4019,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),X2))
| hBOOL(hAPP_pname_bool(X1,sK16(X0,X2,X1))) )
| ~ spl17_169
| ~ spl17_336 ),
inference(resolution,[],[f3974,f2832]) ).
fof(f8692,plain,
( spl17_715
| ~ spl17_177
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3949,f3807,f2876,f8690]) ).
fof(f8690,plain,
( spl17_715
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(X2,X1)),image_pname_a(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_715])]) ).
fof(f3949,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(X2,X1)),image_pname_a(X2,X0))) )
| ~ spl17_177
| ~ spl17_328 ),
inference(resolution,[],[f3808,f2877]) ).
fof(f8688,plain,
( spl17_714
| ~ spl17_113
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f3665,f3621,f2605,f8686]) ).
fof(f8686,plain,
( spl17_714
<=> ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_714])]) ).
fof(f3665,plain,
( ! [X2,X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ spl17_113
| ~ spl17_291 ),
inference(superposition,[],[f2606,f3622]) ).
fof(f8684,plain,
( spl17_713
| ~ spl17_113
| ~ spl17_289 ),
inference(avatar_split_clause,[],[f3650,f3613,f2605,f8682]) ).
fof(f8682,plain,
( spl17_713
<=> ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_713])]) ).
fof(f3650,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),X1) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(minus_minus_nat(X0),X1))) )
| ~ spl17_113
| ~ spl17_289 ),
inference(resolution,[],[f3614,f2606]) ).
fof(f8680,plain,
( spl17_712
| ~ spl17_206
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3643,f3609,f3086,f8678]) ).
fof(f3643,plain,
( ! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1)) = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_206
| ~ spl17_288 ),
inference(resolution,[],[f3610,f3087]) ).
fof(f8676,plain,
( spl17_711
| ~ spl17_113
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3642,f3609,f2605,f8674]) ).
fof(f8674,plain,
( spl17_711
<=> ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_711])]) ).
fof(f3642,plain,
( ! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ spl17_113
| ~ spl17_288 ),
inference(resolution,[],[f3610,f2606]) ).
fof(f8672,plain,
( spl17_710
| ~ spl17_248
| ~ spl17_256 ),
inference(avatar_split_clause,[],[f3539,f3393,f3318,f8670]) ).
fof(f8670,plain,
( spl17_710
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| is_pname(sK16(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_710])]) ).
fof(f3539,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| is_pname(sK16(X0,X2,X1)) )
| ~ spl17_248
| ~ spl17_256 ),
inference(resolution,[],[f3394,f3319]) ).
fof(f8668,plain,
( spl17_709
| ~ spl17_183
| ~ spl17_191 ),
inference(avatar_split_clause,[],[f3034,f2933,f2901,f8666]) ).
fof(f8666,plain,
( spl17_709
<=> ! [X0,X3,X2,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,cOMBB_307249310e_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_709])]) ).
fof(f3034,plain,
( ! [X2,X3,X0,X1] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X3,cOMBB_307249310e_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)))
| ~ spl17_183
| ~ spl17_191 ),
inference(superposition,[],[f2902,f2934]) ).
fof(f8664,plain,
( spl17_708
| ~ spl17_182
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f3032,f2929,f2897,f8662]) ).
fof(f8662,plain,
( spl17_708
<=> ! [X0,X3,X2,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,cOMBB_2140588453a_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_708])]) ).
fof(f3032,plain,
( ! [X2,X3,X0,X1] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X3,cOMBB_2140588453a_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)))
| ~ spl17_182
| ~ spl17_190 ),
inference(superposition,[],[f2898,f2930]) ).
fof(f8660,plain,
( spl17_707
| ~ spl17_460
| ~ spl17_695 ),
inference(avatar_split_clause,[],[f8465,f8422,f5153,f8658]) ).
fof(f8658,plain,
( spl17_707
<=> ! [X0] : hAPP_a85458249l_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_707])]) ).
fof(f8422,plain,
( spl17_695
<=> is_a(sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_695])]) ).
fof(f8465,plain,
( ! [X0] : hAPP_a85458249l_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))))
| ~ spl17_460
| ~ spl17_695 ),
inference(resolution,[],[f8424,f5154]) ).
fof(f8424,plain,
( is_a(sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))
| ~ spl17_695 ),
inference(avatar_component_clause,[],[f8422]) ).
fof(f8656,plain,
( spl17_706
| ~ spl17_181
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f3030,f2925,f2893,f8654]) ).
fof(f8654,plain,
( spl17_706
<=> ! [X0,X3,X2,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,cOMBB_238756964t_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_706])]) ).
fof(f3030,plain,
( ! [X2,X3,X0,X1] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X3,cOMBB_238756964t_bool(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))
| ~ spl17_181
| ~ spl17_189 ),
inference(superposition,[],[f2894,f2926]) ).
fof(f8652,plain,
( spl17_705
| ~ spl17_180
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f3028,f2921,f2889,f8650]) ).
fof(f8650,plain,
( spl17_705
<=> ! [X0,X3,X2,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,cOMBB_bool_bool_nat(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_705])]) ).
fof(f3028,plain,
( ! [X2,X3,X0,X1] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X3,cOMBB_bool_bool_nat(X0,X1)),X2) = hAPP_b589554111l_bool(X3,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl17_180
| ~ spl17_188 ),
inference(superposition,[],[f2890,f2922]) ).
fof(f8579,plain,
( spl17_704
| ~ spl17_506
| ~ spl17_695 ),
inference(avatar_split_clause,[],[f8464,f8422,f5745,f8577]) ).
fof(f8577,plain,
( spl17_704
<=> ! [X0] : hAPP_a93125764e_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_pname(hAPP_a93125764e_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_704])]) ).
fof(f8464,plain,
( ! [X0] : hAPP_a93125764e_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))) = collect_pname(hAPP_a93125764e_bool(X0,sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))))
| ~ spl17_506
| ~ spl17_695 ),
inference(resolution,[],[f8424,f5746]) ).
fof(f8457,plain,
( spl17_703
| ~ spl17_167
| ~ spl17_327 ),
inference(avatar_split_clause,[],[f3945,f3803,f2823,f8455]) ).
fof(f8455,plain,
( spl17_703
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_a_bool(image_pname_a(X2,X1),hAPP_pname_a(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_703])]) ).
fof(f3945,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_a_bool(image_pname_a(X2,X1),hAPP_pname_a(X2,X0))) )
| ~ spl17_167
| ~ spl17_327 ),
inference(resolution,[],[f3804,f2824]) ).
fof(f8453,plain,
( spl17_702
| ~ spl17_162
| ~ spl17_325 ),
inference(avatar_split_clause,[],[f3928,f3795,f2803,f8451]) ).
fof(f8451,plain,
( spl17_702
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_a(sK4(image_pname_a(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_702])]) ).
fof(f3928,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_a(sK4(image_pname_a(X2,X1),X0)) )
| ~ spl17_162
| ~ spl17_325 ),
inference(resolution,[],[f3796,f2804]) ).
fof(f8449,plain,
( spl17_701
| ~ spl17_206
| ~ spl17_260 ),
inference(avatar_split_clause,[],[f3545,f3409,f3086,f8447]) ).
fof(f8447,plain,
( spl17_701
<=> ! [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),hAPP_nat_nat(suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_701])]) ).
fof(f3545,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),hAPP_nat_nat(suc,X0))) )
| ~ spl17_206
| ~ spl17_260 ),
inference(resolution,[],[f3410,f3087]) ).
fof(f8445,plain,
( spl17_700
| ~ spl17_205
| ~ spl17_259 ),
inference(avatar_split_clause,[],[f3543,f3405,f3082,f8443]) ).
fof(f8443,plain,
( spl17_700
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,hAPP_nat_nat(suc,X1))),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_700])]) ).
fof(f3543,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,hAPP_nat_nat(suc,X1))),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_205
| ~ spl17_259 ),
inference(resolution,[],[f3406,f3083]) ).
fof(f8441,plain,
( spl17_699
| ~ spl17_116
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3025,f2917,f2619,f8439]) ).
fof(f8439,plain,
( spl17_699
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_699])]) ).
fof(f2619,plain,
( spl17_116
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
fof(f3025,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ hBOOL(X0) )
| ~ spl17_116
| ~ spl17_187 ),
inference(superposition,[],[f2620,f2918]) ).
fof(f2620,plain,
( ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) )
| ~ spl17_116 ),
inference(avatar_component_clause,[],[f2619]) ).
fof(f8437,plain,
( spl17_698
| ~ spl17_118
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3022,f2917,f2627,f8435]) ).
fof(f8435,plain,
( spl17_698
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| hBOOL(X0)
| hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_698])]) ).
fof(f2627,plain,
( spl17_118
<=> ! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
fof(f3022,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| hBOOL(X0)
| hBOOL(hAPP_a_bool(X1,X2)) )
| ~ spl17_118
| ~ spl17_187 ),
inference(superposition,[],[f2628,f2918]) ).
fof(f2628,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(X1) )
| ~ spl17_118 ),
inference(avatar_component_clause,[],[f2627]) ).
fof(f8433,plain,
( spl17_697
| ~ spl17_117
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3019,f2917,f2623,f8431]) ).
fof(f8431,plain,
( spl17_697
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X0)
| hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_697])]) ).
fof(f2623,plain,
( spl17_117
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
fof(f3019,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X0)
| hBOOL(hAPP_a_bool(X1,X2)) )
| ~ spl17_117
| ~ spl17_187 ),
inference(superposition,[],[f2624,f2918]) ).
fof(f2624,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(X1) )
| ~ spl17_117 ),
inference(avatar_component_clause,[],[f2623]) ).
fof(f8429,plain,
( spl17_696
| ~ spl17_116
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3013,f2913,f2619,f8427]) ).
fof(f8427,plain,
( spl17_696
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_696])]) ).
fof(f3013,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ hBOOL(X0) )
| ~ spl17_116
| ~ spl17_186 ),
inference(superposition,[],[f2620,f2914]) ).
fof(f8425,plain,
( spl17_695
| ~ spl17_162
| spl17_674 ),
inference(avatar_split_clause,[],[f8380,f8335,f2803,f8422]) ).
fof(f8380,plain,
( is_a(sK4(g,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))
| ~ spl17_162
| spl17_674 ),
inference(resolution,[],[f8337,f2804]) ).
fof(f8420,plain,
( spl17_694
| ~ spl17_118
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3010,f2913,f2627,f8418]) ).
fof(f8418,plain,
( spl17_694
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| hBOOL(X0)
| hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_694])]) ).
fof(f3010,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| hBOOL(X0)
| hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_118
| ~ spl17_186 ),
inference(superposition,[],[f2628,f2914]) ).
fof(f8416,plain,
( spl17_693
| ~ spl17_117
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3007,f2913,f2623,f8414]) ).
fof(f8414,plain,
( spl17_693
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X0)
| hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_693])]) ).
fof(f3007,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X0)
| hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_117
| ~ spl17_186 ),
inference(superposition,[],[f2624,f2914]) ).
fof(f8412,plain,
( spl17_692
| ~ spl17_116
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2999,f2905,f2619,f8410]) ).
fof(f8410,plain,
( spl17_692
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_692])]) ).
fof(f2999,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_184 ),
inference(superposition,[],[f2620,f2906]) ).
fof(f8408,plain,
( spl17_691
| ~ spl17_118
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2996,f2905,f2627,f8406]) ).
fof(f8406,plain,
( spl17_691
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_691])]) ).
fof(f2996,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_184 ),
inference(superposition,[],[f2628,f2906]) ).
fof(f8404,plain,
( spl17_690
| ~ spl17_117
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2993,f2905,f2623,f8402]) ).
fof(f8402,plain,
( spl17_690
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_690])]) ).
fof(f2993,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_184 ),
inference(superposition,[],[f2624,f2906]) ).
fof(f8400,plain,
( spl17_689
| ~ spl17_116
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2985,f2901,f2619,f8398]) ).
fof(f8398,plain,
( spl17_689
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_689])]) ).
fof(f2985,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_183 ),
inference(superposition,[],[f2620,f2902]) ).
fof(f8396,plain,
( spl17_688
| ~ spl17_118
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2982,f2901,f2627,f8394]) ).
fof(f8394,plain,
( spl17_688
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_688])]) ).
fof(f2982,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_183 ),
inference(superposition,[],[f2628,f2902]) ).
fof(f8392,plain,
( spl17_687
| ~ spl17_117
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2979,f2901,f2623,f8390]) ).
fof(f8390,plain,
( spl17_687
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_687])]) ).
fof(f2979,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_183 ),
inference(superposition,[],[f2624,f2902]) ).
fof(f8388,plain,
( spl17_686
| ~ spl17_116
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2976,f2897,f2619,f8386]) ).
fof(f8386,plain,
( spl17_686
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_686])]) ).
fof(f2976,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_182 ),
inference(superposition,[],[f2620,f2898]) ).
fof(f8384,plain,
( spl17_685
| ~ spl17_118
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2973,f2897,f2627,f8382]) ).
fof(f8382,plain,
( spl17_685
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_685])]) ).
fof(f2973,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_182 ),
inference(superposition,[],[f2628,f2898]) ).
fof(f8378,plain,
( spl17_684
| ~ spl17_117
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2970,f2897,f2623,f8376]) ).
fof(f8376,plain,
( spl17_684
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_684])]) ).
fof(f2970,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_182 ),
inference(superposition,[],[f2624,f2898]) ).
fof(f8374,plain,
( spl17_683
| ~ spl17_116
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2967,f2893,f2619,f8372]) ).
fof(f8372,plain,
( spl17_683
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_683])]) ).
fof(f2967,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_181 ),
inference(superposition,[],[f2620,f2894]) ).
fof(f8370,plain,
( spl17_682
| ~ spl17_118
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2964,f2893,f2627,f8368]) ).
fof(f8368,plain,
( spl17_682
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_682])]) ).
fof(f2964,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_181 ),
inference(superposition,[],[f2628,f2894]) ).
fof(f8366,plain,
( spl17_681
| ~ spl17_117
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2961,f2893,f2623,f8364]) ).
fof(f8364,plain,
( spl17_681
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_681])]) ).
fof(f2961,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_181 ),
inference(superposition,[],[f2624,f2894]) ).
fof(f8362,plain,
( spl17_680
| ~ spl17_116
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2958,f2889,f2619,f8360]) ).
fof(f8360,plain,
( spl17_680
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_680])]) ).
fof(f2958,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_180 ),
inference(superposition,[],[f2620,f2890]) ).
fof(f8358,plain,
( spl17_679
| ~ spl17_118
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2955,f2889,f2627,f8356]) ).
fof(f8356,plain,
( spl17_679
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_679])]) ).
fof(f2955,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_180 ),
inference(superposition,[],[f2628,f2890]) ).
fof(f8354,plain,
( spl17_678
| ~ spl17_117
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2952,f2889,f2623,f8352]) ).
fof(f8352,plain,
( spl17_678
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_678])]) ).
fof(f2952,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_180 ),
inference(superposition,[],[f2624,f2890]) ).
fof(f8350,plain,
( spl17_677
| ~ spl17_116
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2949,f2885,f2619,f8348]) ).
fof(f8348,plain,
( spl17_677
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_677])]) ).
fof(f2949,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_116
| ~ spl17_179 ),
inference(superposition,[],[f2620,f2886]) ).
fof(f8346,plain,
( spl17_676
| ~ spl17_118
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2946,f2885,f2627,f8344]) ).
fof(f8344,plain,
( spl17_676
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_676])]) ).
fof(f2946,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_118
| ~ spl17_179 ),
inference(superposition,[],[f2628,f2886]) ).
fof(f8342,plain,
( spl17_675
| ~ spl17_117
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2943,f2885,f2623,f8340]) ).
fof(f8340,plain,
( spl17_675
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_675])]) ).
fof(f2943,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X0,X1))
| hBOOL(X2) )
| ~ spl17_117
| ~ spl17_179 ),
inference(superposition,[],[f2624,f2886]) ).
fof(f8338,plain,
( ~ spl17_674
| spl17_43
| ~ spl17_670 ),
inference(avatar_split_clause,[],[f8310,f8233,f2273,f8335]) ).
fof(f8233,plain,
( spl17_670
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),g)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_670])]) ).
fof(f8310,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),g))
| spl17_43
| ~ spl17_670 ),
inference(resolution,[],[f8234,f2275]) ).
fof(f8234,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),g)) )
| ~ spl17_670 ),
inference(avatar_component_clause,[],[f8233]) ).
fof(f8333,plain,
( spl17_673
| ~ spl17_57
| ~ spl17_97 ),
inference(avatar_split_clause,[],[f2543,f2534,f2331,f8330]) ).
fof(f8330,plain,
( spl17_673
<=> undefi1699038445l_bool(fun(fun(x_a,bool),bool)) = collect_fun_a_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_673])]) ).
fof(f2534,plain,
( spl17_97
<=> is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
fof(f2543,plain,
( undefi1699038445l_bool(fun(fun(x_a,bool),bool)) = collect_fun_a_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool)))
| ~ spl17_57
| ~ spl17_97 ),
inference(resolution,[],[f2536,f2332]) ).
fof(f2536,plain,
( is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool)))
| ~ spl17_97 ),
inference(avatar_component_clause,[],[f2534]) ).
fof(f8328,plain,
( spl17_672
| ~ spl17_56
| ~ spl17_96 ),
inference(avatar_split_clause,[],[f2542,f2529,f2327,f8325]) ).
fof(f8325,plain,
( spl17_672
<=> undefi64961550l_bool(fun(fun(pname,bool),bool)) = collec1974731493e_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_672])]) ).
fof(f2529,plain,
( spl17_96
<=> is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
fof(f2542,plain,
( undefi64961550l_bool(fun(fun(pname,bool),bool)) = collec1974731493e_bool(undefi64961550l_bool(fun(fun(pname,bool),bool)))
| ~ spl17_56
| ~ spl17_96 ),
inference(resolution,[],[f2531,f2328]) ).
fof(f2531,plain,
( is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool)))
| ~ spl17_96 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f8240,plain,
( ~ spl17_3
| ~ spl17_334
| spl17_671
| ~ spl17_100
| ~ spl17_400 ),
inference(avatar_split_clause,[],[f4596,f4567,f2550,f8237,f3962,f2103]) ).
fof(f4596,plain,
( g = image_pname_a(mgt_call,sK9(mgt_call,u,g))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ is_fun_a_bool(g)
| ~ spl17_100
| ~ spl17_400 ),
inference(resolution,[],[f4568,f2552]) ).
fof(f8235,plain,
( spl17_670
| ~ spl17_100
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f4245,f4083,f2550,f8233]) ).
fof(f4245,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),g)) )
| ~ spl17_100
| ~ spl17_358 ),
inference(resolution,[],[f4084,f2552]) ).
fof(f8231,plain,
( spl17_669
| ~ spl17_100
| ~ spl17_357 ),
inference(avatar_split_clause,[],[f4239,f4079,f2550,f8229]) ).
fof(f8229,plain,
( spl17_669
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),g)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_669])]) ).
fof(f4239,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),g)) )
| ~ spl17_100
| ~ spl17_357 ),
inference(resolution,[],[f4080,f2552]) ).
fof(f8222,plain,
( spl17_668
| ~ spl17_194
| ~ spl17_250
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3648,f3609,f3367,f3037,f8219]) ).
fof(f8219,plain,
( spl17_668
<=> hAPP_nat_nat(suc,na) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_fun_a_bool_nat(finite_card_a,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_668])]) ).
fof(f3648,plain,
( hAPP_nat_nat(suc,na) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_fun_a_bool_nat(finite_card_a,g))
| ~ spl17_194
| ~ spl17_250
| ~ spl17_288 ),
inference(forward_demodulation,[],[f3646,f3369]) ).
fof(f3646,plain,
( hAPP_nat_nat(suc,na) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)))
| ~ spl17_194
| ~ spl17_288 ),
inference(resolution,[],[f3610,f3039]) ).
fof(f8217,plain,
( spl17_667
| ~ spl17_194
| ~ spl17_261 ),
inference(avatar_split_clause,[],[f3552,f3413,f3037,f8214]) ).
fof(f3552,plain,
( hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) = hAPP_nat_nat(suc,sK3(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl17_194
| ~ spl17_261 ),
inference(resolution,[],[f3414,f3039]) ).
fof(f8151,plain,
( spl17_666
| ~ spl17_50
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f4364,f4264,f2303,f8149]) ).
fof(f8149,plain,
( spl17_666
<=> ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_666])]) ).
fof(f4364,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X0),X0))
| ~ spl17_50
| ~ spl17_368 ),
inference(resolution,[],[f4265,f2304]) ).
fof(f8147,plain,
( spl17_665
| ~ spl17_104
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f4012,f3969,f2568,f8145]) ).
fof(f4012,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(suc,sK1(X0))),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_104
| ~ spl17_335 ),
inference(resolution,[],[f3970,f2569]) ).
fof(f8143,plain,
( spl17_664
| ~ spl17_162
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f3672,f3633,f2803,f8141]) ).
fof(f8141,plain,
( spl17_664
<=> ! [X2,X0,X1] :
( is_fun_pname_bool(sK10(X0,X1,X2))
| ~ is_fun_a_bool(X0)
| is_a(sK4(image_pname_a(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_664])]) ).
fof(f3672,plain,
( ! [X2,X0,X1] :
( is_fun_pname_bool(sK10(X0,X1,X2))
| ~ is_fun_a_bool(X0)
| is_a(sK4(image_pname_a(X1,X2),X0)) )
| ~ spl17_162
| ~ spl17_294 ),
inference(resolution,[],[f3634,f2804]) ).
fof(f8139,plain,
( spl17_663
| ~ spl17_168
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f3669,f3629,f2827,f8137]) ).
fof(f8137,plain,
( spl17_663
<=> ! [X2,X0,X1] :
( is_pname(sK8(X0,X1,X2))
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_663])]) ).
fof(f3669,plain,
( ! [X2,X0,X1] :
( is_pname(sK8(X0,X1,X2))
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X1,X2),X0)) )
| ~ spl17_168
| ~ spl17_293 ),
inference(resolution,[],[f3630,f2828]) ).
fof(f8135,plain,
( spl17_662
| ~ spl17_168
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f3667,f3625,f2827,f8133]) ).
fof(f8133,plain,
( spl17_662
<=> ! [X2,X0,X1] :
( is_pname(sK7(X0,X1,X2))
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_662])]) ).
fof(f3667,plain,
( ! [X2,X0,X1] :
( is_pname(sK7(X0,X1,X2))
| ~ is_a(X0)
| ~ hBOOL(hAPP_a_bool(image_pname_a(X1,X2),X0)) )
| ~ spl17_168
| ~ spl17_292 ),
inference(resolution,[],[f3626,f2828]) ).
fof(f8131,plain,
( spl17_661
| ~ spl17_186
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3344,f3298,f2913,f8129]) ).
fof(f8129,plain,
( spl17_661
<=> ! [X2,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X0,X2),X1) = hAPP_pname_bool(cOMBB_647938656_pname(hAPP_p393069232l_bool(X0,X1),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_661])]) ).
fof(f3344,plain,
( ! [X2,X0,X1] : hAPP_pname_bool(cOMBS_568398431l_bool(X0,X2),X1) = hAPP_pname_bool(cOMBB_647938656_pname(hAPP_p393069232l_bool(X0,X1),X2),X1)
| ~ spl17_186
| ~ spl17_243 ),
inference(superposition,[],[f3299,f2914]) ).
fof(f8127,plain,
( spl17_660
| ~ spl17_8
| ~ spl17_621 ),
inference(avatar_split_clause,[],[f7948,f7187,f2128,f8125]) ).
fof(f8125,plain,
( spl17_660
<=> ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(u,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_660])]) ).
fof(f7948,plain,
( ! [X0] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| is_pname(sK5(u,X0)) )
| ~ spl17_8
| ~ spl17_621 ),
inference(resolution,[],[f7188,f2130]) ).
fof(f2130,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f2128]) ).
fof(f8123,plain,
( spl17_659
| ~ spl17_187
| ~ spl17_242 ),
inference(avatar_split_clause,[],[f3338,f3294,f2917,f8121]) ).
fof(f8121,plain,
( spl17_659
<=> ! [X2,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X2),X1) = hAPP_a_bool(cOMBB_bool_bool_a(hAPP_a_fun_bool_bool(X0,X1),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_659])]) ).
fof(f3338,plain,
( ! [X2,X0,X1] : hAPP_a_bool(cOMBS_a_bool_bool(X0,X2),X1) = hAPP_a_bool(cOMBB_bool_bool_a(hAPP_a_fun_bool_bool(X0,X1),X2),X1)
| ~ spl17_187
| ~ spl17_242 ),
inference(superposition,[],[f3295,f2918]) ).
fof(f8119,plain,
( spl17_658
| ~ spl17_111
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f3236,f3118,f2597,f8117]) ).
fof(f8117,plain,
( spl17_658
<=> ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_658])]) ).
fof(f2597,plain,
( spl17_111
<=> ! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
fof(f3236,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1)) )
| ~ spl17_111
| ~ spl17_214 ),
inference(superposition,[],[f2598,f3119]) ).
fof(f2598,plain,
( ! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) )
| ~ spl17_111 ),
inference(avatar_component_clause,[],[f2597]) ).
fof(f8115,plain,
( spl17_657
| ~ spl17_112
| ~ spl17_213 ),
inference(avatar_split_clause,[],[f3230,f3114,f2601,f8113]) ).
fof(f8113,plain,
( spl17_657
<=> ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_657])]) ).
fof(f2601,plain,
( spl17_112
<=> ! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
fof(f3230,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1)) )
| ~ spl17_112
| ~ spl17_213 ),
inference(superposition,[],[f2602,f3115]) ).
fof(f2602,plain,
( ! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) )
| ~ spl17_112 ),
inference(avatar_component_clause,[],[f2601]) ).
fof(f8111,plain,
( spl17_656
| ~ spl17_112
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f3226,f3110,f2601,f8109]) ).
fof(f8109,plain,
( spl17_656
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_656])]) ).
fof(f3226,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1)) )
| ~ spl17_112
| ~ spl17_212 ),
inference(superposition,[],[f2602,f3111]) ).
fof(f8107,plain,
( spl17_655
| ~ spl17_111
| ~ spl17_211 ),
inference(avatar_split_clause,[],[f3222,f3106,f2597,f8105]) ).
fof(f8105,plain,
( spl17_655
<=> ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_655])]) ).
fof(f3222,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1))
| ~ is_a(X2)
| ~ is_fun_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1)) )
| ~ spl17_111
| ~ spl17_211 ),
inference(superposition,[],[f2598,f3107]) ).
fof(f8103,plain,
( spl17_654
| ~ spl17_112
| ~ spl17_210 ),
inference(avatar_split_clause,[],[f3217,f3102,f2601,f8101]) ).
fof(f8101,plain,
( spl17_654
<=> ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_654])]) ).
fof(f3217,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1)) )
| ~ spl17_112
| ~ spl17_210 ),
inference(superposition,[],[f2602,f3103]) ).
fof(f8096,plain,
( ~ spl17_3
| ~ spl17_334
| spl17_653
| ~ spl17_100
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f4555,f4546,f2550,f8093,f3962,f2103]) ).
fof(f4555,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(mgt_call,u,g)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ is_fun_a_bool(g)
| ~ spl17_100
| ~ spl17_398 ),
inference(resolution,[],[f4547,f2552]) ).
fof(f8091,plain,
( spl17_652
| ~ spl17_101
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f3264,f3167,f2555,f8089]) ).
fof(f8089,plain,
( spl17_652
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_652])]) ).
fof(f2555,plain,
( spl17_101
<=> ! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
fof(f3264,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1)) )
| ~ spl17_101
| ~ spl17_226 ),
inference(superposition,[],[f2556,f3168]) ).
fof(f2556,plain,
( ! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) )
| ~ spl17_101 ),
inference(avatar_component_clause,[],[f2555]) ).
fof(f8087,plain,
( spl17_651
| ~ spl17_101
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f3262,f3158,f2555,f8085]) ).
fof(f8085,plain,
( spl17_651
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_651])]) ).
fof(f3262,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1)) )
| ~ spl17_101
| ~ spl17_224 ),
inference(superposition,[],[f2556,f3159]) ).
fof(f8083,plain,
( spl17_650
| ~ spl17_102
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f3259,f3154,f2559,f8081]) ).
fof(f8081,plain,
( spl17_650
<=> ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_650])]) ).
fof(f2559,plain,
( spl17_102
<=> ! [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,[spl17_102])]) ).
fof(f3259,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1)) )
| ~ spl17_102
| ~ spl17_223 ),
inference(superposition,[],[f2560,f3155]) ).
fof(f2560,plain,
( ! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) )
| ~ spl17_102 ),
inference(avatar_component_clause,[],[f2559]) ).
fof(f8079,plain,
( spl17_649
| ~ spl17_102
| ~ spl17_222 ),
inference(avatar_split_clause,[],[f3257,f3150,f2559,f8077]) ).
fof(f8077,plain,
( spl17_649
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_649])]) ).
fof(f3257,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1)) )
| ~ spl17_102
| ~ spl17_222 ),
inference(superposition,[],[f2560,f3151]) ).
fof(f8046,plain,
( spl17_648
| ~ spl17_334
| ~ spl17_620 ),
inference(avatar_split_clause,[],[f7932,f7183,f3962,f8044]) ).
fof(f8044,plain,
( spl17_648
<=> ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| is_a(sK4(g,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_648])]) ).
fof(f7932,plain,
( ! [X0] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| is_a(sK4(g,X0)) )
| ~ spl17_334
| ~ spl17_620 ),
inference(resolution,[],[f7184,f3964]) ).
fof(f7699,plain,
( spl17_647
| ~ spl17_36
| ~ spl17_563 ),
inference(avatar_split_clause,[],[f6378,f5976,f2243,f7697]) ).
fof(f7697,plain,
( spl17_647
<=> ! [X0] : hAPP_nat_nat(suc,X0) != sK3(hAPP_nat_nat(suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_647])]) ).
fof(f2243,plain,
( spl17_36
<=> ! [X0] : hAPP_nat_nat(suc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f6378,plain,
( ! [X0] : hAPP_nat_nat(suc,X0) != sK3(hAPP_nat_nat(suc,X0))
| ~ spl17_36
| ~ spl17_563 ),
inference(superposition,[],[f2244,f5977]) ).
fof(f2244,plain,
( ! [X0] : hAPP_nat_nat(suc,X0) != X0
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f7634,plain,
( spl17_646
| ~ spl17_5
| ~ spl17_516 ),
inference(avatar_split_clause,[],[f6072,f5785,f2113,f7632]) ).
fof(f7632,plain,
( spl17_646
<=> ! [X0] : image_1854862208_pname(X0,finite_finite_a) = collect_pname(image_1854862208_pname(X0,finite_finite_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_646])]) ).
fof(f2113,plain,
( spl17_5
<=> is_fun949378684l_bool(finite_finite_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f5785,plain,
( spl17_516
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| image_1854862208_pname(X1,X0) = collect_pname(image_1854862208_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_516])]) ).
fof(f6072,plain,
( ! [X0] : image_1854862208_pname(X0,finite_finite_a) = collect_pname(image_1854862208_pname(X0,finite_finite_a))
| ~ spl17_5
| ~ spl17_516 ),
inference(resolution,[],[f5786,f2115]) ).
fof(f2115,plain,
( is_fun949378684l_bool(finite_finite_a)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f2113]) ).
fof(f5786,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| image_1854862208_pname(X1,X0) = collect_pname(image_1854862208_pname(X1,X0)) )
| ~ spl17_516 ),
inference(avatar_component_clause,[],[f5785]) ).
fof(f7584,plain,
( spl17_645
| ~ spl17_5
| ~ spl17_514 ),
inference(avatar_split_clause,[],[f6060,f5777,f2113,f7582]) ).
fof(f7582,plain,
( spl17_645
<=> ! [X0] : cOMBS_1035972772l_bool(X0,finite_finite_a) = collect_fun_a_bool(cOMBS_1035972772l_bool(X0,finite_finite_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_645])]) ).
fof(f5777,plain,
( spl17_514
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBS_1035972772l_bool(X1,X0) = collect_fun_a_bool(cOMBS_1035972772l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_514])]) ).
fof(f6060,plain,
( ! [X0] : cOMBS_1035972772l_bool(X0,finite_finite_a) = collect_fun_a_bool(cOMBS_1035972772l_bool(X0,finite_finite_a))
| ~ spl17_5
| ~ spl17_514 ),
inference(resolution,[],[f5778,f2115]) ).
fof(f5778,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBS_1035972772l_bool(X1,X0) = collect_fun_a_bool(cOMBS_1035972772l_bool(X1,X0)) )
| ~ spl17_514 ),
inference(avatar_component_clause,[],[f5777]) ).
fof(f7543,plain,
( spl17_644
| ~ spl17_5
| ~ spl17_513 ),
inference(avatar_split_clause,[],[f6048,f5773,f2113,f7541]) ).
fof(f5773,plain,
( spl17_513
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| hAPP_f2117159681l_bool(X1,X0) = collect_fun_a_bool(hAPP_f2117159681l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_513])]) ).
fof(f6048,plain,
( ! [X0] : hAPP_f2117159681l_bool(X0,finite_finite_a) = collect_fun_a_bool(hAPP_f2117159681l_bool(X0,finite_finite_a))
| ~ spl17_5
| ~ spl17_513 ),
inference(resolution,[],[f5774,f2115]) ).
fof(f5774,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| hAPP_f2117159681l_bool(X1,X0) = collect_fun_a_bool(hAPP_f2117159681l_bool(X1,X0)) )
| ~ spl17_513 ),
inference(avatar_component_clause,[],[f5773]) ).
fof(f7490,plain,
( spl17_643
| ~ spl17_5
| ~ spl17_512 ),
inference(avatar_split_clause,[],[f6036,f5769,f2113,f7488]) ).
fof(f7488,plain,
( spl17_643
<=> ! [X0] : cOMBB_2140588453a_bool(X0,finite_finite_a) = collect_fun_a_bool(cOMBB_2140588453a_bool(X0,finite_finite_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_643])]) ).
fof(f5769,plain,
( spl17_512
<=> ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBB_2140588453a_bool(X1,X0) = collect_fun_a_bool(cOMBB_2140588453a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_512])]) ).
fof(f6036,plain,
( ! [X0] : cOMBB_2140588453a_bool(X0,finite_finite_a) = collect_fun_a_bool(cOMBB_2140588453a_bool(X0,finite_finite_a))
| ~ spl17_5
| ~ spl17_512 ),
inference(resolution,[],[f5770,f2115]) ).
fof(f5770,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBB_2140588453a_bool(X1,X0) = collect_fun_a_bool(cOMBB_2140588453a_bool(X1,X0)) )
| ~ spl17_512 ),
inference(avatar_component_clause,[],[f5769]) ).
fof(f7347,plain,
( spl17_642
| ~ spl17_564
| ~ spl17_640 ),
inference(avatar_split_clause,[],[f7316,f7266,f6009,f7344]) ).
fof(f6009,plain,
( spl17_564
<=> ! [X0] : hAPP_p61793385e_bool(X0,pn) = collect_pname(hAPP_p61793385e_bool(X0,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_564])]) ).
fof(f7316,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),pn)))
| ~ spl17_564
| ~ spl17_640 ),
inference(superposition,[],[f7267,f6010]) ).
fof(f6010,plain,
( ! [X0] : hAPP_p61793385e_bool(X0,pn) = collect_pname(hAPP_p61793385e_bool(X0,pn))
| ~ spl17_564 ),
inference(avatar_component_clause,[],[f6009]) ).
fof(f7307,plain,
( spl17_574
| ~ spl17_144
| ~ spl17_634 ),
inference(avatar_split_clause,[],[f7305,f7240,f2731,f6453]) ).
fof(f6453,plain,
( spl17_574
<=> ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_574])]) ).
fof(f2731,plain,
( spl17_144
<=> ! [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,[spl17_144])]) ).
fof(f7240,plain,
( spl17_634
<=> ! [X0] : ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_634])]) ).
fof(f7305,plain,
( ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ spl17_144
| ~ spl17_634 ),
inference(resolution,[],[f7241,f2732]) ).
fof(f2732,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_144 ),
inference(avatar_component_clause,[],[f2731]) ).
fof(f7241,plain,
( ! [X0] : ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ spl17_634 ),
inference(avatar_component_clause,[],[f7240]) ).
fof(f7304,plain,
( spl17_641
| ~ spl17_584
| ~ spl17_633 ),
inference(avatar_split_clause,[],[f7243,f7237,f6538,f7301]) ).
fof(f7301,plain,
( spl17_641
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_641])]) ).
fof(f7243,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),u)))
| ~ spl17_584
| ~ spl17_633 ),
inference(superposition,[],[f7238,f6539]) ).
fof(f7299,plain,
( ~ spl17_8
| ~ spl17_581 ),
inference(avatar_contradiction_clause,[],[f7298]) ).
fof(f7298,plain,
( $false
| ~ spl17_8
| ~ spl17_581 ),
inference(resolution,[],[f6510,f2130]) ).
fof(f6510,plain,
( ! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ spl17_581 ),
inference(avatar_component_clause,[],[f6509]) ).
fof(f6509,plain,
( spl17_581
<=> ! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_581])]) ).
fof(f7268,plain,
( spl17_640
| spl17_581
| ~ spl17_285
| ~ spl17_385 ),
inference(avatar_split_clause,[],[f4476,f4334,f3522,f6509,f7266]) ).
fof(f3522,plain,
( spl17_285
<=> ! [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,[spl17_285])]) ).
fof(f4476,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)))) )
| ~ spl17_285
| ~ spl17_385 ),
inference(resolution,[],[f4335,f3523]) ).
fof(f3523,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(X0))) )
| ~ spl17_285 ),
inference(avatar_component_clause,[],[f3522]) ).
fof(f7264,plain,
( spl17_639
| ~ spl17_286
| ~ spl17_385 ),
inference(avatar_split_clause,[],[f4475,f4334,f3526,f7262]) ).
fof(f4475,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))) )
| ~ spl17_286
| ~ spl17_385 ),
inference(resolution,[],[f4335,f3527]) ).
fof(f7259,plain,
( spl17_638
| ~ spl17_515
| ~ spl17_630 ),
inference(avatar_split_clause,[],[f7231,f7225,f5781,f7256]) ).
fof(f7256,plain,
( spl17_638
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_638])]) ).
fof(f7231,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),g)))
| ~ spl17_515
| ~ spl17_630 ),
inference(superposition,[],[f7226,f5782]) ).
fof(f7254,plain,
( spl17_636
| spl17_637
| ~ spl17_283
| ~ spl17_384 ),
inference(avatar_split_clause,[],[f4473,f4330,f3514,f7252,f7249]) ).
fof(f3514,plain,
( spl17_283
<=> ! [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,[spl17_283])]) ).
fof(f4473,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)))) )
| ~ spl17_283
| ~ spl17_384 ),
inference(resolution,[],[f4331,f3515]) ).
fof(f3515,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(X0))) )
| ~ spl17_283 ),
inference(avatar_component_clause,[],[f3514]) ).
fof(f7247,plain,
( spl17_635
| ~ spl17_284
| ~ spl17_384 ),
inference(avatar_split_clause,[],[f4472,f4330,f3518,f7245]) ).
fof(f7245,plain,
( spl17_635
<=> ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_635])]) ).
fof(f4472,plain,
( ! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))) )
| ~ spl17_284
| ~ spl17_384 ),
inference(resolution,[],[f4331,f3519]) ).
fof(f7242,plain,
( spl17_633
| spl17_634
| ~ spl17_279
| ~ spl17_383 ),
inference(avatar_split_clause,[],[f4471,f4326,f3485,f7240,f7237]) ).
fof(f3485,plain,
( spl17_279
<=> ! [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,[spl17_279])]) ).
fof(f4471,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)))) )
| ~ spl17_279
| ~ spl17_383 ),
inference(resolution,[],[f4327,f3486]) ).
fof(f3486,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(X0))) )
| ~ spl17_279 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f7235,plain,
( spl17_632
| ~ spl17_280
| ~ spl17_383 ),
inference(avatar_split_clause,[],[f4470,f4326,f3502,f7233]) ).
fof(f4470,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X0)))) )
| ~ spl17_280
| ~ spl17_383 ),
inference(resolution,[],[f4327,f3503]) ).
fof(f7230,plain,
( spl17_630
| spl17_631
| ~ spl17_281
| ~ spl17_382 ),
inference(avatar_split_clause,[],[f4469,f4322,f3506,f7228,f7225]) ).
fof(f7228,plain,
( spl17_631
<=> ! [X0] : ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_631])]) ).
fof(f3506,plain,
( spl17_281
<=> ! [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,[spl17_281])]) ).
fof(f4469,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)))) )
| ~ spl17_281
| ~ spl17_382 ),
inference(resolution,[],[f4323,f3507]) ).
fof(f3507,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(X0))) )
| ~ spl17_281 ),
inference(avatar_component_clause,[],[f3506]) ).
fof(f7223,plain,
( spl17_629
| ~ spl17_282
| ~ spl17_382 ),
inference(avatar_split_clause,[],[f4468,f4322,f3510,f7221]) ).
fof(f4468,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X0)))) )
| ~ spl17_282
| ~ spl17_382 ),
inference(resolution,[],[f4323,f3511]) ).
fof(f7219,plain,
( spl17_628
| ~ spl17_261
| ~ spl17_277 ),
inference(avatar_split_clause,[],[f3582,f3477,f3413,f7217]) ).
fof(f7217,plain,
( spl17_628
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,sK3(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_628])]) ).
fof(f3582,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| hAPP_nat_nat(suc,sK3(X0)) = X0 )
| ~ spl17_261
| ~ spl17_277 ),
inference(resolution,[],[f3478,f3414]) ).
fof(f7215,plain,
( spl17_627
| ~ spl17_166
| ~ spl17_276 ),
inference(avatar_split_clause,[],[f3579,f3473,f2819,f7213]) ).
fof(f7213,plain,
( spl17_627
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,sK6(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_627])]) ).
fof(f3579,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,sK6(X1,X0))) )
| ~ spl17_166
| ~ spl17_276 ),
inference(resolution,[],[f3474,f2820]) ).
fof(f7209,plain,
( spl17_626
| ~ spl17_165
| ~ spl17_275 ),
inference(avatar_split_clause,[],[f3577,f3469,f2815,f7207]) ).
fof(f7207,plain,
( spl17_626
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_nat_bool(X0,sK6(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_626])]) ).
fof(f3577,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| hBOOL(hAPP_nat_bool(X0,sK6(X1,X0))) )
| ~ spl17_165
| ~ spl17_275 ),
inference(resolution,[],[f3470,f2816]) ).
fof(f7205,plain,
( spl17_625
| ~ spl17_170
| ~ spl17_274 ),
inference(avatar_split_clause,[],[f3574,f3465,f2835,f7203]) ).
fof(f7203,plain,
( spl17_625
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,sK5(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_625])]) ).
fof(f3574,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,sK5(X1,X0))) )
| ~ spl17_170
| ~ spl17_274 ),
inference(resolution,[],[f3466,f2836]) ).
fof(f7201,plain,
( spl17_624
| ~ spl17_169
| ~ spl17_273 ),
inference(avatar_split_clause,[],[f3572,f3461,f2831,f7199]) ).
fof(f7199,plain,
( spl17_624
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_pname_bool(X0,sK5(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_624])]) ).
fof(f3572,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| hBOOL(hAPP_pname_bool(X0,sK5(X1,X0))) )
| ~ spl17_169
| ~ spl17_273 ),
inference(resolution,[],[f3462,f2832]) ).
fof(f7197,plain,
( spl17_623
| ~ spl17_168
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f3570,f3457,f2827,f7195]) ).
fof(f7195,plain,
( spl17_623
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,sK4(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_623])]) ).
fof(f3570,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,sK4(X1,X0))) )
| ~ spl17_168
| ~ spl17_272 ),
inference(resolution,[],[f3458,f2828]) ).
fof(f7193,plain,
( spl17_622
| ~ spl17_167
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f3568,f3453,f2823,f7191]) ).
fof(f3568,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_a_bool(X0,sK4(X1,X0))) )
| ~ spl17_167
| ~ spl17_271 ),
inference(resolution,[],[f3454,f2824]) ).
fof(f7189,plain,
( spl17_621
| ~ spl17_164
| ~ spl17_257 ),
inference(avatar_split_clause,[],[f3541,f3397,f2811,f7187]) ).
fof(f3541,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_pname(sK5(X1,X0)) )
| ~ spl17_164
| ~ spl17_257 ),
inference(resolution,[],[f3398,f2812]) ).
fof(f7185,plain,
( spl17_620
| ~ spl17_162
| ~ spl17_256 ),
inference(avatar_split_clause,[],[f3537,f3393,f2803,f7183]) ).
fof(f3537,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| is_a(sK4(X1,X0)) )
| ~ spl17_162
| ~ spl17_256 ),
inference(resolution,[],[f3394,f2804]) ).
fof(f7181,plain,
( spl17_619
| ~ spl17_177
| ~ spl17_248 ),
inference(avatar_split_clause,[],[f3365,f3318,f2876,f7179]) ).
fof(f3365,plain,
( ! [X2,X0,X1] :
( is_pname(sK16(X0,X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),image_pname_a(X0,X2))) )
| ~ spl17_177
| ~ spl17_248 ),
inference(resolution,[],[f3319,f2877]) ).
fof(f7177,plain,
( spl17_618
| ~ spl17_205
| ~ spl17_206 ),
inference(avatar_split_clause,[],[f3208,f3086,f3082,f7175]) ).
fof(f7175,plain,
( spl17_618
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sK0(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_618])]) ).
fof(f3208,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sK0(X0,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_205
| ~ spl17_206 ),
inference(resolution,[],[f3087,f3083]) ).
fof(f7173,plain,
( spl17_617
| ~ spl17_109
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3027,f2917,f2588,f7171]) ).
fof(f7171,plain,
( spl17_617
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_617])]) ).
fof(f2588,plain,
( spl17_109
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
fof(f3027,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X1,X2)) )
| ~ spl17_109
| ~ spl17_187 ),
inference(superposition,[],[f2589,f2918]) ).
fof(f2589,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1))
| hBOOL(X1) )
| ~ spl17_109 ),
inference(avatar_component_clause,[],[f2588]) ).
fof(f7167,plain,
( spl17_616
| ~ spl17_107
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3023,f2917,f2580,f7165]) ).
fof(f7165,plain,
( spl17_616
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_616])]) ).
fof(f2580,plain,
( spl17_107
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f3023,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) )
| ~ spl17_107
| ~ spl17_187 ),
inference(superposition,[],[f2581,f2918]) ).
fof(f2581,plain,
( ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) )
| ~ spl17_107 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f7163,plain,
( spl17_615
| ~ spl17_105
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3021,f2917,f2572,f7161]) ).
fof(f7161,plain,
( spl17_615
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_615])]) ).
fof(f2572,plain,
( spl17_105
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f3021,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) )
| ~ spl17_105
| ~ spl17_187 ),
inference(superposition,[],[f2573,f2918]) ).
fof(f2573,plain,
( ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) )
| ~ spl17_105 ),
inference(avatar_component_clause,[],[f2572]) ).
fof(f7159,plain,
( spl17_614
| ~ spl17_109
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3015,f2913,f2588,f7157]) ).
fof(f7157,plain,
( spl17_614
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_614])]) ).
fof(f3015,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_109
| ~ spl17_186 ),
inference(superposition,[],[f2589,f2914]) ).
fof(f7155,plain,
( spl17_613
| ~ spl17_107
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3011,f2913,f2580,f7153]) ).
fof(f7153,plain,
( spl17_613
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_613])]) ).
fof(f3011,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_107
| ~ spl17_186 ),
inference(superposition,[],[f2581,f2914]) ).
fof(f7151,plain,
( spl17_612
| ~ spl17_105
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3009,f2913,f2572,f7149]) ).
fof(f7149,plain,
( spl17_612
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_612])]) ).
fof(f3009,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) )
| ~ spl17_105
| ~ spl17_186 ),
inference(superposition,[],[f2573,f2914]) ).
fof(f7147,plain,
( spl17_611
| ~ spl17_110
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f3000,f2905,f2593,f7145]) ).
fof(f7145,plain,
( spl17_611
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_611])]) ).
fof(f2593,plain,
( spl17_110
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
fof(f3000,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_184 ),
inference(superposition,[],[f2594,f2906]) ).
fof(f2594,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1))
| hBOOL(X0) )
| ~ spl17_110 ),
inference(avatar_component_clause,[],[f2593]) ).
fof(f7143,plain,
( spl17_610
| ~ spl17_106
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2998,f2905,f2576,f7141]) ).
fof(f7141,plain,
( spl17_610
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_610])]) ).
fof(f2576,plain,
( spl17_106
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
fof(f2998,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_184 ),
inference(superposition,[],[f2577,f2906]) ).
fof(f2577,plain,
( ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) )
| ~ spl17_106 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f7139,plain,
( spl17_609
| ~ spl17_108
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2994,f2905,f2584,f7137]) ).
fof(f7137,plain,
( spl17_609
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_609])]) ).
fof(f2584,plain,
( spl17_108
<=> ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
fof(f2994,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_184 ),
inference(superposition,[],[f2585,f2906]) ).
fof(f2585,plain,
( ! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) )
| ~ spl17_108 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f7135,plain,
( spl17_608
| ~ spl17_110
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2986,f2901,f2593,f7133]) ).
fof(f7133,plain,
( spl17_608
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_608])]) ).
fof(f2986,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_183 ),
inference(superposition,[],[f2594,f2902]) ).
fof(f7131,plain,
( spl17_607
| ~ spl17_106
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2984,f2901,f2576,f7129]) ).
fof(f7129,plain,
( spl17_607
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_607])]) ).
fof(f2984,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_183 ),
inference(superposition,[],[f2577,f2902]) ).
fof(f7125,plain,
( spl17_606
| ~ spl17_108
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2980,f2901,f2584,f7123]) ).
fof(f7123,plain,
( spl17_606
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_606])]) ).
fof(f2980,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_f1664156314l_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_183 ),
inference(superposition,[],[f2585,f2902]) ).
fof(f7121,plain,
( spl17_605
| ~ spl17_110
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2977,f2897,f2593,f7119]) ).
fof(f7119,plain,
( spl17_605
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_605])]) ).
fof(f2977,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_182 ),
inference(superposition,[],[f2594,f2898]) ).
fof(f7117,plain,
( spl17_604
| ~ spl17_106
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2975,f2897,f2576,f7115]) ).
fof(f7115,plain,
( spl17_604
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_604])]) ).
fof(f2975,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_182 ),
inference(superposition,[],[f2577,f2898]) ).
fof(f7113,plain,
( spl17_603
| ~ spl17_108
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2971,f2897,f2584,f7111]) ).
fof(f7111,plain,
( spl17_603
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_603])]) ).
fof(f2971,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_182 ),
inference(superposition,[],[f2585,f2898]) ).
fof(f7109,plain,
( spl17_602
| ~ spl17_110
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2968,f2893,f2593,f7107]) ).
fof(f7107,plain,
( spl17_602
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_602])]) ).
fof(f2968,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_181 ),
inference(superposition,[],[f2594,f2894]) ).
fof(f7105,plain,
( spl17_601
| ~ spl17_106
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2966,f2893,f2576,f7103]) ).
fof(f7103,plain,
( spl17_601
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_601])]) ).
fof(f2966,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_181 ),
inference(superposition,[],[f2577,f2894]) ).
fof(f7101,plain,
( spl17_600
| ~ spl17_108
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2962,f2893,f2584,f7099]) ).
fof(f7099,plain,
( spl17_600
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_600])]) ).
fof(f2962,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| hBOOL(hAPP_f54304608l_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_181 ),
inference(superposition,[],[f2585,f2894]) ).
fof(f7097,plain,
( spl17_599
| ~ spl17_110
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2959,f2889,f2593,f7095]) ).
fof(f7095,plain,
( spl17_599
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_599])]) ).
fof(f2959,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_180 ),
inference(superposition,[],[f2594,f2890]) ).
fof(f7093,plain,
( spl17_598
| ~ spl17_106
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2957,f2889,f2576,f7091]) ).
fof(f7091,plain,
( spl17_598
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_598])]) ).
fof(f2957,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_180 ),
inference(superposition,[],[f2577,f2890]) ).
fof(f7089,plain,
( spl17_597
| ~ spl17_108
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2953,f2889,f2584,f7087]) ).
fof(f7087,plain,
( spl17_597
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_597])]) ).
fof(f2953,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| hBOOL(hAPP_nat_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_180 ),
inference(superposition,[],[f2585,f2890]) ).
fof(f7083,plain,
( spl17_596
| ~ spl17_233
| ~ spl17_362 ),
inference(avatar_split_clause,[],[f4257,f4099,f3195,f7081]) ).
fof(f7081,plain,
( spl17_596
<=> ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_596])]) ).
fof(f4257,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))) )
| ~ spl17_233
| ~ spl17_362 ),
inference(resolution,[],[f4100,f3196]) ).
fof(f7079,plain,
( spl17_595
| spl17_574
| ~ spl17_234
| ~ spl17_362 ),
inference(avatar_split_clause,[],[f4256,f4099,f3199,f6453,f7077]) ).
fof(f3199,plain,
( spl17_234
<=> ! [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,[spl17_234])]) ).
fof(f4256,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))) )
| ~ spl17_234
| ~ spl17_362 ),
inference(resolution,[],[f4100,f3200]) ).
fof(f3200,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)) )
| ~ spl17_234 ),
inference(avatar_component_clause,[],[f3199]) ).
fof(f7075,plain,
( spl17_594
| ~ spl17_231
| ~ spl17_361 ),
inference(avatar_split_clause,[],[f4255,f4095,f3187,f7073]) ).
fof(f7073,plain,
( spl17_594
<=> ! [X0] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_594])]) ).
fof(f3187,plain,
( spl17_231
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_231])]) ).
fof(f4095,plain,
( spl17_361
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_361])]) ).
fof(f4255,plain,
( ! [X0] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X0))) )
| ~ spl17_231
| ~ spl17_361 ),
inference(resolution,[],[f4096,f3188]) ).
fof(f3188,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_231 ),
inference(avatar_component_clause,[],[f3187]) ).
fof(f4096,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_361 ),
inference(avatar_component_clause,[],[f4095]) ).
fof(f6785,plain,
( spl17_593
| ~ spl17_11
| ~ spl17_362
| ~ spl17_423 ),
inference(avatar_split_clause,[],[f6527,f4694,f4099,f2141,f6783]) ).
fof(f6783,plain,
( spl17_593
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_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)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_593])]) ).
fof(f6527,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_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)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_11
| ~ spl17_362
| ~ spl17_423 ),
inference(forward_demodulation,[],[f4100,f4760]) ).
fof(f6781,plain,
( spl17_592
| ~ spl17_11
| ~ spl17_364
| ~ spl17_423 ),
inference(avatar_split_clause,[],[f6525,f4694,f4107,f2141,f6779]) ).
fof(f6779,plain,
( spl17_592
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_592])]) ).
fof(f6525,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_11
| ~ spl17_364
| ~ spl17_423 ),
inference(forward_demodulation,[],[f4108,f4760]) ).
fof(f6775,plain,
( spl17_591
| ~ spl17_10
| ~ spl17_363
| ~ spl17_422 ),
inference(avatar_split_clause,[],[f6514,f4690,f4103,f2137,f6773]) ).
fof(f6773,plain,
( spl17_591
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_591])]) ).
fof(f6514,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_10
| ~ spl17_363
| ~ spl17_422 ),
inference(forward_demodulation,[],[f4104,f4758]) ).
fof(f6771,plain,
( spl17_590
| ~ spl17_10
| ~ spl17_361
| ~ spl17_422 ),
inference(avatar_split_clause,[],[f6513,f4690,f4095,f2137,f6769]) ).
fof(f6769,plain,
( spl17_590
<=> ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_590])]) ).
fof(f6513,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_10
| ~ spl17_361
| ~ spl17_422 ),
inference(forward_demodulation,[],[f4096,f4758]) ).
fof(f6723,plain,
( spl17_589
| ~ spl17_4
| ~ spl17_524 ),
inference(avatar_split_clause,[],[f6243,f5817,f2108,f6721]) ).
fof(f6664,plain,
( spl17_588
| ~ spl17_4
| ~ spl17_523 ),
inference(avatar_split_clause,[],[f6223,f5813,f2108,f6662]) ).
fof(f5813,plain,
( spl17_523
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f759274231e_bool(X1,X0) = collect_pname(hAPP_f759274231e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_523])]) ).
fof(f6223,plain,
( ! [X0] : hAPP_f759274231e_bool(X0,u) = collect_pname(hAPP_f759274231e_bool(X0,u))
| ~ spl17_4
| ~ spl17_523 ),
inference(resolution,[],[f5814,f2110]) ).
fof(f5814,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f759274231e_bool(X1,X0) = collect_pname(hAPP_f759274231e_bool(X1,X0)) )
| ~ spl17_523 ),
inference(avatar_component_clause,[],[f5813]) ).
fof(f6610,plain,
( spl17_587
| ~ spl17_4
| ~ spl17_522 ),
inference(avatar_split_clause,[],[f6203,f5809,f2108,f6608]) ).
fof(f6608,plain,
( spl17_587
<=> ! [X0] : cOMBB_647938656_pname(X0,u) = collect_pname(cOMBB_647938656_pname(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_587])]) ).
fof(f5809,plain,
( spl17_522
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBB_647938656_pname(X1,X0) = collect_pname(cOMBB_647938656_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_522])]) ).
fof(f6203,plain,
( ! [X0] : cOMBB_647938656_pname(X0,u) = collect_pname(cOMBB_647938656_pname(X0,u))
| ~ spl17_4
| ~ spl17_522 ),
inference(resolution,[],[f5810,f2110]) ).
fof(f5810,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBB_647938656_pname(X1,X0) = collect_pname(cOMBB_647938656_pname(X1,X0)) )
| ~ spl17_522 ),
inference(avatar_component_clause,[],[f5809]) ).
fof(f6578,plain,
( spl17_586
| ~ spl17_4
| ~ spl17_521 ),
inference(avatar_split_clause,[],[f6183,f5805,f2108,f6576]) ).
fof(f6576,plain,
( spl17_586
<=> ! [X0] : image_pname_pname(X0,u) = collect_pname(image_pname_pname(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_586])]) ).
fof(f5805,plain,
( spl17_521
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_pname_pname(X1,X0) = collect_pname(image_pname_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_521])]) ).
fof(f6183,plain,
( ! [X0] : image_pname_pname(X0,u) = collect_pname(image_pname_pname(X0,u))
| ~ spl17_4
| ~ spl17_521 ),
inference(resolution,[],[f5806,f2110]) ).
fof(f5806,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_pname_pname(X1,X0) = collect_pname(image_pname_pname(X1,X0)) )
| ~ spl17_521 ),
inference(avatar_component_clause,[],[f5805]) ).
fof(f6545,plain,
( spl17_585
| ~ spl17_4
| ~ spl17_520 ),
inference(avatar_split_clause,[],[f6159,f5801,f2108,f6543]) ).
fof(f6543,plain,
( spl17_585
<=> ! [X0] : image_112932426a_bool(X0,u) = collect_fun_a_bool(image_112932426a_bool(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_585])]) ).
fof(f5801,plain,
( spl17_520
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_112932426a_bool(X1,X0) = collect_fun_a_bool(image_112932426a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_520])]) ).
fof(f6159,plain,
( ! [X0] : image_112932426a_bool(X0,u) = collect_fun_a_bool(image_112932426a_bool(X0,u))
| ~ spl17_4
| ~ spl17_520 ),
inference(resolution,[],[f5802,f2110]) ).
fof(f5802,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_112932426a_bool(X1,X0) = collect_fun_a_bool(image_112932426a_bool(X1,X0)) )
| ~ spl17_520 ),
inference(avatar_component_clause,[],[f5801]) ).
fof(f6540,plain,
( spl17_584
| ~ spl17_4
| ~ spl17_519 ),
inference(avatar_split_clause,[],[f6139,f5797,f2108,f6538]) ).
fof(f5797,plain,
( spl17_519
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f434788991l_bool(X1,X0) = collec1974731493e_bool(hAPP_f434788991l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_519])]) ).
fof(f6139,plain,
( ! [X0] : hAPP_f434788991l_bool(X0,u) = collec1974731493e_bool(hAPP_f434788991l_bool(X0,u))
| ~ spl17_4
| ~ spl17_519 ),
inference(resolution,[],[f5798,f2110]) ).
fof(f5798,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f434788991l_bool(X1,X0) = collec1974731493e_bool(hAPP_f434788991l_bool(X1,X0)) )
| ~ spl17_519 ),
inference(avatar_component_clause,[],[f5797]) ).
fof(f6535,plain,
( spl17_583
| ~ spl17_4
| ~ spl17_518 ),
inference(avatar_split_clause,[],[f6119,f5793,f2108,f6533]) ).
fof(f6533,plain,
( spl17_583
<=> ! [X0] : image_47868345e_bool(X0,u) = collec1974731493e_bool(image_47868345e_bool(X0,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_583])]) ).
fof(f5793,plain,
( spl17_518
<=> ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_47868345e_bool(X1,X0) = collec1974731493e_bool(image_47868345e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_518])]) ).
fof(f6119,plain,
( ! [X0] : image_47868345e_bool(X0,u) = collec1974731493e_bool(image_47868345e_bool(X0,u))
| ~ spl17_4
| ~ spl17_518 ),
inference(resolution,[],[f5794,f2110]) ).
fof(f5794,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_47868345e_bool(X1,X0) = collec1974731493e_bool(image_47868345e_bool(X1,X0)) )
| ~ spl17_518 ),
inference(avatar_component_clause,[],[f5793]) ).
fof(f6531,plain,
( spl17_582
| ~ spl17_3
| ~ spl17_517 ),
inference(avatar_split_clause,[],[f6100,f5789,f2103,f6529]) ).
fof(f6529,plain,
( spl17_582
<=> ! [X0] : image_a_pname(X0,g) = collect_pname(image_a_pname(X0,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_582])]) ).
fof(f5789,plain,
( spl17_517
<=> ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| image_a_pname(X1,X0) = collect_pname(image_a_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_517])]) ).
fof(f6100,plain,
( ! [X0] : image_a_pname(X0,g) = collect_pname(image_a_pname(X0,g))
| ~ spl17_3
| ~ spl17_517 ),
inference(resolution,[],[f5790,f2105]) ).
fof(f5790,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| image_a_pname(X1,X0) = collect_pname(image_a_pname(X1,X0)) )
| ~ spl17_517 ),
inference(avatar_component_clause,[],[f5789]) ).
fof(f6524,plain,
( ~ spl17_98
| ~ spl17_574 ),
inference(avatar_contradiction_clause,[],[f6523]) ).
fof(f6523,plain,
( $false
| ~ spl17_98
| ~ spl17_574 ),
inference(resolution,[],[f6454,f2540]) ).
fof(f2540,plain,
( ! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))
| ~ spl17_98 ),
inference(avatar_component_clause,[],[f2539]) ).
fof(f2539,plain,
( spl17_98
<=> ! [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,[spl17_98])]) ).
fof(f6454,plain,
( ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ spl17_574 ),
inference(avatar_component_clause,[],[f6453]) ).
fof(f6511,plain,
( spl17_581
| ~ spl17_155
| ~ spl17_573 ),
inference(avatar_split_clause,[],[f6434,f6429,f2775,f6509]) ).
fof(f2775,plain,
( spl17_155
<=> ! [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,[spl17_155])]) ).
fof(f6429,plain,
( spl17_573
<=> ! [X0] : ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_573])]) ).
fof(f6434,plain,
( ! [X0] : ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ spl17_155
| ~ spl17_573 ),
inference(resolution,[],[f6430,f2776]) ).
fof(f2776,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
| ~ spl17_155 ),
inference(avatar_component_clause,[],[f2775]) ).
fof(f6430,plain,
( ! [X0] : ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ spl17_573 ),
inference(avatar_component_clause,[],[f6429]) ).
fof(f6507,plain,
( spl17_580
| ~ spl17_110
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2950,f2885,f2593,f6505]) ).
fof(f6505,plain,
( spl17_580
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_580])]) ).
fof(f2950,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_110
| ~ spl17_179 ),
inference(superposition,[],[f2594,f2886]) ).
fof(f6503,plain,
( spl17_579
| ~ spl17_106
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2948,f2885,f2576,f6501]) ).
fof(f6501,plain,
( spl17_579
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_579])]) ).
fof(f2948,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| ~ hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_106
| ~ spl17_179 ),
inference(superposition,[],[f2577,f2886]) ).
fof(f6499,plain,
( spl17_578
| ~ spl17_108
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2944,f2885,f2584,f6497]) ).
fof(f6497,plain,
( spl17_578
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_578])]) ).
fof(f2944,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_108
| ~ spl17_179 ),
inference(superposition,[],[f2585,f2886]) ).
fof(f6478,plain,
( spl17_577
| ~ spl17_113
| ~ spl17_250 ),
inference(avatar_split_clause,[],[f3371,f3367,f2605,f6475]) ).
fof(f6475,plain,
( spl17_577
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_577])]) ).
fof(f3371,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,g)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl17_113
| ~ spl17_250 ),
inference(superposition,[],[f2606,f3369]) ).
fof(f6473,plain,
( spl17_576
| ~ spl17_101
| ~ spl17_191 ),
inference(avatar_split_clause,[],[f3035,f2933,f2555,f6471]) ).
fof(f6471,plain,
( spl17_576
<=> ! [X2,X0,X1] :
( is_bool(hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_576])]) ).
fof(f3035,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1)) )
| ~ spl17_101
| ~ spl17_191 ),
inference(superposition,[],[f2556,f2934]) ).
fof(f6469,plain,
( spl17_575
| ~ spl17_102
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f3033,f2929,f2559,f6467]) ).
fof(f6467,plain,
( spl17_575
<=> ! [X2,X0,X1] :
( is_bool(hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_575])]) ).
fof(f3033,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1)) )
| ~ spl17_102
| ~ spl17_190 ),
inference(superposition,[],[f2560,f2930]) ).
fof(f6455,plain,
( spl17_574
| ~ spl17_192
| ~ spl17_573 ),
inference(avatar_split_clause,[],[f6432,f6429,f2937,f6453]) ).
fof(f2937,plain,
( spl17_192
<=> ! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_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,[spl17_192])]) ).
fof(f6432,plain,
( ! [X0] : ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ spl17_192
| ~ spl17_573 ),
inference(resolution,[],[f6430,f2938]) ).
fof(f2938,plain,
( ! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
| ~ spl17_192 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f6431,plain,
( spl17_572
| spl17_573
| ~ spl17_232
| ~ spl17_361 ),
inference(avatar_split_clause,[],[f4254,f4095,f3191,f6429,f6426]) ).
fof(f3191,plain,
( spl17_232
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_232])]) ).
fof(f4254,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))) )
| ~ spl17_232
| ~ spl17_361 ),
inference(resolution,[],[f4096,f3192]) ).
fof(f3192,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) )
| ~ spl17_232 ),
inference(avatar_component_clause,[],[f3191]) ).
fof(f6424,plain,
( spl17_571
| ~ spl17_52
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f3671,f3633,f2311,f6422]) ).
fof(f3671,plain,
( ! [X0,X1] :
( is_fun_pname_bool(sK10(image_pname_a(X0,X1),X0,X1))
| ~ is_fun_a_bool(image_pname_a(X0,X1)) )
| ~ spl17_52
| ~ spl17_294 ),
inference(resolution,[],[f3634,f2312]) ).
fof(f6420,plain,
( spl17_570
| ~ spl17_113
| ~ spl17_237 ),
inference(avatar_split_clause,[],[f3321,f3271,f2605,f6418]) ).
fof(f6418,plain,
( spl17_570
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_570])]) ).
fof(f3321,plain,
( ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),hAPP_nat_nat(suc,X0)))
| ~ spl17_113
| ~ spl17_237 ),
inference(superposition,[],[f2606,f3272]) ).
fof(f6406,plain,
( ~ spl17_3
| ~ spl17_334
| spl17_569
| ~ spl17_100
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f4459,f4310,f2550,f6403,f3962,f2103]) ).
fof(f4459,plain,
( is_fun_pname_bool(sK9(mgt_call,u,g))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ is_fun_a_bool(g)
| ~ spl17_100
| ~ spl17_379 ),
inference(resolution,[],[f4311,f2552]) ).
fof(f6369,plain,
( spl17_568
| ~ spl17_2
| ~ spl17_511 ),
inference(avatar_split_clause,[],[f6025,f5765,f2098,f6367]) ).
fof(f6367,plain,
( spl17_568
<=> ! [X0] : image_1283814551_pname(X0,finite_finite_pname) = collect_pname(image_1283814551_pname(X0,finite_finite_pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_568])]) ).
fof(f2098,plain,
( spl17_2
<=> is_fun1661590463l_bool(finite_finite_pname) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f5765,plain,
( spl17_511
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| image_1283814551_pname(X1,X0) = collect_pname(image_1283814551_pname(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_511])]) ).
fof(f6025,plain,
( ! [X0] : image_1283814551_pname(X0,finite_finite_pname) = collect_pname(image_1283814551_pname(X0,finite_finite_pname))
| ~ spl17_2
| ~ spl17_511 ),
inference(resolution,[],[f5766,f2100]) ).
fof(f2100,plain,
( is_fun1661590463l_bool(finite_finite_pname)
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f5766,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| image_1283814551_pname(X1,X0) = collect_pname(image_1283814551_pname(X1,X0)) )
| ~ spl17_511 ),
inference(avatar_component_clause,[],[f5765]) ).
fof(f6330,plain,
( spl17_567
| ~ spl17_2
| ~ spl17_510 ),
inference(avatar_split_clause,[],[f6014,f5761,f2098,f6328]) ).
fof(f6328,plain,
( spl17_567
<=> ! [X0] : cOMBS_350070575l_bool(X0,finite_finite_pname) = collec1974731493e_bool(cOMBS_350070575l_bool(X0,finite_finite_pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_567])]) ).
fof(f5761,plain,
( spl17_510
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBS_350070575l_bool(X1,X0) = collec1974731493e_bool(cOMBS_350070575l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_510])]) ).
fof(f6014,plain,
( ! [X0] : cOMBS_350070575l_bool(X0,finite_finite_pname) = collec1974731493e_bool(cOMBS_350070575l_bool(X0,finite_finite_pname))
| ~ spl17_2
| ~ spl17_510 ),
inference(resolution,[],[f5762,f2100]) ).
fof(f5762,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBS_350070575l_bool(X1,X0) = collec1974731493e_bool(cOMBS_350070575l_bool(X1,X0)) )
| ~ spl17_510 ),
inference(avatar_component_clause,[],[f5761]) ).
fof(f6266,plain,
( spl17_566
| ~ spl17_2
| ~ spl17_509 ),
inference(avatar_split_clause,[],[f5999,f5757,f2098,f6264]) ).
fof(f5757,plain,
( spl17_509
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| hAPP_f559147733l_bool(X1,X0) = collec1974731493e_bool(hAPP_f559147733l_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_509])]) ).
fof(f5999,plain,
( ! [X0] : hAPP_f559147733l_bool(X0,finite_finite_pname) = collec1974731493e_bool(hAPP_f559147733l_bool(X0,finite_finite_pname))
| ~ spl17_2
| ~ spl17_509 ),
inference(resolution,[],[f5758,f2100]) ).
fof(f5758,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| hAPP_f559147733l_bool(X1,X0) = collec1974731493e_bool(hAPP_f559147733l_bool(X1,X0)) )
| ~ spl17_509 ),
inference(avatar_component_clause,[],[f5757]) ).
fof(f6164,plain,
( spl17_565
| ~ spl17_2
| ~ spl17_508 ),
inference(avatar_split_clause,[],[f5988,f5753,f2098,f6162]) ).
fof(f6162,plain,
( spl17_565
<=> ! [X0] : cOMBB_307249310e_bool(X0,finite_finite_pname) = collec1974731493e_bool(cOMBB_307249310e_bool(X0,finite_finite_pname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_565])]) ).
fof(f5753,plain,
( spl17_508
<=> ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBB_307249310e_bool(X1,X0) = collec1974731493e_bool(cOMBB_307249310e_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_508])]) ).
fof(f5988,plain,
( ! [X0] : cOMBB_307249310e_bool(X0,finite_finite_pname) = collec1974731493e_bool(cOMBB_307249310e_bool(X0,finite_finite_pname))
| ~ spl17_2
| ~ spl17_508 ),
inference(resolution,[],[f5754,f2100]) ).
fof(f5754,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBB_307249310e_bool(X1,X0) = collec1974731493e_bool(cOMBB_307249310e_bool(X1,X0)) )
| ~ spl17_508 ),
inference(avatar_component_clause,[],[f5753]) ).
fof(f6011,plain,
( spl17_564
| ~ spl17_1
| ~ spl17_507 ),
inference(avatar_split_clause,[],[f5984,f5749,f2093,f6009]) ).
fof(f2093,plain,
( spl17_1
<=> is_pname(pn) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f5984,plain,
( ! [X0] : hAPP_p61793385e_bool(X0,pn) = collect_pname(hAPP_p61793385e_bool(X0,pn))
| ~ spl17_1
| ~ spl17_507 ),
inference(resolution,[],[f5750,f2095]) ).
fof(f2095,plain,
( is_pname(pn)
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f2093]) ).
fof(f5978,plain,
( spl17_563
| ~ spl17_50
| ~ spl17_261 ),
inference(avatar_split_clause,[],[f3549,f3413,f2303,f5976]) ).
fof(f3549,plain,
( ! [X0] : hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,sK3(hAPP_nat_nat(suc,X0)))
| ~ spl17_50
| ~ spl17_261 ),
inference(resolution,[],[f3414,f2304]) ).
fof(f5974,plain,
( spl17_562
| ~ spl17_104
| ~ spl17_259 ),
inference(avatar_split_clause,[],[f3542,f3405,f2568,f5972]) ).
fof(f5972,plain,
( spl17_562
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_562])]) ).
fof(f3542,plain,
( ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))),X0))
| ~ spl17_104
| ~ spl17_259 ),
inference(resolution,[],[f3406,f2569]) ).
fof(f5970,plain,
( spl17_561
| ~ spl17_75
| ~ spl17_247 ),
inference(avatar_split_clause,[],[f3364,f3314,f2403,f5968]) ).
fof(f5968,plain,
( spl17_561
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X2),X1))
| ~ is_bool(hAPP_f1664156314l_bool(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_561])]) ).
fof(f2403,plain,
( spl17_75
<=> ! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f3364,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X2),X1))
| ~ is_bool(hAPP_f1664156314l_bool(X2,X1)) )
| ~ spl17_75
| ~ spl17_247 ),
inference(superposition,[],[f2404,f3315]) ).
fof(f2404,plain,
( ! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) )
| ~ spl17_75 ),
inference(avatar_component_clause,[],[f2403]) ).
fof(f5966,plain,
( spl17_560
| ~ spl17_75
| ~ spl17_246 ),
inference(avatar_split_clause,[],[f3360,f3310,f2403,f5964]) ).
fof(f5964,plain,
( spl17_560
<=> ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X2),X1))
| ~ is_bool(hAPP_fun_a_bool_bool(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_560])]) ).
fof(f3360,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X2),X1))
| ~ is_bool(hAPP_fun_a_bool_bool(X2,X1)) )
| ~ spl17_75
| ~ spl17_246 ),
inference(superposition,[],[f2404,f3311]) ).
fof(f5962,plain,
( spl17_559
| ~ spl17_75
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3346,f3298,f2403,f5960]) ).
fof(f5960,plain,
( spl17_559
<=> ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(cOMBS_568398431l_bool(X0,X2),X1))
| ~ is_bool(hAPP_pname_bool(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_559])]) ).
fof(f3346,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(cOMBS_568398431l_bool(X0,X2),X1))
| ~ is_bool(hAPP_pname_bool(X2,X1)) )
| ~ spl17_75
| ~ spl17_243 ),
inference(superposition,[],[f2404,f3299]) ).
fof(f5958,plain,
( spl17_558
| ~ spl17_75
| ~ spl17_242 ),
inference(avatar_split_clause,[],[f3340,f3294,f2403,f5956]) ).
fof(f5956,plain,
( spl17_558
<=> ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(cOMBS_a_bool_bool(X0,X2),X1))
| ~ is_bool(hAPP_a_bool(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_558])]) ).
fof(f3340,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(cOMBS_a_bool_bool(X0,X2),X1))
| ~ is_bool(hAPP_a_bool(X2,X1)) )
| ~ spl17_75
| ~ spl17_242 ),
inference(superposition,[],[f2404,f3295]) ).
fof(f5954,plain,
( spl17_557
| ~ spl17_165
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f3206,f3074,f2815,f5952]) ).
fof(f5952,plain,
( spl17_557
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(X0,sK0(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_557])]) ).
fof(f3206,plain,
( ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_nat_bool(X0,sK0(X0,X1))) )
| ~ spl17_165
| ~ spl17_203 ),
inference(resolution,[],[f3075,f2816]) ).
fof(f5950,plain,
( spl17_556
| ~ spl17_110
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3026,f2917,f2593,f5948]) ).
fof(f3026,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_110
| ~ spl17_187 ),
inference(superposition,[],[f2594,f2918]) ).
fof(f5946,plain,
( spl17_555
| ~ spl17_106
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3024,f2917,f2576,f5944]) ).
fof(f5944,plain,
( spl17_555
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_555])]) ).
fof(f3024,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X0) )
| ~ spl17_106
| ~ spl17_187 ),
inference(superposition,[],[f2577,f2918]) ).
fof(f5942,plain,
( spl17_554
| ~ spl17_108
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3020,f2917,f2584,f5940]) ).
fof(f5940,plain,
( spl17_554
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_554])]) ).
fof(f3020,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_108
| ~ spl17_187 ),
inference(superposition,[],[f2585,f2918]) ).
fof(f5938,plain,
( spl17_553
| ~ spl17_75
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3018,f2917,f2403,f5936]) ).
fof(f5936,plain,
( spl17_553
<=> ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2))
| ~ is_bool(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_553])]) ).
fof(f3018,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2))
| ~ is_bool(hAPP_a_bool(X1,X2)) )
| ~ spl17_75
| ~ spl17_187 ),
inference(superposition,[],[f2404,f2918]) ).
fof(f5934,plain,
( spl17_552
| ~ spl17_54
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3017,f2917,f2319,f5932]) ).
fof(f5932,plain,
( spl17_552
<=> ! [X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(fNot,X0),X1))
| hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_552])]) ).
fof(f2319,plain,
( spl17_54
<=> ! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f3017,plain,
( ! [X0,X1] :
( hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(fNot,X0),X1))
| hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_54
| ~ spl17_187 ),
inference(superposition,[],[f2320,f2918]) ).
fof(f2320,plain,
( ! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) )
| ~ spl17_54 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f5930,plain,
( spl17_551
| ~ spl17_55
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f3016,f2917,f2323,f5928]) ).
fof(f5928,plain,
( spl17_551
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(fNot,X0),X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_551])]) ).
fof(f2323,plain,
( spl17_55
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f3016,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_a_bool(cOMBB_bool_bool_a(fNot,X0),X1))
| ~ hBOOL(hAPP_a_bool(X0,X1)) )
| ~ spl17_55
| ~ spl17_187 ),
inference(superposition,[],[f2324,f2918]) ).
fof(f2324,plain,
( ! [X0] :
( ~ hBOOL(hAPP_bool_bool(fNot,X0))
| ~ hBOOL(X0) )
| ~ spl17_55 ),
inference(avatar_component_clause,[],[f2323]) ).
fof(f5926,plain,
( spl17_550
| ~ spl17_110
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3014,f2913,f2593,f5924]) ).
fof(f3014,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fconj,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_110
| ~ spl17_186 ),
inference(superposition,[],[f2594,f2914]) ).
fof(f5922,plain,
( spl17_549
| ~ spl17_106
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3012,f2913,f2576,f5920]) ).
fof(f5920,plain,
( spl17_549
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_549])]) ).
fof(f3012,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X0) )
| ~ spl17_106
| ~ spl17_186 ),
inference(superposition,[],[f2577,f2914]) ).
fof(f5918,plain,
( spl17_548
| ~ spl17_108
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3008,f2913,f2584,f5916]) ).
fof(f5916,plain,
( spl17_548
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_548])]) ).
fof(f3008,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(hAPP_b589554111l_bool(fimplies,X0),X1),X2))
| hBOOL(X0) )
| ~ spl17_108
| ~ spl17_186 ),
inference(superposition,[],[f2585,f2914]) ).
fof(f5914,plain,
( spl17_547
| ~ spl17_75
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3006,f2913,f2403,f5912]) ).
fof(f5912,plain,
( spl17_547
<=> ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2))
| ~ is_bool(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_547])]) ).
fof(f3006,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2))
| ~ is_bool(hAPP_pname_bool(X1,X2)) )
| ~ spl17_75
| ~ spl17_186 ),
inference(superposition,[],[f2404,f2914]) ).
fof(f5910,plain,
( spl17_546
| ~ spl17_54
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3005,f2913,f2319,f5908]) ).
fof(f5908,plain,
( spl17_546
<=> ! [X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(fNot,X0),X1))
| hBOOL(hAPP_pname_bool(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_546])]) ).
fof(f3005,plain,
( ! [X0,X1] :
( hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(fNot,X0),X1))
| hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_54
| ~ spl17_186 ),
inference(superposition,[],[f2320,f2914]) ).
fof(f5906,plain,
( spl17_545
| ~ spl17_55
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f3004,f2913,f2323,f5904]) ).
fof(f3004,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_pname_bool(cOMBB_647938656_pname(fNot,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X0,X1)) )
| ~ spl17_55
| ~ spl17_186 ),
inference(superposition,[],[f2324,f2914]) ).
fof(f5902,plain,
( spl17_544
| ~ spl17_89
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f3003,f2909,f2459,f5900]) ).
fof(f5900,plain,
( spl17_544
<=> ! [X0,X1] : hBOOL(hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(fequal_a,X0),X1),hAPP_pname_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_544])]) ).
fof(f2459,plain,
( spl17_89
<=> ! [X1] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
fof(f3003,plain,
( ! [X0,X1] : hBOOL(hAPP_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(fequal_a,X0),X1),hAPP_pname_a(X0,X1)))
| ~ spl17_89
| ~ spl17_185 ),
inference(superposition,[],[f2460,f2910]) ).
fof(f2460,plain,
( ! [X1] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1))
| ~ spl17_89 ),
inference(avatar_component_clause,[],[f2459]) ).
fof(f5898,plain,
( spl17_543
| ~ spl17_59
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f3002,f2909,f2339,f5896]) ).
fof(f5896,plain,
( spl17_543
<=> ! [X2,X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2))
| ~ is_a(hAPP_pname_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_543])]) ).
fof(f2339,plain,
( spl17_59
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f3002,plain,
( ! [X2,X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2))
| ~ is_a(hAPP_pname_a(X1,X2)) )
| ~ spl17_59
| ~ spl17_185 ),
inference(superposition,[],[f2340,f2910]) ).
fof(f2340,plain,
( ! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl17_59 ),
inference(avatar_component_clause,[],[f2339]) ).
fof(f5894,plain,
( spl17_542
| ~ spl17_109
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f3001,f2905,f2588,f5892]) ).
fof(f5892,plain,
( spl17_542
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_542])]) ).
fof(f3001,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_184 ),
inference(superposition,[],[f2589,f2906]) ).
fof(f5890,plain,
( spl17_541
| ~ spl17_107
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2997,f2905,f2580,f5888]) ).
fof(f5888,plain,
( spl17_541
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_541])]) ).
fof(f2997,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_184 ),
inference(superposition,[],[f2581,f2906]) ).
fof(f5886,plain,
( spl17_540
| ~ spl17_105
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2995,f2905,f2572,f5884]) ).
fof(f5884,plain,
( spl17_540
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_540])]) ).
fof(f2995,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_p393069232l_bool(cOMBB_675860798_pname(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_184 ),
inference(superposition,[],[f2573,f2906]) ).
fof(f5882,plain,
( spl17_539
| ~ spl17_109
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2987,f2901,f2588,f5880]) ).
fof(f5880,plain,
( spl17_539
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_539])]) ).
fof(f2987,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_183 ),
inference(superposition,[],[f2589,f2902]) ).
fof(f5878,plain,
( spl17_538
| ~ spl17_107
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2983,f2901,f2580,f5876]) ).
fof(f5876,plain,
( spl17_538
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_538])]) ).
fof(f2983,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_183 ),
inference(superposition,[],[f2581,f2902]) ).
fof(f5874,plain,
( spl17_537
| ~ spl17_105
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2981,f2901,f2572,f5872]) ).
fof(f5872,plain,
( spl17_537
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_537])]) ).
fof(f2981,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_183 ),
inference(superposition,[],[f2573,f2902]) ).
fof(f5870,plain,
( spl17_536
| ~ spl17_109
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2978,f2897,f2588,f5868]) ).
fof(f5868,plain,
( spl17_536
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_536])]) ).
fof(f2978,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_182 ),
inference(superposition,[],[f2589,f2898]) ).
fof(f5866,plain,
( spl17_535
| ~ spl17_107
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2974,f2897,f2580,f5864]) ).
fof(f5864,plain,
( spl17_535
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_535])]) ).
fof(f2974,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_182 ),
inference(superposition,[],[f2581,f2898]) ).
fof(f5862,plain,
( spl17_534
| ~ spl17_105
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2972,f2897,f2572,f5860]) ).
fof(f5860,plain,
( spl17_534
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_534])]) ).
fof(f2972,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f198738859l_bool(cOMBB_338059395a_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_182 ),
inference(superposition,[],[f2573,f2898]) ).
fof(f5858,plain,
( spl17_533
| ~ spl17_109
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2969,f2893,f2588,f5856]) ).
fof(f5856,plain,
( spl17_533
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_533])]) ).
fof(f2969,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_181 ),
inference(superposition,[],[f2589,f2894]) ).
fof(f5854,plain,
( spl17_532
| ~ spl17_107
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2965,f2893,f2580,f5852]) ).
fof(f5852,plain,
( spl17_532
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_532])]) ).
fof(f2965,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_181 ),
inference(superposition,[],[f2581,f2894]) ).
fof(f5850,plain,
( spl17_531
| ~ spl17_105
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2963,f2893,f2572,f5848]) ).
fof(f5848,plain,
( spl17_531
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_531])]) ).
fof(f2963,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_f1748468828l_bool(cOMBB_444170502t_bool(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_181 ),
inference(superposition,[],[f2573,f2894]) ).
fof(f5846,plain,
( spl17_530
| ~ spl17_109
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2960,f2889,f2588,f5844]) ).
fof(f5844,plain,
( spl17_530
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_530])]) ).
fof(f2960,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_180 ),
inference(superposition,[],[f2589,f2890]) ).
fof(f5842,plain,
( spl17_529
| ~ spl17_107
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2956,f2889,f2580,f5840]) ).
fof(f5840,plain,
( spl17_529
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_529])]) ).
fof(f2956,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_180 ),
inference(superposition,[],[f2581,f2890]) ).
fof(f5838,plain,
( spl17_528
| ~ spl17_105
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2954,f2889,f2572,f5836]) ).
fof(f5836,plain,
( spl17_528
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_528])]) ).
fof(f2954,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_180 ),
inference(superposition,[],[f2573,f2890]) ).
fof(f5834,plain,
( spl17_527
| ~ spl17_109
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2951,f2885,f2588,f5832]) ).
fof(f5832,plain,
( spl17_527
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_527])]) ).
fof(f2951,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fconj,X0),X1),X2))
| hBOOL(X2) )
| ~ spl17_109
| ~ spl17_179 ),
inference(superposition,[],[f2589,f2886]) ).
fof(f5830,plain,
( spl17_526
| ~ spl17_107
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2947,f2885,f2580,f5828]) ).
fof(f5828,plain,
( spl17_526
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_526])]) ).
fof(f2947,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_107
| ~ spl17_179 ),
inference(superposition,[],[f2581,f2886]) ).
fof(f5823,plain,
( spl17_525
| ~ spl17_105
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2945,f2885,f2572,f5821]) ).
fof(f5821,plain,
( spl17_525
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_525])]) ).
fof(f2945,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(fimplies,X0),X1),X2))
| ~ hBOOL(X2) )
| ~ spl17_105
| ~ spl17_179 ),
inference(superposition,[],[f2573,f2886]) ).
fof(f5819,plain,
( spl17_524
| ~ spl17_58
| ~ spl17_87 ),
inference(avatar_split_clause,[],[f2526,f2451,f2335,f5817]) ).
fof(f2451,plain,
( spl17_87
<=> ! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
fof(f2526,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBS_568398431l_bool(X1,X0) = collect_pname(cOMBS_568398431l_bool(X1,X0)) )
| ~ spl17_58
| ~ spl17_87 ),
inference(resolution,[],[f2452,f2336]) ).
fof(f2452,plain,
( ! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_87 ),
inference(avatar_component_clause,[],[f2451]) ).
fof(f5815,plain,
( spl17_523
| ~ spl17_58
| ~ spl17_86 ),
inference(avatar_split_clause,[],[f2525,f2447,f2335,f5813]) ).
fof(f2447,plain,
( spl17_86
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f2525,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f759274231e_bool(X1,X0) = collect_pname(hAPP_f759274231e_bool(X1,X0)) )
| ~ spl17_58
| ~ spl17_86 ),
inference(resolution,[],[f2448,f2336]) ).
fof(f2448,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_86 ),
inference(avatar_component_clause,[],[f2447]) ).
fof(f5811,plain,
( spl17_522
| ~ spl17_58
| ~ spl17_85 ),
inference(avatar_split_clause,[],[f2524,f2443,f2335,f5809]) ).
fof(f2443,plain,
( spl17_85
<=> ! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f2524,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| cOMBB_647938656_pname(X1,X0) = collect_pname(cOMBB_647938656_pname(X1,X0)) )
| ~ spl17_58
| ~ spl17_85 ),
inference(resolution,[],[f2444,f2336]) ).
fof(f2444,plain,
( ! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_85 ),
inference(avatar_component_clause,[],[f2443]) ).
fof(f5807,plain,
( spl17_521
| ~ spl17_58
| ~ spl17_84 ),
inference(avatar_split_clause,[],[f2523,f2439,f2335,f5805]) ).
fof(f2439,plain,
( spl17_84
<=> ! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f2523,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_pname_pname(X1,X0) = collect_pname(image_pname_pname(X1,X0)) )
| ~ spl17_58
| ~ spl17_84 ),
inference(resolution,[],[f2440,f2336]) ).
fof(f2440,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_84 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f5803,plain,
( spl17_520
| ~ spl17_57
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f2521,f2435,f2331,f5801]) ).
fof(f2435,plain,
( spl17_83
<=> ! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f2521,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_112932426a_bool(X1,X0) = collect_fun_a_bool(image_112932426a_bool(X1,X0)) )
| ~ spl17_57
| ~ spl17_83 ),
inference(resolution,[],[f2436,f2332]) ).
fof(f2436,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_83 ),
inference(avatar_component_clause,[],[f2435]) ).
fof(f5799,plain,
( spl17_519
| ~ spl17_56
| ~ spl17_82 ),
inference(avatar_split_clause,[],[f2520,f2431,f2327,f5797]) ).
fof(f2431,plain,
( spl17_82
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f2520,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| hAPP_f434788991l_bool(X1,X0) = collec1974731493e_bool(hAPP_f434788991l_bool(X1,X0)) )
| ~ spl17_56
| ~ spl17_82 ),
inference(resolution,[],[f2432,f2328]) ).
fof(f2432,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_82 ),
inference(avatar_component_clause,[],[f2431]) ).
fof(f5795,plain,
( spl17_518
| ~ spl17_56
| ~ spl17_81 ),
inference(avatar_split_clause,[],[f2519,f2427,f2327,f5793]) ).
fof(f2427,plain,
( spl17_81
<=> ! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f2519,plain,
( ! [X0,X1] :
( ~ is_fun_pname_bool(X0)
| image_47868345e_bool(X1,X0) = collec1974731493e_bool(image_47868345e_bool(X1,X0)) )
| ~ spl17_56
| ~ spl17_81 ),
inference(resolution,[],[f2428,f2328]) ).
fof(f2428,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) )
| ~ spl17_81 ),
inference(avatar_component_clause,[],[f2427]) ).
fof(f5791,plain,
( spl17_517
| ~ spl17_58
| ~ spl17_80 ),
inference(avatar_split_clause,[],[f2518,f2423,f2335,f5789]) ).
fof(f2423,plain,
( spl17_80
<=> ! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f2518,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X0)
| image_a_pname(X1,X0) = collect_pname(image_a_pname(X1,X0)) )
| ~ spl17_58
| ~ spl17_80 ),
inference(resolution,[],[f2424,f2336]) ).
fof(f2424,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl17_80 ),
inference(avatar_component_clause,[],[f2423]) ).
fof(f5787,plain,
( spl17_516
| ~ spl17_58
| ~ spl17_74 ),
inference(avatar_split_clause,[],[f2517,f2399,f2335,f5785]) ).
fof(f2399,plain,
( spl17_74
<=> ! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f2517,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| image_1854862208_pname(X1,X0) = collect_pname(image_1854862208_pname(X1,X0)) )
| ~ spl17_58
| ~ spl17_74 ),
inference(resolution,[],[f2400,f2336]) ).
fof(f2400,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl17_74 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f5783,plain,
( spl17_515
| ~ spl17_3
| ~ spl17_465 ),
inference(avatar_split_clause,[],[f5729,f5198,f2103,f5781]) ).
fof(f5198,plain,
( spl17_465
<=> ! [X0,X1] :
( hAPP_f1631501043l_bool(X0,X1) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_465])]) ).
fof(f5729,plain,
( ! [X0] : hAPP_f1631501043l_bool(X0,g) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,g))
| ~ spl17_3
| ~ spl17_465 ),
inference(resolution,[],[f5199,f2105]) ).
fof(f5199,plain,
( ! [X0,X1] :
( ~ is_fun_a_bool(X1)
| hAPP_f1631501043l_bool(X0,X1) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1)) )
| ~ spl17_465 ),
inference(avatar_component_clause,[],[f5198]) ).
fof(f5779,plain,
( spl17_514
| ~ spl17_57
| ~ spl17_71 ),
inference(avatar_split_clause,[],[f2511,f2387,f2331,f5777]) ).
fof(f2387,plain,
( spl17_71
<=> ! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f2511,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBS_1035972772l_bool(X1,X0) = collect_fun_a_bool(cOMBS_1035972772l_bool(X1,X0)) )
| ~ spl17_57
| ~ spl17_71 ),
inference(resolution,[],[f2388,f2332]) ).
fof(f2388,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl17_71 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f5775,plain,
( spl17_513
| ~ spl17_57
| ~ spl17_70 ),
inference(avatar_split_clause,[],[f2510,f2383,f2331,f5773]) ).
fof(f2383,plain,
( spl17_70
<=> ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f2510,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| hAPP_f2117159681l_bool(X1,X0) = collect_fun_a_bool(hAPP_f2117159681l_bool(X1,X0)) )
| ~ spl17_57
| ~ spl17_70 ),
inference(resolution,[],[f2384,f2332]) ).
fof(f2384,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl17_70 ),
inference(avatar_component_clause,[],[f2383]) ).
fof(f5771,plain,
( spl17_512
| ~ spl17_57
| ~ spl17_69 ),
inference(avatar_split_clause,[],[f2509,f2379,f2331,f5769]) ).
fof(f2379,plain,
( spl17_69
<=> ! [X0,X1] :
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f2509,plain,
( ! [X0,X1] :
( ~ is_fun949378684l_bool(X0)
| cOMBB_2140588453a_bool(X1,X0) = collect_fun_a_bool(cOMBB_2140588453a_bool(X1,X0)) )
| ~ spl17_57
| ~ spl17_69 ),
inference(resolution,[],[f2380,f2332]) ).
fof(f2380,plain,
( ! [X0,X1] :
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl17_69 ),
inference(avatar_component_clause,[],[f2379]) ).
fof(f5767,plain,
( spl17_511
| ~ spl17_58
| ~ spl17_68 ),
inference(avatar_split_clause,[],[f2508,f2375,f2335,f5765]) ).
fof(f2375,plain,
( spl17_68
<=> ! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f2508,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| image_1283814551_pname(X1,X0) = collect_pname(image_1283814551_pname(X1,X0)) )
| ~ spl17_58
| ~ spl17_68 ),
inference(resolution,[],[f2376,f2336]) ).
fof(f2376,plain,
( ! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl17_68 ),
inference(avatar_component_clause,[],[f2375]) ).
fof(f5763,plain,
( spl17_510
| ~ spl17_56
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f2507,f2363,f2327,f5761]) ).
fof(f2363,plain,
( spl17_65
<=> ! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f2507,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBS_350070575l_bool(X1,X0) = collec1974731493e_bool(cOMBS_350070575l_bool(X1,X0)) )
| ~ spl17_56
| ~ spl17_65 ),
inference(resolution,[],[f2364,f2328]) ).
fof(f2364,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl17_65 ),
inference(avatar_component_clause,[],[f2363]) ).
fof(f5759,plain,
( spl17_509
| ~ spl17_56
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f2506,f2359,f2327,f5757]) ).
fof(f2359,plain,
( spl17_64
<=> ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f2506,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| hAPP_f559147733l_bool(X1,X0) = collec1974731493e_bool(hAPP_f559147733l_bool(X1,X0)) )
| ~ spl17_56
| ~ spl17_64 ),
inference(resolution,[],[f2360,f2328]) ).
fof(f2360,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl17_64 ),
inference(avatar_component_clause,[],[f2359]) ).
fof(f5755,plain,
( spl17_508
| ~ spl17_56
| ~ spl17_63 ),
inference(avatar_split_clause,[],[f2500,f2355,f2327,f5753]) ).
fof(f2355,plain,
( spl17_63
<=> ! [X0,X1] :
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f2500,plain,
( ! [X0,X1] :
( ~ is_fun1661590463l_bool(X0)
| cOMBB_307249310e_bool(X1,X0) = collec1974731493e_bool(cOMBB_307249310e_bool(X1,X0)) )
| ~ spl17_56
| ~ spl17_63 ),
inference(resolution,[],[f2356,f2328]) ).
fof(f2356,plain,
( ! [X0,X1] :
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl17_63 ),
inference(avatar_component_clause,[],[f2355]) ).
fof(f5751,plain,
( spl17_507
| ~ spl17_58
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f2499,f2351,f2335,f5749]) ).
fof(f2351,plain,
( spl17_62
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f2499,plain,
( ! [X0,X1] :
( ~ is_pname(X0)
| hAPP_p61793385e_bool(X1,X0) = collect_pname(hAPP_p61793385e_bool(X1,X0)) )
| ~ spl17_58
| ~ spl17_62 ),
inference(resolution,[],[f2352,f2336]) ).
fof(f2352,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) )
| ~ spl17_62 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f5747,plain,
( spl17_506
| ~ spl17_58
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f2498,f2343,f2335,f5745]) ).
fof(f2343,plain,
( spl17_60
<=> ! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f2498,plain,
( ! [X0,X1] :
( ~ is_a(X0)
| hAPP_a93125764e_bool(X1,X0) = collect_pname(hAPP_a93125764e_bool(X1,X0)) )
| ~ spl17_58
| ~ spl17_60 ),
inference(resolution,[],[f2344,f2336]) ).
fof(f2344,plain,
( ! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl17_60 ),
inference(avatar_component_clause,[],[f2343]) ).
fof(f5743,plain,
( spl17_505
| ~ spl17_35
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2489,f2335,f2238,f5740]) ).
fof(f5740,plain,
( spl17_505
<=> undefi17486888e_bool(fun(pname,bool)) = collect_pname(undefi17486888e_bool(fun(pname,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_505])]) ).
fof(f2238,plain,
( spl17_35
<=> is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f2489,plain,
( undefi17486888e_bool(fun(pname,bool)) = collect_pname(undefi17486888e_bool(fun(pname,bool)))
| ~ spl17_35
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2240]) ).
fof(f2240,plain,
( is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool)))
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f5633,plain,
spl17_504,
inference(avatar_split_clause,[],[f2068,f5631]) ).
fof(f5629,plain,
spl17_503,
inference(avatar_split_clause,[],[f2067,f5627]) ).
fof(f5612,plain,
( spl17_502
| ~ spl17_1
| ~ spl17_453 ),
inference(avatar_split_clause,[],[f5507,f5043,f2093,f5610]) ).
fof(f5610,plain,
( spl17_502
<=> ! [X0] : hAPP_p338031245l_bool(X0,pn) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_502])]) ).
fof(f5507,plain,
( ! [X0] : hAPP_p338031245l_bool(X0,pn) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,pn))
| ~ spl17_1
| ~ spl17_453 ),
inference(resolution,[],[f5044,f2095]) ).
fof(f5608,plain,
spl17_501,
inference(avatar_split_clause,[],[f1938,f5606]) ).
fof(f5606,plain,
( spl17_501
<=> ! [X2,X0,X1] :
( X0 = X2
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_501])]) ).
fof(f1938,plain,
! [X2,X0,X1] :
( X0 = X2
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ),
inference(definition_unfolding,[],[f1795,f1384,f1384]) ).
fof(f1795,plain,
! [X2,X0,X1] :
( X0 = X2
| insert_pname(X1,X0) != insert_pname(X1,X2)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f1258,plain,
! [X0,X1,X2] :
( ( ( insert_pname(X1,X0) = insert_pname(X1,X2)
| X0 != X2 )
& ( X0 = X2
| insert_pname(X1,X0) != insert_pname(X1,X2) ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ),
inference(nnf_transformation,[],[f1164]) ).
fof(f1164,plain,
! [X0,X1,X2] :
( ( insert_pname(X1,X0) = insert_pname(X1,X2)
<=> X0 = X2 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f1163]) ).
fof(f1163,plain,
! [X0,X1,X2] :
( ( insert_pname(X1,X0) = insert_pname(X1,X2)
<=> X0 = X2 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f797]) ).
fof(f797,plain,
! [X0,X1,X2] :
( ( is_fun_pname_bool(X2)
& is_fun_pname_bool(X0) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
=> ( insert_pname(X1,X0) = insert_pname(X1,X2)
<=> X0 = X2 ) ) ) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X9,X10,X4] :
( ( is_fun_pname_bool(X4)
& is_fun_pname_bool(X9) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9))
=> ( insert_pname(X10,X4) = insert_pname(X10,X9)
<=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5604,plain,
spl17_500,
inference(avatar_split_clause,[],[f1936,f5602]) ).
fof(f5602,plain,
( spl17_500
<=> ! [X2,X0,X1] :
( X0 = X2
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_500])]) ).
fof(f1936,plain,
! [X2,X0,X1] :
( X0 = X2
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ),
inference(definition_unfolding,[],[f1793,f1386,f1386]) ).
fof(f1793,plain,
! [X2,X0,X1] :
( X0 = X2
| insert_a(X1,X0) != insert_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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f1257,plain,
! [X0,X1,X2] :
( ( ( insert_a(X1,X0) = insert_a(X1,X2)
| X0 != X2 )
& ( X0 = X2
| insert_a(X1,X0) != insert_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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ),
inference(nnf_transformation,[],[f1162]) ).
fof(f1162,plain,
! [X0,X1,X2] :
( ( insert_a(X1,X0) = insert_a(X1,X2)
<=> X0 = 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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f1161]) ).
fof(f1161,plain,
! [X0,X1,X2] :
( ( insert_a(X1,X0) = insert_a(X1,X2)
<=> X0 = 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),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f796]) ).
fof(f796,plain,
! [X0,X1,X2] :
( ( is_fun_a_bool(X2)
& is_fun_a_bool(X0) )
=> ( ~ 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))
=> ( insert_a(X1,X0) = insert_a(X1,X2)
<=> X0 = X2 ) ) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X9,X10,X4] :
( ( is_fun_a_bool(X4)
& is_fun_a_bool(X9) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X4))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X10),X9))
=> ( insert_a(X10,X4) = insert_a(X10,X9)
<=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5585,plain,
( spl17_499
| ~ spl17_11
| ~ spl17_423
| ~ spl17_498 ),
inference(avatar_split_clause,[],[f5581,f5577,f4694,f2141,f5583]) ).
fof(f5577,plain,
( spl17_498
<=> ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_498])]) ).
fof(f5581,plain,
( ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ spl17_11
| ~ spl17_423
| ~ spl17_498 ),
inference(forward_demodulation,[],[f5580,f4760]) ).
fof(f5580,plain,
( ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2))
| ~ spl17_11
| ~ spl17_423
| ~ spl17_498 ),
inference(forward_demodulation,[],[f5578,f4760]) ).
fof(f5578,plain,
( ! [X2,X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X2)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))
| ~ spl17_498 ),
inference(avatar_component_clause,[],[f5577]) ).
fof(f5579,plain,
spl17_498,
inference(avatar_split_clause,[],[f2066,f5577]) ).
fof(f5573,plain,
( spl17_497
| ~ spl17_11
| ~ spl17_423
| ~ spl17_496 ),
inference(avatar_split_clause,[],[f5569,f5565,f4694,f2141,f5571]) ).
fof(f5571,plain,
( spl17_497
<=> ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)
| X0 = X2
| 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,[spl17_497])]) ).
fof(f5565,plain,
( spl17_496
<=> ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))
| X0 = X2
| 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,[spl17_496])]) ).
fof(f5569,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X0) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)
| X0 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_496 ),
inference(forward_demodulation,[],[f5568,f4760]) ).
fof(f5568,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)
| X0 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_496 ),
inference(forward_demodulation,[],[f5566,f4760]) ).
fof(f5566,plain,
( ! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))
| X0 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_496 ),
inference(avatar_component_clause,[],[f5565]) ).
fof(f5567,plain,
spl17_496,
inference(avatar_split_clause,[],[f2071,f5565]) ).
fof(f2071,plain,
! [X2,X0,X1] :
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))
| X0 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(forward_demodulation,[],[f2070,f1307]) ).
fof(f2070,plain,
! [X2,X0,X1] :
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))
| X0 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(forward_demodulation,[],[f1903,f1307]) ).
fof(f1903,plain,
! [X2,X0,X1] :
( X0 = X2
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))) != collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(definition_unfolding,[],[f1735,f1382,f1382]) ).
fof(f1735,plain,
! [X2,X0,X1] :
( X0 = X2
| insert_nat(X1,X0) != insert_nat(X1,X2)
| 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,[],[f1243]) ).
fof(f1243,plain,
! [X0,X1,X2] :
( ( ( insert_nat(X1,X0) = insert_nat(X1,X2)
| X0 != X2 )
& ( X0 = X2
| insert_nat(X1,X0) != insert_nat(X1,X2) ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(nnf_transformation,[],[f1091]) ).
fof(f1091,plain,
! [X0,X1,X2] :
( ( insert_nat(X1,X0) = insert_nat(X1,X2)
<=> X0 = X2 )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(flattening,[],[f1090]) ).
fof(f1090,plain,
! [X0,X1,X2] :
( ( insert_nat(X1,X0) = insert_nat(X1,X2)
<=> X0 = X2 )
| 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,[],[f752]) ).
fof(f752,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))
=> ( insert_nat(X1,X0) = insert_nat(X1,X2)
<=> X0 = X2 ) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X9,X10,X4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X4))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X10),X9))
=> ( insert_nat(X10,X4) = insert_nat(X10,X9)
<=> X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5506,plain,
spl17_495,
inference(avatar_split_clause,[],[f1837,f5504]) ).
fof(f1837,plain,
! [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))) = 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),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(definition_unfolding,[],[f1373,f1386,f1386,f1386]) ).
fof(f1373,plain,
! [X0,X1] : insert_a(X0,X1) = insert_a(X0,insert_a(X0,X1)),
inference(cnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0,X1] : insert_a(X0,X1) = insert_a(X0,insert_a(X0,X1)),
inference(rectify,[],[f288]) ).
fof(f288,axiom,
! [X10,X4] : insert_a(X10,X4) = insert_a(X10,insert_a(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5502,plain,
spl17_494,
inference(avatar_split_clause,[],[f1836,f5500]) ).
fof(f1836,plain,
! [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))) = 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),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(definition_unfolding,[],[f1372,f1384,f1384,f1384]) ).
fof(f1372,plain,
! [X0,X1] : insert_pname(X0,X1) = insert_pname(X0,insert_pname(X0,X1)),
inference(cnf_transformation,[],[f489]) ).
fof(f489,plain,
! [X0,X1] : insert_pname(X0,X1) = insert_pname(X0,insert_pname(X0,X1)),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X10,X4] : insert_pname(X10,X4) = insert_pname(X10,insert_pname(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5476,plain,
( spl17_493
| ~ spl17_11
| ~ spl17_423
| ~ spl17_492 ),
inference(avatar_split_clause,[],[f5472,f5468,f4694,f2141,f5474]) ).
fof(f5468,plain,
( spl17_492
<=> ! [X0,X1] : 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)) = 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),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))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_492])]) ).
fof(f5472,plain,
( ! [X0,X1] : cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),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))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)))
| ~ spl17_11
| ~ spl17_423
| ~ spl17_492 ),
inference(forward_demodulation,[],[f5471,f4760]) ).
fof(f5471,plain,
( ! [X0,X1] : 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)) = 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))),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))))
| ~ spl17_492 ),
inference(forward_demodulation,[],[f5469,f2066]) ).
fof(f5469,plain,
( ! [X0,X1] : 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)) = 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),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)))))
| ~ spl17_492 ),
inference(avatar_component_clause,[],[f5468]) ).
fof(f5470,plain,
spl17_492,
inference(avatar_split_clause,[],[f2021,f5468]) ).
fof(f2021,plain,
! [X0,X1] : 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)) = 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),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(forward_demodulation,[],[f1835,f1307]) ).
fof(f1835,plain,
! [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))) = 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),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(definition_unfolding,[],[f1371,f1382,f1382,f1382]) ).
fof(f1371,plain,
! [X0,X1] : insert_nat(X0,X1) = insert_nat(X0,insert_nat(X0,X1)),
inference(cnf_transformation,[],[f488]) ).
fof(f488,plain,
! [X0,X1] : insert_nat(X0,X1) = insert_nat(X0,insert_nat(X0,X1)),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X10,X4] : insert_nat(X10,X4) = insert_nat(X10,insert_nat(X10,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5466,plain,
spl17_491,
inference(avatar_split_clause,[],[f1919,f5464]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1773,f1384,f1384]) ).
fof(f1773,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f784]) ).
fof(f784,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2))) ),
inference(rectify,[],[f364]) ).
fof(f364,axiom,
! [X7,X33,X36] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X33),X36))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X7,X33)),insert_pname(X7,X36))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5462,plain,
spl17_490,
inference(avatar_split_clause,[],[f1915,f5460]) ).
fof(f1915,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1762,f1386,f1386]) ).
fof(f1762,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f773]) ).
fof(f773,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,insert_a(X0,X1)),insert_a(X0,X2))) ),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X7,X33,X36] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X33),X36))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X7,X33)),insert_a(X7,X36))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5435,plain,
( spl17_489
| ~ spl17_11
| ~ spl17_423
| ~ spl17_488 ),
inference(avatar_split_clause,[],[f5431,f5427,f4694,f2141,f5433]) ).
fof(f5427,plain,
( spl17_488
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_488])]) ).
fof(f5431,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_488 ),
inference(forward_demodulation,[],[f5430,f4760]) ).
fof(f5430,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_488 ),
inference(forward_demodulation,[],[f5428,f4760]) ).
fof(f5428,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) )
| ~ spl17_488 ),
inference(avatar_component_clause,[],[f5427]) ).
fof(f5429,plain,
spl17_488,
inference(avatar_split_clause,[],[f2077,f5427]) ).
fof(f2077,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(forward_demodulation,[],[f2076,f1307]) ).
fof(f2076,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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)))),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(forward_demodulation,[],[f1912,f1307]) ).
fof(f1912,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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)))),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),X2)))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1754,f1382,f1382]) ).
fof(f1754,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f765]) ).
fof(f765,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,insert_nat(X0,X1)),insert_nat(X0,X2))) ),
inference(rectify,[],[f363]) ).
fof(f363,axiom,
! [X7,X33,X36] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X33),X36))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X7,X33)),insert_nat(X7,X36))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5418,plain,
spl17_487,
inference(avatar_split_clause,[],[f2069,f5416]) ).
fof(f5414,plain,
spl17_486,
inference(avatar_split_clause,[],[f1458,f5412]) ).
fof(f1458,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,sK2(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,[],[f1188]) ).
fof(f1188,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,sK2(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1))
& is_pname(sK2(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,[sK2])],[f886,f1187]) ).
fof(f1187,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,sK2(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1))
& is_pname(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f886,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,[],[f885]) ).
fof(f885,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,[],[f541]) ).
fof(f541,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,[],[f257]) ).
fof(f257,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(f5370,plain,
( ~ spl17_3
| spl17_485
| ~ spl17_100
| ~ spl17_349 ),
inference(avatar_split_clause,[],[f4127,f4047,f2550,f5367,f2103]) ).
fof(f4127,plain,
( g = image_pname_a(mgt_call,sK10(g,mgt_call,u))
| ~ is_fun_a_bool(g)
| ~ spl17_100
| ~ spl17_349 ),
inference(resolution,[],[f4048,f2552]) ).
fof(f5328,plain,
spl17_484,
inference(avatar_split_clause,[],[f1928,f5326]) ).
fof(f1928,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(definition_unfolding,[],[f1786,f1384]) ).
fof(f1786,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(flattening,[],[f1155]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2)))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(ennf_transformation,[],[f793]) ).
fof(f793,plain,
! [X0,X1,X2] :
( ( is_pname(X1)
& is_pname(X0) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2)))
=> ( X0 != X1
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X7,X30,X4] :
( ( is_pname(X30)
& is_pname(X7) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),insert_pname(X30,X4)))
=> ( X7 != X30
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5324,plain,
spl17_483,
inference(avatar_split_clause,[],[f1921,f5322]) ).
fof(f1921,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(definition_unfolding,[],[f1779,f1386]) ).
fof(f1779,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f1149]) ).
fof(f1149,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| X0 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2)))
| ~ is_a(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f790]) ).
fof(f790,plain,
! [X0,X1,X2] :
( ( is_a(X1)
& is_a(X0) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2)))
=> ( X0 != X1
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ) ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X7,X30,X4] :
( ( is_a(X30)
& is_a(X7) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),insert_a(X30,X4)))
=> ( X7 != X30
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5320,plain,
spl17_482,
inference(avatar_split_clause,[],[f1879,f5318]) ).
fof(f1879,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) = hAPP_f921600141ol_nat(finite_card_pname,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))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_unfolding,[],[f1563,f1384]) ).
fof(f1563,plain,
! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,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))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f1002]) ).
fof(f1002,plain,
! [X0,X1] :
( ( ( hAPP_f921600141ol_nat(finite_card_pname,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,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,[],[f640]) ).
fof(f640,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,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,insert_pname(X0,X1)) ) ) ),
inference(rectify,[],[f184]) ).
fof(f184,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,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,insert_pname(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5316,plain,
( ~ spl17_481
| ~ spl17_194
| ~ spl17_278 ),
inference(avatar_split_clause,[],[f3588,f3481,f3037,f5313]) ).
fof(f5313,plain,
( spl17_481
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_481])]) ).
fof(f3588,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na))
| ~ spl17_194
| ~ spl17_278 ),
inference(resolution,[],[f3482,f3039]) ).
fof(f5311,plain,
spl17_480,
inference(avatar_split_clause,[],[f1874,f5309]) ).
fof(f1874,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) = hAPP_fun_a_bool_nat(finite_card_a,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))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_unfolding,[],[f1541,f1386]) ).
fof(f1541,plain,
! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,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))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f978]) ).
fof(f978,plain,
! [X0,X1] :
( ( ( hAPP_fun_a_bool_nat(finite_card_a,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,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,[],[f619]) ).
fof(f619,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,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,insert_a(X0,X1)) ) ) ),
inference(rectify,[],[f185]) ).
fof(f185,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,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,insert_a(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5307,plain,
spl17_479,
inference(avatar_split_clause,[],[f1862,f5305]) ).
fof(f5305,plain,
( spl17_479
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),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,[spl17_479])]) ).
fof(f1862,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(definition_unfolding,[],[f1500,f1380]) ).
fof(f1380,plain,
! [X0,X1] : insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))),
inference(cnf_transformation,[],[f497]) ).
fof(f497,plain,
! [X0,X1] : insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))),
inference(rectify,[],[f279]) ).
fof(f279,axiom,
! [X7,X9] : insert_fun_a_bool(X7,X9) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X7)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1500,plain,
! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_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))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f925]) ).
fof(f925,plain,
! [X0,X1] :
( ( ( hAPP_f2009550088ol_nat(finite1306199131a_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,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,[],[f580]) ).
fof(f580,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,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,insert_fun_a_bool(X0,X1)) ) ) ),
inference(rectify,[],[f182]) ).
fof(f182,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,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,insert_fun_a_bool(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5303,plain,
spl17_478,
inference(avatar_split_clause,[],[f1860,f5301]) ).
fof(f5301,plain,
( spl17_478
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),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,[spl17_478])]) ).
fof(f1860,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(definition_unfolding,[],[f1498,f1378]) ).
fof(f1378,plain,
! [X0,X1] : insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))),
inference(cnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0,X1] : insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X29,X35] : insert1325755072e_bool(X29,X35) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X29)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X35))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1498,plain,
! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_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))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f924]) ).
fof(f924,plain,
! [X0,X1] :
( ( ( hAPP_f55526627ol_nat(finite1340463720e_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,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,[],[f579]) ).
fof(f579,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,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,insert1325755072e_bool(X0,X1)) ) ) ),
inference(rectify,[],[f181]) ).
fof(f181,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,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,insert1325755072e_bool(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5299,plain,
spl17_477,
inference(avatar_split_clause,[],[f1806,f5297]) ).
fof(f1806,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,sK15(X2))),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))))) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f1266,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,sK15(X2))),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1175,f1265]) ).
fof(f1265,plain,
! [X2] :
( ? [X3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X3)),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,X3))))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,sK15(X2))),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,sK15(X2))))) ),
introduced(choice_axiom,[]) ).
fof(f1175,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X3)),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(flattening,[],[f1174]) ).
fof(f1174,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X3)),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(ennf_transformation,[],[f804]) ).
fof(f804,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X3)),hAPP_n1025906991e_bool(X2,hAPP_nat_nat(suc,X3))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2,X0)),hAPP_n1025906991e_bool(X2,X1))) ) ),
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X16,X27,X8] :
( ! [X28] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X8,X28)),hAPP_n1025906991e_bool(X8,hAPP_nat_nat(suc,X28))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X27))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X8,X16)),hAPP_n1025906991e_bool(X8,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5295,plain,
spl17_476,
inference(avatar_split_clause,[],[f1805,f5293]) ).
fof(f1805,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,sK14(X2))),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))))) ),
inference(cnf_transformation,[],[f1264]) ).
fof(f1264,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,sK14(X2))),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f1173,f1263]) ).
fof(f1263,plain,
! [X2] :
( ? [X3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X3)),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,X3))))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,sK14(X2))),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,sK14(X2))))) ),
introduced(choice_axiom,[]) ).
fof(f1173,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X3)),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(flattening,[],[f1172]) ).
fof(f1172,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X3)),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(ennf_transformation,[],[f803]) ).
fof(f803,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X3)),hAPP_nat_fun_a_bool(X2,hAPP_nat_nat(suc,X3))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2,X0)),hAPP_nat_fun_a_bool(X2,X1))) ) ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X16,X27,X8] :
( ! [X28] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X8,X28)),hAPP_nat_fun_a_bool(X8,hAPP_nat_nat(suc,X28))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X27))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X8,X16)),hAPP_nat_fun_a_bool(X8,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5291,plain,
spl17_475,
inference(avatar_split_clause,[],[f1804,f5289]) ).
fof(f5289,plain,
( spl17_475
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,sK13(X2))),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,sK13(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_475])]) ).
fof(f1804,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,sK13(X2))),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,sK13(X2))))) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1262,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,sK13(X2))),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,sK13(X2))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f1171,f1261]) ).
fof(f1261,plain,
! [X2] :
( ? [X3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X3)),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,X3))))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,sK13(X2))),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,sK13(X2))))) ),
introduced(choice_axiom,[]) ).
fof(f1171,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X3)),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(flattening,[],[f1170]) ).
fof(f1170,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X3)),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,X3)))) ),
inference(ennf_transformation,[],[f802]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X3)),hAPP_n1699378549t_bool(X2,hAPP_nat_nat(suc,X3))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2,X0)),hAPP_n1699378549t_bool(X2,X1))) ) ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X16,X27,X8] :
( ! [X28] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X8,X28)),hAPP_n1699378549t_bool(X8,hAPP_nat_nat(suc,X28))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X27))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X8,X16)),hAPP_n1699378549t_bool(X8,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5287,plain,
spl17_474,
inference(avatar_split_clause,[],[f1803,f5285]) ).
fof(f5285,plain,
( spl17_474
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X0)),hAPP_nat_nat(X2,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(X2,sK12(X2))),hAPP_nat_nat(X2,hAPP_nat_nat(suc,sK12(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_474])]) ).
fof(f1803,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X0)),hAPP_nat_nat(X2,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(X2,sK12(X2))),hAPP_nat_nat(X2,hAPP_nat_nat(suc,sK12(X2))))) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1260,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X0)),hAPP_nat_nat(X2,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(X2,sK12(X2))),hAPP_nat_nat(X2,hAPP_nat_nat(suc,sK12(X2))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f1169,f1259]) ).
fof(f1259,plain,
! [X2] :
( ? [X3] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,hAPP_nat_nat(suc,X3))))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,sK12(X2))),hAPP_nat_nat(X2,hAPP_nat_nat(suc,sK12(X2))))) ),
introduced(choice_axiom,[]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X0)),hAPP_nat_nat(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,hAPP_nat_nat(suc,X3)))) ),
inference(flattening,[],[f1168]) ).
fof(f1168,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X0)),hAPP_nat_nat(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ? [X3] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,hAPP_nat_nat(suc,X3)))) ),
inference(ennf_transformation,[],[f801]) ).
fof(f801,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2,X3)),hAPP_nat_nat(X2,hAPP_nat_nat(suc,X3))))
=> ( 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(X2,X0)),hAPP_nat_nat(X2,X1))) ) ),
inference(rectify,[],[f255]) ).
fof(f255,axiom,
! [X16,X27,X8] :
( ! [X28] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X8,X28)),hAPP_nat_nat(X8,hAPP_nat_nat(suc,X28))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X27))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X8,X16)),hAPP_nat_nat(X8,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5283,plain,
spl17_473,
inference(avatar_split_clause,[],[f1749,f5281]) ).
fof(f1749,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ),
inference(cnf_transformation,[],[f1248]) ).
fof(f1248,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),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,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ),
inference(nnf_transformation,[],[f1104]) ).
fof(f1104,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
<=> 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))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(flattening,[],[f1103]) ).
fof(f1103,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
<=> 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))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f761]) ).
fof(f761,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),X0))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X16,X15,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X24),X15)),hAPP_nat_nat(minus_minus_nat(X16),X15)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5255,plain,
( spl17_472
| ~ spl17_194
| ~ spl17_260 ),
inference(avatar_split_clause,[],[f3547,f3409,f3037,f5252]) ).
fof(f3547,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
| ~ spl17_194
| ~ spl17_260 ),
inference(resolution,[],[f3410,f3039]) ).
fof(f5228,plain,
( spl17_471
| ~ spl17_11
| ~ spl17_423
| ~ spl17_470 ),
inference(avatar_split_clause,[],[f5224,f5221,f4694,f2141,f5226]) ).
fof(f5221,plain,
( spl17_470
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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)))
| 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,[spl17_470])]) ).
fof(f5224,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_470 ),
inference(forward_demodulation,[],[f5222,f4760]) ).
fof(f5222,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_470 ),
inference(avatar_component_clause,[],[f5221]) ).
fof(f5223,plain,
spl17_470,
inference(avatar_split_clause,[],[f2033,f5221]) ).
fof(f2033,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_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)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1869,f1307]) ).
fof(f1869,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) = hAPP_f22106695ol_nat(finite_card_nat,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))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(definition_unfolding,[],[f1527,f1382]) ).
fof(f1527,plain,
! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,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))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f961]) ).
fof(f961,plain,
! [X0,X1] :
( ( ( hAPP_f22106695ol_nat(finite_card_nat,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,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,[],[f606]) ).
fof(f606,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,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,insert_nat(X0,X1)) ) ) ),
inference(rectify,[],[f183]) ).
fof(f183,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,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,insert_nat(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5217,plain,
( spl17_469
| ~ spl17_10
| ~ spl17_422
| ~ spl17_468 ),
inference(avatar_split_clause,[],[f5213,f5210,f4690,f2137,f5215]) ).
fof(f5210,plain,
( spl17_468
<=> ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),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,[spl17_468])]) ).
fof(f5213,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_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)) )
| ~ spl17_10
| ~ spl17_422
| ~ spl17_468 ),
inference(forward_demodulation,[],[f5211,f4758]) ).
fof(f5211,plain,
( ! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_468 ),
inference(avatar_component_clause,[],[f5210]) ).
fof(f5212,plain,
spl17_468,
inference(avatar_split_clause,[],[f2028,f5210]) ).
fof(f2028,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1858,f1306]) ).
fof(f1306,plain,
! [X0] : collect_fun_nat_bool(X0) = X0,
inference(cnf_transformation,[],[f452]) ).
fof(f452,plain,
! [X0] : collect_fun_nat_bool(X0) = X0,
inference(rectify,[],[f338]) ).
fof(f338,axiom,
! [X12] : collect_fun_nat_bool(X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1858,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(definition_unfolding,[],[f1496,f1376]) ).
fof(f1376,plain,
! [X0,X1] : insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))),
inference(cnf_transformation,[],[f493]) ).
fof(f493,plain,
! [X0,X1] : insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X7,X9] : insert_fun_nat_bool(X7,X9) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X7)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1496,plain,
! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_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))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f923]) ).
fof(f923,plain,
! [X0,X1] :
( ( ( hAPP_f696928925ol_nat(finite346522414t_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,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,[],[f578]) ).
fof(f578,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,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,insert_fun_nat_bool(X0,X1)) ) ) ),
inference(rectify,[],[f180]) ).
fof(f180,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,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,insert_fun_nat_bool(X10,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5208,plain,
spl17_467,
inference(avatar_split_clause,[],[f1957,f5206]) ).
fof(f1957,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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)))),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(definition_unfolding,[],[f1824,f1384]) ).
fof(f1824,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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,[],[f1278]) ).
fof(f1278,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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,insert_pname(X0,X1)),X2)) ) ),
inference(flattening,[],[f1277]) ).
fof(f1277,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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,insert_pname(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f810]) ).
fof(f810,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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,[],[f355]) ).
fof(f355,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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(f5204,plain,
spl17_466,
inference(avatar_split_clause,[],[f1954,f5202]) ).
fof(f1954,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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)))),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(definition_unfolding,[],[f1821,f1386]) ).
fof(f1821,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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,[],[f1276]) ).
fof(f1276,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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,insert_a(X0,X1)),X2)) ) ),
inference(flattening,[],[f1275]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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,insert_a(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f809]) ).
fof(f809,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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,[],[f356]) ).
fof(f356,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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(f5200,plain,
( spl17_465
| ~ spl17_48
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2487,f2331,f2295,f5198]) ).
fof(f2487,plain,
( ! [X0,X1] :
( hAPP_f1631501043l_bool(X0,X1) = collect_fun_a_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) )
| ~ spl17_48
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2296]) ).
fof(f5196,plain,
spl17_464,
inference(avatar_split_clause,[],[f1909,f5194]) ).
fof(f1909,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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(definition_unfolding,[],[f1741,f1384]) ).
fof(f1741,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),insert_pname(X1,X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f1246]) ).
fof(f1246,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),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),insert_pname(X1,X0))) ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(nnf_transformation,[],[f1094]) ).
fof(f1094,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),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,[],[f755]) ).
fof(f755,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),insert_pname(X1,X0)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) ) ),
inference(rectify,[],[f358]) ).
fof(f358,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),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(f5192,plain,
spl17_463,
inference(avatar_split_clause,[],[f1907,f5190]) ).
fof(f1907,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(definition_unfolding,[],[f1739,f1386]) ).
fof(f1739,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),insert_a(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1245,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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),insert_a(X1,X0))) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(nnf_transformation,[],[f1093]) ).
fof(f1093,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),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,[],[f754]) ).
fof(f754,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),insert_a(X1,X0)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
inference(rectify,[],[f359]) ).
fof(f359,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),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(f5165,plain,
( spl17_462
| ~ spl17_11
| ~ spl17_423
| ~ spl17_461 ),
inference(avatar_split_clause,[],[f5161,f5158,f4694,f2141,f5163]) ).
fof(f5158,plain,
( spl17_461
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),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,[spl17_461])]) ).
fof(f5161,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_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)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_461 ),
inference(forward_demodulation,[],[f5159,f4760]) ).
fof(f5159,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ spl17_461 ),
inference(avatar_component_clause,[],[f5158]) ).
fof(f5160,plain,
spl17_461,
inference(avatar_split_clause,[],[f2089,f5158]) ).
fof(f2089,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),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(forward_demodulation,[],[f1951,f1307]) ).
fof(f1951,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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)))),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(definition_unfolding,[],[f1818,f1382]) ).
fof(f1818,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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,[],[f1274]) ).
fof(f1274,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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,insert_nat(X0,X1)),X2)) ) ),
inference(flattening,[],[f1273]) ).
fof(f1273,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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,insert_nat(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f808]) ).
fof(f808,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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,[],[f354]) ).
fof(f354,axiom,
! [X10,X4,X9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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(f5155,plain,
( spl17_460
| ~ spl17_45
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2486,f2331,f2283,f5153]) ).
fof(f2486,plain,
( ! [X0,X1] :
( hAPP_a85458249l_bool(X0,X1) = collect_fun_a_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) )
| ~ spl17_45
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2284]) ).
fof(f5151,plain,
( spl17_459
| ~ spl17_11
| ~ spl17_423
| ~ spl17_458 ),
inference(avatar_split_clause,[],[f5147,f5144,f4694,f2141,f5149]) ).
fof(f5149,plain,
( spl17_459
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_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,[spl17_459])]) ).
fof(f5144,plain,
( spl17_458
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),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,[spl17_458])]) ).
fof(f5147,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_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)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_458 ),
inference(forward_demodulation,[],[f5145,f4760]) ).
fof(f5145,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
| ~ spl17_458 ),
inference(avatar_component_clause,[],[f5144]) ).
fof(f5146,plain,
spl17_458,
inference(avatar_split_clause,[],[f2073,f5144]) ).
fof(f2073,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),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(forward_demodulation,[],[f1905,f1307]) ).
fof(f1905,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),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(definition_unfolding,[],[f1737,f1382]) ).
fof(f1737,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),insert_nat(X1,X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1244]) ).
fof(f1244,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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),insert_nat(X1,X0))) ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(nnf_transformation,[],[f1092]) ).
fof(f1092,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),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,[],[f753]) ).
fof(f753,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),insert_nat(X1,X0)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
inference(rectify,[],[f357]) ).
fof(f357,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),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(f5142,plain,
spl17_457,
inference(avatar_split_clause,[],[f1880,f5140]) ).
fof(f1880,plain,
! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,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))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_unfolding,[],[f1562,f1384]) ).
fof(f1562,plain,
! [X0,X1] :
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,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,[],[f1002]) ).
fof(f5138,plain,
spl17_456,
inference(avatar_split_clause,[],[f1875,f5136]) ).
fof(f1875,plain,
! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,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))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_unfolding,[],[f1540,f1386]) ).
fof(f1540,plain,
! [X0,X1] :
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,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,[],[f978]) ).
fof(f5134,plain,
spl17_455,
inference(avatar_split_clause,[],[f1863,f5132]) ).
fof(f5132,plain,
( spl17_455
<=> ! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),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,[spl17_455])]) ).
fof(f1863,plain,
! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(definition_unfolding,[],[f1499,f1380]) ).
fof(f1499,plain,
! [X0,X1] :
( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_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,[],[f925]) ).
fof(f5130,plain,
spl17_454,
inference(avatar_split_clause,[],[f1861,f5128]) ).
fof(f5128,plain,
( spl17_454
<=> ! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),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,[spl17_454])]) ).
fof(f1861,plain,
! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(definition_unfolding,[],[f1497,f1378]) ).
fof(f1497,plain,
! [X0,X1] :
( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_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,[],[f924]) ).
fof(f5045,plain,
( spl17_453
| ~ spl17_47
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f2482,f2327,f2291,f5043]) ).
fof(f2482,plain,
( ! [X0,X1] :
( hAPP_p338031245l_bool(X0,X1) = collec1974731493e_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) )
| ~ spl17_47
| ~ spl17_56 ),
inference(resolution,[],[f2328,f2292]) ).
fof(f5025,plain,
( spl17_452
| ~ spl17_11
| ~ spl17_423
| ~ spl17_451 ),
inference(avatar_split_clause,[],[f5021,f5018,f4694,f2141,f5023]) ).
fof(f5018,plain,
( spl17_451
<=> ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_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)))
| ~ 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,[spl17_451])]) ).
fof(f5021,plain,
( ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_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))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_451 ),
inference(forward_demodulation,[],[f5019,f4760]) ).
fof(f5019,plain,
( ! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_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)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_451 ),
inference(avatar_component_clause,[],[f5018]) ).
fof(f5020,plain,
spl17_451,
inference(avatar_split_clause,[],[f2034,f5018]) ).
fof(f2034,plain,
! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_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)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1870,f1307]) ).
fof(f1870,plain,
! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,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))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(definition_unfolding,[],[f1526,f1382]) ).
fof(f1526,plain,
! [X0,X1] :
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,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,[],[f961]) ).
fof(f5016,plain,
( spl17_450
| ~ spl17_10
| ~ spl17_422
| ~ spl17_449 ),
inference(avatar_split_clause,[],[f5012,f5009,f4690,f2137,f5014]) ).
fof(f5009,plain,
( spl17_449
<=> ! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),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,[spl17_449])]) ).
fof(f5012,plain,
( ! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_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)) )
| ~ spl17_10
| ~ spl17_422
| ~ spl17_449 ),
inference(forward_demodulation,[],[f5010,f4758]) ).
fof(f5010,plain,
( ! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_449 ),
inference(avatar_component_clause,[],[f5009]) ).
fof(f5011,plain,
spl17_449,
inference(avatar_split_clause,[],[f2029,f5009]) ).
fof(f2029,plain,
! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1859,f1306]) ).
fof(f1859,plain,
! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(definition_unfolding,[],[f1495,f1376]) ).
fof(f1495,plain,
! [X0,X1] :
( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_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,[],[f923]) ).
fof(f5007,plain,
spl17_448,
inference(avatar_split_clause,[],[f1746,f5005]) ).
fof(f1746,plain,
! [X2,X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ),
inference(flattening,[],[f1099]) ).
fof(f1099,plain,
! [X0,X1,X2] :
( hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(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,X1),X2)) ),
inference(ennf_transformation,[],[f759]) ).
fof(f759,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),X0))
=> hAPP_nat_nat(minus_minus_nat(X2),X0) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X0),X1)) ) ),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X13,X21,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X13))
=> hAPP_nat_nat(minus_minus_nat(X14),X13) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X14),X21)),hAPP_nat_nat(minus_minus_nat(X13),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5003,plain,
spl17_447,
inference(avatar_split_clause,[],[f1600,f5001]) ).
fof(f1600,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f1063]) ).
fof(f1063,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f670]) ).
fof(f670,plain,
! [X0,X1] :
( ( is_fun_pname_bool(X1)
& is_fun_pname_bool(X0) )
=> ( 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,X1)),hAPP_f921600141ol_nat(finite_card_pname,X0)))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X4,X9] :
( ( is_fun_pname_bool(X9)
& is_fun_pname_bool(X4) )
=> ( 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,X9)),hAPP_f921600141ol_nat(finite_card_pname,X4)))
=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4999,plain,
spl17_446,
inference(avatar_split_clause,[],[f1592,f4997]) ).
fof(f1592,plain,
! [X0,X1] :
( 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,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))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1] :
( 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,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))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f1051]) ).
fof(f1051,plain,
! [X0,X1] :
( 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,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))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f666]) ).
fof(f666,plain,
! [X0,X1] :
( ( is_fun_a_bool(X1)
& is_fun_a_bool(X0) )
=> ( 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,X1)),hAPP_fun_a_bool_nat(finite_card_a,X0)))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X4,X9] :
( ( is_fun_a_bool(X9)
& is_fun_a_bool(X4) )
=> ( 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,X9)),hAPP_fun_a_bool_nat(finite_card_a,X4)))
=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4981,plain,
spl17_445,
inference(avatar_split_clause,[],[f1588,f4979]) ).
fof(f1588,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(flattening,[],[f1043]) ).
fof(f1043,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f664]) ).
fof(f664,plain,
! [X0,X1] :
( ( is_fun949378684l_bool(X1)
& is_fun949378684l_bool(X0) )
=> ( 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,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X4,X9] :
( ( is_fun949378684l_bool(X9)
& is_fun949378684l_bool(X4) )
=> ( 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,X9)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X4)))
=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4977,plain,
spl17_444,
inference(avatar_split_clause,[],[f1587,f4975]) ).
fof(f1587,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(flattening,[],[f1041]) ).
fof(f1041,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f663]) ).
fof(f663,plain,
! [X0,X1] :
( ( is_fun1661590463l_bool(X1)
& is_fun1661590463l_bool(X0) )
=> ( 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,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X4,X9] :
( ( is_fun1661590463l_bool(X9)
& is_fun1661590463l_bool(X4) )
=> ( 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,X9)),hAPP_f55526627ol_nat(finite1340463720e_bool,X4)))
=> X4 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4966,plain,
spl17_443,
inference(avatar_split_clause,[],[f1931,f4964]) ).
fof(f1931,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_pname_bool(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))),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(definition_unfolding,[],[f1787,f1384]) ).
fof(f1787,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1254,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( ~ hBOOL(hAPP_pname_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ) )
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(flattening,[],[f1253]) ).
fof(f1253,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( ~ hBOOL(hAPP_pname_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ) )
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(nnf_transformation,[],[f1158]) ).
fof(f1158,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
<=> ( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2 ) )
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(flattening,[],[f1157]) ).
fof(f1157,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
<=> ( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2 ) )
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(ennf_transformation,[],[f794]) ).
fof(f794,plain,
! [X0,X1,X2] :
( ( is_pname(X2)
& is_pname(X0) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
<=> ( hBOOL(hAPP_pname_bool(X1,X2))
| X0 = X2 ) ) ),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X32,X4,X10] :
( ( is_pname(X10)
& is_pname(X32) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X32,X4),X10))
<=> ( hBOOL(hAPP_pname_bool(X4,X10))
| X10 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4962,plain,
spl17_442,
inference(avatar_split_clause,[],[f1924,f4960]) ).
fof(f1924,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(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))),X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(definition_unfolding,[],[f1780,f1386]) ).
fof(f1780,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f1250]) ).
fof(f1250,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_a_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(insert_a(X0,X1),X2)) ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(flattening,[],[f1249]) ).
fof(f1249,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_a_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(insert_a(X0,X1),X2)) ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(nnf_transformation,[],[f1152]) ).
fof(f1152,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(flattening,[],[f1151]) ).
fof(f1151,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) )
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0,X1,X2] :
( ( is_a(X2)
& is_a(X0) )
=> ( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| X0 = X2 ) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X32,X4,X10] :
( ( is_a(X10)
& is_a(X32) )
=> ( hBOOL(hAPP_a_bool(insert_a(X32,X4),X10))
<=> ( hBOOL(hAPP_a_bool(X4,X10))
| X10 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4871,plain,
( spl17_441
| ~ spl17_11
| ~ spl17_423
| ~ spl17_440 ),
inference(avatar_split_clause,[],[f4867,f4864,f4694,f2141,f4869]) ).
fof(f4864,plain,
( spl17_440
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_440])]) ).
fof(f4867,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_440 ),
inference(forward_demodulation,[],[f4865,f4760]) ).
fof(f4865,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 )
| ~ spl17_440 ),
inference(avatar_component_clause,[],[f4864]) ).
fof(f4866,plain,
spl17_440,
inference(avatar_split_clause,[],[f2080,f4864]) ).
fof(f2080,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| X0 = X1 ),
inference(forward_demodulation,[],[f1920,f1307]) ).
fof(f1920,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),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))) ),
inference(definition_unfolding,[],[f1778,f1382]) ).
fof(f1778,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),insert_nat(X1,X2))) ),
inference(cnf_transformation,[],[f1148]) ).
fof(f1148,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),insert_nat(X1,X2))) ),
inference(flattening,[],[f1147]) ).
fof(f1147,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),insert_nat(X1,X2))) ),
inference(ennf_transformation,[],[f789]) ).
fof(f789,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2)))
=> ( X0 != X1
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X7,X30,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),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(f4862,plain,
spl17_439,
inference(avatar_split_clause,[],[f1878,f4860]) ).
fof(f1878,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,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))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_unfolding,[],[f1555,f1384]) ).
fof(f1555,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,insert_pname(X0,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f995]) ).
fof(f995,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,insert_pname(X0,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f633]) ).
fof(f633,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,insert_pname(X0,X1)))) ),
inference(rectify,[],[f177]) ).
fof(f177,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,insert_pname(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4858,plain,
spl17_438,
inference(avatar_split_clause,[],[f1873,f4856]) ).
fof(f1873,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,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))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_unfolding,[],[f1536,f1386]) ).
fof(f1536,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,insert_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f974]) ).
fof(f974,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,insert_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f615]) ).
fof(f615,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,insert_a(X0,X1)))) ),
inference(rectify,[],[f179]) ).
fof(f179,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,insert_a(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4854,plain,
spl17_437,
inference(avatar_split_clause,[],[f1857,f4852]) ).
fof(f1857,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,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(definition_unfolding,[],[f1485,f1378]) ).
fof(f1485,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,insert1325755072e_bool(X0,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f913]) ).
fof(f913,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,insert1325755072e_bool(X0,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f568]) ).
fof(f568,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,insert1325755072e_bool(X0,X1)))) ),
inference(rectify,[],[f175]) ).
fof(f175,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,insert1325755072e_bool(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4850,plain,
( spl17_436
| ~ spl17_50
| ~ spl17_288 ),
inference(avatar_split_clause,[],[f3641,f3609,f2303,f4848]) ).
fof(f4848,plain,
( spl17_436
<=> ! [X0] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_436])]) ).
fof(f3641,plain,
( ! [X0] : hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X0)) = X0
| ~ spl17_50
| ~ spl17_288 ),
inference(resolution,[],[f3610,f2304]) ).
fof(f4846,plain,
spl17_435,
inference(avatar_split_clause,[],[f1856,f4844]) ).
fof(f1856,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,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(definition_unfolding,[],[f1484,f1380]) ).
fof(f1484,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,insert_fun_a_bool(X0,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f912]) ).
fof(f912,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,insert_fun_a_bool(X0,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f567]) ).
fof(f567,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,insert_fun_a_bool(X0,X1)))) ),
inference(rectify,[],[f176]) ).
fof(f176,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,insert_fun_a_bool(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4842,plain,
spl17_434,
inference(avatar_split_clause,[],[f1849,f4840]) ).
fof(f4838,plain,
spl17_433,
inference(avatar_split_clause,[],[f1848,f4836]) ).
fof(f4834,plain,
spl17_432,
inference(avatar_split_clause,[],[f1846,f4832]) ).
fof(f1846,plain,
! [X0,X1] : collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X1)))),
inference(definition_unfolding,[],[f1390,f1380]) ).
fof(f1390,plain,
! [X0,X1] : insert_fun_a_bool(X0,collect_fun_a_bool(X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)),
inference(cnf_transformation,[],[f507]) ).
fof(f507,plain,
! [X0,X1] : insert_fun_a_bool(X0,collect_fun_a_bool(X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X7,X12] : insert_fun_a_bool(X7,collect_fun_a_bool(X12)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4830,plain,
spl17_431,
inference(avatar_split_clause,[],[f1845,f4828]) ).
fof(f1845,plain,
! [X0,X1] : collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X1)))),
inference(definition_unfolding,[],[f1389,f1378]) ).
fof(f1389,plain,
! [X0,X1] : insert1325755072e_bool(X0,collec1974731493e_bool(X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)),
inference(cnf_transformation,[],[f506]) ).
fof(f506,plain,
! [X0,X1] : insert1325755072e_bool(X0,collec1974731493e_bool(X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)),
inference(rectify,[],[f284]) ).
fof(f284,axiom,
! [X7,X12] : insert1325755072e_bool(X7,collec1974731493e_bool(X12)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4804,plain,
spl17_430,
inference(avatar_split_clause,[],[f2079,f4802]) ).
fof(f2079,plain,
! [X2,X0,X1] :
( image_pname_a(X0,X2) = image_pname_a(X0,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(forward_demodulation,[],[f2078,f2069]) ).
fof(f2078,plain,
! [X2,X0,X1] :
( image_pname_a(X0,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),X0),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(forward_demodulation,[],[f1917,f1679]) ).
fof(f1917,plain,
! [X2,X0,X1] :
( image_pname_a(X0,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X0,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X0,X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(definition_unfolding,[],[f1769,f1386]) ).
fof(f1769,plain,
! [X2,X0,X1] :
( image_pname_a(X0,X2) = 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,[],[f1133]) ).
fof(f1133,plain,
! [X0,X1,X2] :
( image_pname_a(X0,X2) = 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,[],[f780]) ).
fof(f780,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> image_pname_a(X0,X2) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) ),
inference(rectify,[],[f367]) ).
fof(f367,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X4))
=> image_pname_a(X8,X4) = insert_a(hAPP_pname_a(X8,X10),image_pname_a(X8,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4793,plain,
( spl17_429
| ~ spl17_11
| ~ spl17_423
| ~ spl17_427 ),
inference(avatar_split_clause,[],[f4785,f4782,f4694,f2141,f4791]) ).
fof(f4782,plain,
( spl17_427
<=> ! [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,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)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_427])]) ).
fof(f4785,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,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_11
| ~ spl17_423
| ~ spl17_427 ),
inference(forward_demodulation,[],[f4783,f4760]) ).
fof(f4783,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,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)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
| ~ spl17_427 ),
inference(avatar_component_clause,[],[f4782]) ).
fof(f4789,plain,
( spl17_428
| ~ spl17_162
| ~ spl17_177 ),
inference(avatar_split_clause,[],[f2941,f2876,f2803,f4787]) ).
fof(f4787,plain,
( spl17_428
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),X1))
| is_a(sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_428])]) ).
fof(f2941,plain,
( ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(p(X0),X1))
| is_a(sK4(X0,X1)) )
| ~ spl17_162
| ~ spl17_177 ),
inference(resolution,[],[f2877,f2804]) ).
fof(f4784,plain,
spl17_427,
inference(avatar_split_clause,[],[f2032,f4782]) ).
fof(f2032,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,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)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1868,f1307]) ).
fof(f1868,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,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))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(definition_unfolding,[],[f1520,f1382]) ).
fof(f1520,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,insert_nat(X0,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f955]) ).
fof(f955,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,insert_nat(X0,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f600]) ).
fof(f600,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,insert_nat(X0,X1)))) ),
inference(rectify,[],[f178]) ).
fof(f178,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,insert_nat(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4774,plain,
( spl17_426
| ~ spl17_10
| ~ spl17_422
| ~ spl17_425 ),
inference(avatar_split_clause,[],[f4770,f4767,f4690,f2137,f4772]) ).
fof(f4767,plain,
( spl17_425
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_425])]) ).
fof(f4770,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,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_10
| ~ spl17_422
| ~ spl17_425 ),
inference(forward_demodulation,[],[f4768,f4758]) ).
fof(f4768,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,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
| ~ spl17_425 ),
inference(avatar_component_clause,[],[f4767]) ).
fof(f4769,plain,
spl17_425,
inference(avatar_split_clause,[],[f2027,f4767]) ).
fof(f2027,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,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1855,f1306]) ).
fof(f1855,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,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(definition_unfolding,[],[f1483,f1376]) ).
fof(f1483,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,insert_fun_nat_bool(X0,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f911]) ).
fof(f911,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,insert_fun_nat_bool(X0,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f566]) ).
fof(f566,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,insert_fun_nat_bool(X0,X1)))) ),
inference(rectify,[],[f174]) ).
fof(f174,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,insert_fun_nat_bool(X10,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4765,plain,
spl17_424,
inference(avatar_split_clause,[],[f1747,f4763]) ).
fof(f1747,plain,
! [X2,X0,X1] :
( X0 = X2
| hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),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,X1),X2)) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1247,plain,
! [X0,X1,X2] :
( ( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X2),X1)
| X0 != X2 )
& ( X0 = X2
| hAPP_nat_nat(minus_minus_nat(X0),X1) != hAPP_nat_nat(minus_minus_nat(X2),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,X1),X2)) ),
inference(nnf_transformation,[],[f1102]) ).
fof(f1102,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X2),X1)
<=> X0 = 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,X1),X2)) ),
inference(flattening,[],[f1101]) ).
fof(f1101,plain,
! [X0,X1,X2] :
( ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X2),X1)
<=> X0 = 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,X1),X2)) ),
inference(ennf_transformation,[],[f760]) ).
fof(f760,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),X0))
=> ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(X2),X1)
<=> X0 = X2 ) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X16,X15,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( hAPP_nat_nat(minus_minus_nat(X24),X15) = hAPP_nat_nat(minus_minus_nat(X16),X15)
<=> X16 = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4696,plain,
spl17_423,
inference(avatar_split_clause,[],[f2025,f4694]) ).
fof(f4692,plain,
spl17_422,
inference(avatar_split_clause,[],[f2023,f4690]) ).
fof(f2023,plain,
! [X0,X1] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1),
inference(forward_demodulation,[],[f2022,f1306]) ).
fof(f2022,plain,
! [X0,X1] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)),
inference(forward_demodulation,[],[f1844,f1306]) ).
fof(f1844,plain,
! [X0,X1] : collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),collect_fun_nat_bool(X1)))),
inference(definition_unfolding,[],[f1388,f1376]) ).
fof(f1388,plain,
! [X0,X1] : insert_fun_nat_bool(X0,collect_fun_nat_bool(X1)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)),
inference(cnf_transformation,[],[f505]) ).
fof(f505,plain,
! [X0,X1] : insert_fun_nat_bool(X0,collect_fun_nat_bool(X1)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)),
inference(rectify,[],[f283]) ).
fof(f283,axiom,
! [X7,X12] : insert_fun_nat_bool(X7,collect_fun_nat_bool(X12)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X7))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4688,plain,
spl17_421,
inference(avatar_split_clause,[],[f1959,f4686]) ).
fof(f1959,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1822,f1384]) ).
fof(f1822,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,insert_pname(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f4684,plain,
spl17_420,
inference(avatar_split_clause,[],[f1958,f4682]) ).
fof(f1958,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1823,f1384]) ).
fof(f1823,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,insert_pname(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f4680,plain,
spl17_419,
inference(avatar_split_clause,[],[f1956,f4678]) ).
fof(f1956,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1819,f1386]) ).
fof(f1819,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,insert_a(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f4676,plain,
spl17_418,
inference(avatar_split_clause,[],[f1955,f4674]) ).
fof(f1955,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1820,f1386]) ).
fof(f1820,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,insert_a(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f4672,plain,
spl17_417,
inference(avatar_split_clause,[],[f1929,f4670]) ).
fof(f1929,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(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))),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(definition_unfolding,[],[f1789,f1384]) ).
fof(f1789,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f4668,plain,
spl17_416,
inference(avatar_split_clause,[],[f1922,f4666]) ).
fof(f1922,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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))),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(definition_unfolding,[],[f1782,f1386]) ).
fof(f1782,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f1250]) ).
fof(f4664,plain,
spl17_415,
inference(avatar_split_clause,[],[f1918,f4662]) ).
fof(f1918,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1771,f1384]) ).
fof(f1771,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f782]) ).
fof(f782,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2))) ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X30,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),insert_pname(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4660,plain,
spl17_414,
inference(avatar_split_clause,[],[f1916,f4658]) ).
fof(f1916,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,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),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(definition_unfolding,[],[f1767,f1384]) ).
fof(f1767,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f778]) ).
fof(f778,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),insert_pname(X0,X2))) ),
inference(rectify,[],[f302]) ).
fof(f302,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),insert_pname(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4656,plain,
( spl17_413
| ~ spl17_220
| ~ spl17_236 ),
inference(avatar_split_clause,[],[f3283,f3267,f3142,f4654]) ).
fof(f4654,plain,
( spl17_413
<=> ! [X2,X0,X1,X3] : is_bool(hAPP_bool_bool(X3,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_413])]) ).
fof(f3267,plain,
( spl17_236
<=> ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_236])]) ).
fof(f3283,plain,
( ! [X2,X3,X0,X1] : is_bool(hAPP_bool_bool(X3,hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1)))
| ~ spl17_220
| ~ spl17_236 ),
inference(superposition,[],[f3268,f3143]) ).
fof(f3268,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))
| ~ spl17_236 ),
inference(avatar_component_clause,[],[f3267]) ).
fof(f4652,plain,
spl17_412,
inference(avatar_split_clause,[],[f1914,f4650]) ).
fof(f1914,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1761,f1386]) ).
fof(f1761,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f772]) ).
fof(f772,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),insert_a(X0,X2))) ),
inference(rectify,[],[f362]) ).
fof(f362,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),insert_a(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4648,plain,
spl17_411,
inference(avatar_split_clause,[],[f1913,f4646]) ).
fof(f1913,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,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),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(definition_unfolding,[],[f1759,f1386]) ).
fof(f1759,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f770]) ).
fof(f770,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),insert_a(X0,X2))) ),
inference(rectify,[],[f303]) ).
fof(f303,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),insert_a(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4644,plain,
spl17_410,
inference(avatar_split_clause,[],[f1725,f4642]) ).
fof(f1725,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK9(X0,X1,X2)),X1))
| ~ 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,[],[f1236]) ).
fof(f1236,plain,
! [X0,X1,X2] :
( ( image_pname_a(X0,sK9(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK9(X0,X1,X2)),X1))
& is_fun_pname_bool(sK9(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,[sK9])],[f1084,f1235]) ).
fof(f1235,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,sK9(X0,X1,X2)) = X2
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK9(X0,X1,X2)),X1))
& is_fun_pname_bool(sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1084,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,[],[f1083]) ).
fof(f1083,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,[],[f748]) ).
fof(f748,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,[],[f252]) ).
fof(f252,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(f4640,plain,
spl17_409,
inference(avatar_split_clause,[],[f1531,f4638]) ).
fof(f1531,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f969]) ).
fof(f969,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f968]) ).
fof(f968,plain,
! [X0,X1] :
( 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,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f610]) ).
fof(f610,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,X1)),hAPP_f22106695ol_nat(finite_card_nat,X0)))
=> X0 = X1 ) ) ),
inference(rectify,[],[f173]) ).
fof(f173,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,X9)),hAPP_f22106695ol_nat(finite_card_nat,X4)))
=> X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4636,plain,
spl17_408,
inference(avatar_split_clause,[],[f1510,f4634]) ).
fof(f1510,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f945,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(flattening,[],[f944]) ).
fof(f944,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f590]) ).
fof(f590,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,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
=> X0 = X1 ) ) ),
inference(rectify,[],[f168]) ).
fof(f168,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,X9)),hAPP_f696928925ol_nat(finite346522414t_bool,X4)))
=> X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4608,plain,
( spl17_407
| ~ spl17_189
| ~ spl17_236 ),
inference(avatar_split_clause,[],[f3282,f3267,f2925,f4606]) ).
fof(f3282,plain,
( ! [X2,X3,X0,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2))))
| ~ spl17_189
| ~ spl17_236 ),
inference(superposition,[],[f3268,f2926]) ).
fof(f4593,plain,
spl17_406,
inference(avatar_split_clause,[],[f2091,f4591]) ).
fof(f2091,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
inference(forward_demodulation,[],[f1953,f1307]) ).
fof(f1953,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1816,f1382]) ).
fof(f1816,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,insert_nat(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1274]) ).
fof(f4589,plain,
spl17_405,
inference(avatar_split_clause,[],[f2090,f4587]) ).
fof(f2090,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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))),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(forward_demodulation,[],[f1952,f1307]) ).
fof(f1952,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,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)))),X2)) ),
inference(definition_unfolding,[],[f1817,f1382]) ).
fof(f1817,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,insert_nat(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1274]) ).
fof(f4585,plain,
spl17_404,
inference(avatar_split_clause,[],[f2075,f4583]) ).
fof(f2075,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(forward_demodulation,[],[f1911,f1307]) ).
fof(f1911,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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),X2)))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(definition_unfolding,[],[f1753,f1382]) ).
fof(f1753,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f764]) ).
fof(f764,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),insert_nat(X0,X2))) ),
inference(rectify,[],[f360]) ).
fof(f360,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),insert_nat(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4581,plain,
spl17_403,
inference(avatar_split_clause,[],[f2074,f4579]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),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),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(forward_demodulation,[],[f1910,f1307]) ).
fof(f1910,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,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),X2)))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(definition_unfolding,[],[f1751,f1382]) ).
fof(f1751,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f762]) ).
fof(f762,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),insert_nat(X0,X2))) ),
inference(rectify,[],[f301]) ).
fof(f301,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),insert_nat(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4577,plain,
spl17_402,
inference(avatar_split_clause,[],[f1851,f4575]) ).
fof(f1851,plain,
! [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))) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(definition_unfolding,[],[f1442,f1384]) ).
fof(f1442,plain,
! [X0,X1] :
( insert_pname(X0,X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f874]) ).
fof(f874,plain,
! [X0,X1] :
( insert_pname(X0,X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(flattening,[],[f873]) ).
fof(f873,plain,
! [X0,X1] :
( insert_pname(X0,X1) = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0,X1] :
( is_fun_pname_bool(X1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> insert_pname(X0,X1) = X1 ) ),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X7,X4] :
( is_fun_pname_bool(X4)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),X4))
=> insert_pname(X7,X4) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4573,plain,
spl17_401,
inference(avatar_split_clause,[],[f1850,f4571]) ).
fof(f1850,plain,
! [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))) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ is_fun_a_bool(X1) ),
inference(definition_unfolding,[],[f1434,f1386]) ).
fof(f1434,plain,
! [X0,X1] :
( 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,[],[f865]) ).
fof(f865,plain,
! [X0,X1] :
( 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,[],[f864]) ).
fof(f864,plain,
! [X0,X1] :
( 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,[],[f529]) ).
fof(f529,plain,
! [X0,X1] :
( is_fun_a_bool(X1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> insert_a(X0,X1) = X1 ) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X7,X4] :
( is_fun_a_bool(X4)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),X4))
=> insert_a(X7,X4) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4569,plain,
spl17_400,
inference(avatar_split_clause,[],[f1727,f4567]) ).
fof(f1727,plain,
! [X2,X0,X1] :
( image_pname_a(X0,sK9(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,[],[f1236]) ).
fof(f4552,plain,
spl17_399,
inference(avatar_split_clause,[],[f2085,f4550]) ).
fof(f2085,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(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)),X2))
| hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2 ),
inference(forward_demodulation,[],[f1947,f1307]) ).
fof(f1947,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(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))),X2)) ),
inference(definition_unfolding,[],[f1810,f1382]) ).
fof(f1810,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1270,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( ~ hBOOL(hAPP_nat_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ) ),
inference(flattening,[],[f1269]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( ~ hBOOL(hAPP_nat_bool(X1,X2))
& X0 != X2 ) )
& ( hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f806]) ).
fof(f806,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
<=> ( hBOOL(hAPP_nat_bool(X1,X2))
| X0 = X2 ) ),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X32,X4,X10] :
( hBOOL(hAPP_nat_bool(insert_nat(X32,X4),X10))
<=> ( hBOOL(hAPP_nat_bool(X4,X10))
| X10 = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4548,plain,
spl17_398,
inference(avatar_split_clause,[],[f1726,f4546]) ).
fof(f1726,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK9(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,[],[f1236]) ).
fof(f4518,plain,
spl17_397,
inference(avatar_split_clause,[],[f1566,f4516]) ).
fof(f1566,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,[],[f1008]) ).
fof(f1008,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,[],[f1007]) ).
fof(f1007,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,[],[f643]) ).
fof(f643,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,[],[f165]) ).
fof(f165,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(f4514,plain,
( spl17_396
| ~ spl17_188
| ~ spl17_235 ),
inference(avatar_split_clause,[],[f3241,f3203,f2921,f4512]) ).
fof(f3203,plain,
( spl17_235
<=> ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_235])]) ).
fof(f3241,plain,
( ! [X2,X3,X0,X1] : is_bool(hAPP_bool_bool(X3,hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2))))
| ~ spl17_188
| ~ spl17_235 ),
inference(superposition,[],[f3204,f2922]) ).
fof(f3204,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl17_235 ),
inference(avatar_component_clause,[],[f3203]) ).
fof(f4510,plain,
spl17_395,
inference(avatar_split_clause,[],[f1544,f4508]) ).
fof(f1544,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,[],[f984]) ).
fof(f984,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,[],[f983]) ).
fof(f983,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,[],[f622]) ).
fof(f622,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,[],[f166]) ).
fof(f166,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(f4506,plain,
spl17_394,
inference(avatar_split_clause,[],[f1530,f4504]) ).
fof(f1530,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,[],[f967]) ).
fof(f967,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,[],[f966]) ).
fof(f966,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,[],[f609]) ).
fof(f609,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,[],[f167]) ).
fof(f167,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(f4502,plain,
spl17_393,
inference(avatar_split_clause,[],[f1509,f4500]) ).
fof(f1509,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,[],[f943]) ).
fof(f943,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,[],[f942]) ).
fof(f942,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,[],[f589]) ).
fof(f589,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,[],[f163]) ).
fof(f163,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(f4498,plain,
spl17_392,
inference(avatar_split_clause,[],[f1508,f4496]) ).
fof(f1508,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,[],[f941]) ).
fof(f941,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,[],[f940]) ).
fof(f940,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,[],[f588]) ).
fof(f588,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,[],[f164]) ).
fof(f164,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(f4494,plain,
spl17_391,
inference(avatar_split_clause,[],[f1507,f4492]) ).
fof(f1507,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,[],[f939]) ).
fof(f939,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,[],[f938]) ).
fof(f938,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,[],[f587]) ).
fof(f587,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,[],[f162]) ).
fof(f162,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(f4363,plain,
spl17_390,
inference(avatar_split_clause,[],[f2036,f4361]) ).
fof(f2036,plain,
! [X0,X1] :
( 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)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(forward_demodulation,[],[f1882,f1307]) ).
fof(f1882,plain,
! [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))) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(definition_unfolding,[],[f1574,f1382]) ).
fof(f1574,plain,
! [X0,X1] :
( insert_nat(X0,X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,plain,
! [X0,X1] :
( insert_nat(X0,X1) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(ennf_transformation,[],[f651]) ).
fof(f651,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> insert_nat(X0,X1) = X1 ),
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X7,X4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),X4))
=> insert_nat(X7,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4359,plain,
spl17_389,
inference(avatar_split_clause,[],[f1897,f4357]) ).
fof(f1897,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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(definition_unfolding,[],[f1644,f1384]) ).
fof(f1644,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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,insert_pname(X0,X1))) ) ),
inference(nnf_transformation,[],[f691]) ).
fof(f691,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rectify,[],[f218]) ).
fof(f218,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X7,X4)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4348,plain,
spl17_388,
inference(avatar_split_clause,[],[f1895,f4346]) ).
fof(f1895,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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(definition_unfolding,[],[f1640,f1386]) ).
fof(f1640,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,plain,
! [X0,X1] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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,insert_a(X0,X1))) ) ),
inference(nnf_transformation,[],[f689]) ).
fof(f689,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rectify,[],[f219]) ).
fof(f219,axiom,
! [X7,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X7,X4)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4344,plain,
spl17_387,
inference(avatar_split_clause,[],[f1891,f4342]) ).
fof(f1891,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))) ),
inference(definition_unfolding,[],[f1634,f1380]) ).
fof(f1634,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_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,insert_fun_a_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f686]) ).
fof(f686,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rectify,[],[f222]) ).
fof(f222,axiom,
! [X7,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X7,X4)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4340,plain,
spl17_386,
inference(avatar_split_clause,[],[f1889,f4338]) ).
fof(f1889,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))) ),
inference(definition_unfolding,[],[f1632,f1378]) ).
fof(f1632,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_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,insert1325755072e_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f685]) ).
fof(f685,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rectify,[],[f221]) ).
fof(f221,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X7,X4)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4336,plain,
spl17_385,
inference(avatar_split_clause,[],[f1877,f4334]) ).
fof(f1877,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(definition_unfolding,[],[f1554,f1384]) ).
fof(f1554,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f994]) ).
fof(f994,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4332,plain,
spl17_384,
inference(avatar_split_clause,[],[f1872,f4330]) ).
fof(f1872,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(definition_unfolding,[],[f1534,f1386]) ).
fof(f1534,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f972]) ).
fof(f972,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X7,X4] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4328,plain,
spl17_383,
inference(avatar_split_clause,[],[f1854,f4326]) ).
fof(f1854,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(definition_unfolding,[],[f1473,f1378]) ).
fof(f1473,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f901]) ).
fof(f901,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f556]) ).
fof(f556,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4324,plain,
spl17_382,
inference(avatar_split_clause,[],[f1853,f4322]) ).
fof(f1853,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(definition_unfolding,[],[f1472,f1380]) ).
fof(f1472,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f900]) ).
fof(f900,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f555]) ).
fof(f555,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X7,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4320,plain,
spl17_381,
inference(avatar_split_clause,[],[f1809,f4318]) ).
fof(f1809,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,sK16(X0,X1,X2))),X1)) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,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,sK16(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(X0,X1,X2)),X2))
& is_pname(sK16(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1177,f1267]) ).
fof(f1267,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,sK16(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(X0,X1,X2)),X2))
& is_pname(sK16(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1177,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,[],[f1176]) ).
fof(f1176,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,[],[f805]) ).
fof(f805,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,[],[f376]) ).
fof(f376,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(f4316,plain,
spl17_380,
inference(avatar_split_clause,[],[f1729,f4314]) ).
fof(f1729,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK10(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,[],[f1240]) ).
fof(f1240,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,sK10(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK10(X0,X1,X2)),X2))
& is_fun_pname_bool(sK10(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,[sK10])],[f1238,f1239]) ).
fof(f1239,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,sK10(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK10(X0,X1,X2)),X2))
& is_fun_pname_bool(sK10(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1238,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,[],[f1237]) ).
fof(f1237,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,[],[f1085]) ).
fof(f1085,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,[],[f749]) ).
fof(f749,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,[],[f368]) ).
fof(f368,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)))
<=> ? [X37] :
( image_pname_a(X8,X37) = X9
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X37),X4))
& is_fun_pname_bool(X37) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4312,plain,
spl17_379,
inference(avatar_split_clause,[],[f1724,f4310]) ).
fof(f1724,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK9(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,[],[f1236]) ).
fof(f4307,plain,
spl17_378,
inference(avatar_split_clause,[],[f1721,f4305]) ).
fof(f1721,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK8(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,[],[f1234]) ).
fof(f1234,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,sK8(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK8(X0,X1,X2)),X2))
& is_pname(sK8(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,[sK8])],[f1232,f1233]) ).
fof(f1233,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,sK8(X0,X1,X2)) = X0
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK8(X0,X1,X2)),X2))
& is_pname(sK8(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1232,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,[],[f1231]) ).
fof(f1231,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,[],[f1082]) ).
fof(f1082,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,[],[f747]) ).
fof(f747,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,[],[f342]) ).
fof(f342,axiom,
! [X34,X8,X4] :
( is_a(X34)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X34),image_pname_a(X8,X4)))
<=> ? [X29] :
( hAPP_pname_a(X8,X29) = X34
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X4))
& is_pname(X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4303,plain,
spl17_377,
inference(avatar_split_clause,[],[f1719,f4301]) ).
fof(f1719,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(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,[],[f1230]) ).
fof(f1230,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(X0,X1,X2)),X2))
& hAPP_pname_a(X1,sK7(X0,X1,X2)) = X0
& is_pname(sK7(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,[sK7])],[f1081,f1229]) ).
fof(f1229,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,sK7(X0,X1,X2)),X2))
& hAPP_pname_a(X1,sK7(X0,X1,X2)) = X0
& is_pname(sK7(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1081,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,[],[f1080]) ).
fof(f1080,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,[],[f746]) ).
fof(f746,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,[],[f370]) ).
fof(f370,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(f4299,plain,
spl17_376,
inference(avatar_split_clause,[],[f1716,f4297]) ).
fof(f1716,plain,
! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)),
inference(cnf_transformation,[],[f745]) ).
fof(f745,plain,
! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X14,X13,X21] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X14)),X13)),hAPP_nat_nat(suc,X21)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X14),X13)),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4295,plain,
spl17_375,
inference(avatar_split_clause,[],[f1670,f4293]) ).
fof(f1670,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,[],[f1227]) ).
fof(f1227,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,[],[f1226]) ).
fof(f1226,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,[],[f700]) ).
fof(f700,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,[],[f211]) ).
fof(f211,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(f4291,plain,
spl17_374,
inference(avatar_split_clause,[],[f1667,f4289]) ).
fof(f1667,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,[],[f1225]) ).
fof(f1225,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,[],[f1224]) ).
fof(f1224,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,[],[f699]) ).
fof(f699,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,[],[f216]) ).
fof(f216,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(f4287,plain,
spl17_373,
inference(avatar_split_clause,[],[f1661,f4285]) ).
fof(f1661,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,[],[f1221]) ).
fof(f1221,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,[],[f1220]) ).
fof(f1220,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,[],[f697]) ).
fof(f697,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,[],[f214]) ).
fof(f214,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(f4283,plain,
spl17_372,
inference(avatar_split_clause,[],[f1658,f4281]) ).
fof(f1658,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,[],[f1219]) ).
fof(f1219,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,[],[f1218]) ).
fof(f1218,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,[],[f696]) ).
fof(f696,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,[],[f213]) ).
fof(f213,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(f4279,plain,
spl17_371,
inference(avatar_split_clause,[],[f1601,f4277]) ).
fof(f1601,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f1065]) ).
fof(f1065,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f671]) ).
fof(f671,plain,
! [X0,X1] :
( ( is_fun_pname_bool(X1)
& is_fun_pname_bool(X0) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
=> X0 = X1 ) ) ),
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X4,X9] :
( ( is_fun_pname_bool(X9)
& is_fun_pname_bool(X4) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),X4))
=> X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4275,plain,
spl17_370,
inference(avatar_split_clause,[],[f1593,f4273]) ).
fof(f1593,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,[],[f1054]) ).
fof(f1054,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,[],[f1053]) ).
fof(f1053,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,[],[f667]) ).
fof(f667,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,[],[f261]) ).
fof(f261,axiom,
! [X4,X9] :
( ( is_fun_a_bool(X9)
& is_fun_a_bool(X4) )
=> ( 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),X4))
=> X4 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4271,plain,
spl17_369,
inference(avatar_split_clause,[],[f1581,f4269]) ).
fof(f1581,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,[],[f1032]) ).
fof(f1032,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,[],[f1031]) ).
fof(f1031,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,[],[f658]) ).
fof(f658,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,[],[f236]) ).
fof(f236,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(f4266,plain,
spl17_368,
inference(avatar_split_clause,[],[f1572,f4264]) ).
fof(f1572,plain,
! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,plain,
! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f649]) ).
fof(f649,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X13,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X14))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X14)),X13) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4235,plain,
( spl17_367
| ~ spl17_72
| ~ spl17_216 ),
inference(avatar_split_clause,[],[f3240,f3126,f2391,f4233]) ).
fof(f4233,plain,
( spl17_367
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1))
| ~ is_fun949378684l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_367])]) ).
fof(f2391,plain,
( spl17_72
<=> ! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f3126,plain,
( spl17_216
<=> ! [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,[spl17_216])]) ).
fof(f3240,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1))
| ~ is_fun949378684l_bool(X2) )
| ~ spl17_72
| ~ spl17_216 ),
inference(superposition,[],[f2392,f3127]) ).
fof(f3127,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)
| ~ spl17_216 ),
inference(avatar_component_clause,[],[f3126]) ).
fof(f2392,plain,
( ! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) )
| ~ spl17_72 ),
inference(avatar_component_clause,[],[f2391]) ).
fof(f4117,plain,
( spl17_366
| ~ spl17_66
| ~ spl17_215 ),
inference(avatar_split_clause,[],[f3239,f3122,f2367,f4115]) ).
fof(f4115,plain,
( spl17_366
<=> ! [X2,X0,X1] :
( is_bool(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1))
| ~ is_fun1661590463l_bool(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_366])]) ).
fof(f2367,plain,
( spl17_66
<=> ! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f3122,plain,
( spl17_215
<=> ! [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,[spl17_215])]) ).
fof(f3239,plain,
( ! [X2,X0,X1] :
( is_bool(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1))
| ~ is_fun1661590463l_bool(X2) )
| ~ spl17_66
| ~ spl17_215 ),
inference(superposition,[],[f2368,f3123]) ).
fof(f3123,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)
| ~ spl17_215 ),
inference(avatar_component_clause,[],[f3122]) ).
fof(f2368,plain,
( ! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) )
| ~ spl17_66 ),
inference(avatar_component_clause,[],[f2367]) ).
fof(f4113,plain,
spl17_365,
inference(avatar_split_clause,[],[f2083,f4111]) ).
fof(f2083,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(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)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(forward_demodulation,[],[f1945,f1307]) ).
fof(f1945,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(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))),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(definition_unfolding,[],[f1812,f1382]) ).
fof(f1812,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f4109,plain,
spl17_364,
inference(avatar_split_clause,[],[f2048,f4107]) ).
fof(f2048,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1893,f1307]) ).
fof(f1893,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,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))) ),
inference(definition_unfolding,[],[f1636,f1382]) ).
fof(f1636,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,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,insert_nat(X0,X1))) ) ),
inference(nnf_transformation,[],[f687]) ).
fof(f687,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rectify,[],[f217]) ).
fof(f217,axiom,
! [X7,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X7,X4)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4105,plain,
spl17_363,
inference(avatar_split_clause,[],[f2046,f4103]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1887,f1306]) ).
fof(f1887,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))) ),
inference(definition_unfolding,[],[f1630,f1376]) ).
fof(f1630,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_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,insert_fun_nat_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f684]) ).
fof(f684,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X7,X4)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4101,plain,
spl17_362,
inference(avatar_split_clause,[],[f2031,f4099]) ).
fof(f2031,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_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))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1867,f1307]) ).
fof(f1867,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,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)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(definition_unfolding,[],[f1517,f1382]) ).
fof(f1517,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f952]) ).
fof(f952,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f597]) ).
fof(f597,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X7,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4097,plain,
spl17_361,
inference(avatar_split_clause,[],[f2026,f4095]) ).
fof(f2026,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1852,f1306]) ).
fof(f1852,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(definition_unfolding,[],[f1471,f1376]) ).
fof(f1471,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f899]) ).
fof(f899,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f554]) ).
fof(f554,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X7,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4093,plain,
spl17_360,
inference(avatar_split_clause,[],[f1777,f4091]) ).
fof(f1777,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(flattening,[],[f1145]) ).
fof(f1145,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f788]) ).
fof(f788,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ) ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X33,X4,X9] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X9))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),X33))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4089,plain,
spl17_359,
inference(avatar_split_clause,[],[f1770,f4087]) ).
fof(f1770,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_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,[],[f1135]) ).
fof(f1135,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_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(flattening,[],[f1134]) ).
fof(f1134,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_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,[],[f781]) ).
fof(f781,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),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ),
inference(rectify,[],[f324]) ).
fof(f324,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),X9))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4085,plain,
spl17_358,
inference(avatar_split_clause,[],[f1766,f4083]) ).
fof(f1766,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,[],[f1130]) ).
fof(f1130,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,[],[f1129]) ).
fof(f1129,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,[],[f777]) ).
fof(f777,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,[],[f330]) ).
fof(f330,axiom,
! [X33,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),X33))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4081,plain,
spl17_357,
inference(avatar_split_clause,[],[f1760,f4079]) ).
fof(f1760,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,[],[f1120]) ).
fof(f1120,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,[],[f1119]) ).
fof(f1119,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,[],[f771]) ).
fof(f771,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,[],[f323]) ).
fof(f323,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(f4077,plain,
spl17_356,
inference(avatar_split_clause,[],[f1758,f4075]) ).
fof(f1758,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,[],[f1117]) ).
fof(f1117,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,[],[f1116]) ).
fof(f1116,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,[],[f769]) ).
fof(f769,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,[],[f328]) ).
fof(f328,axiom,
! [X33,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),X33))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4073,plain,
( spl17_355
| ~ spl17_104
| ~ spl17_206 ),
inference(avatar_split_clause,[],[f3207,f3086,f2568,f4071]) ).
fof(f3207,plain,
( ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X0)))
| ~ spl17_104
| ~ spl17_206 ),
inference(resolution,[],[f3087,f2569]) ).
fof(f4069,plain,
spl17_354,
inference(avatar_split_clause,[],[f1752,f4067]) ).
fof(f1752,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,[],[f1107]) ).
fof(f1107,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,[],[f1106]) ).
fof(f1106,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,[],[f763]) ).
fof(f763,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,[],[f322]) ).
fof(f322,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(f4065,plain,
spl17_353,
inference(avatar_split_clause,[],[f1745,f4063]) ).
fof(f1745,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,[],[f1098]) ).
fof(f1098,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,[],[f1097]) ).
fof(f1097,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,[],[f758]) ).
fof(f758,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,[],[f206]) ).
fof(f206,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(f4061,plain,
spl17_352,
inference(avatar_split_clause,[],[f1744,f4059]) ).
fof(f1744,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f757]) ).
fof(f757,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(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
inference(rectify,[],[f248]) ).
fof(f248,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(minus_minus_nat(X14),X25)),hAPP_nat_nat(minus_minus_nat(X13),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4057,plain,
spl17_351,
inference(avatar_split_clause,[],[f1743,f4055]) ).
fof(f1743,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f756]) ).
fof(f756,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(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
inference(rectify,[],[f249]) ).
fof(f249,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(minus_minus_nat(X25),X13)),hAPP_nat_nat(minus_minus_nat(X25),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4053,plain,
spl17_350,
inference(avatar_split_clause,[],[f1733,f4051]) ).
fof(f1733,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f1242,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ( ~ hBOOL(hAPP_nat_bool(X1,sK11(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(X1)))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f1089,f1241]) ).
fof(f1241,plain,
! [X1] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
=> ( ~ hBOOL(hAPP_nat_bool(X1,sK11(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK11(X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f1089,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_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,[],[f1088]) ).
fof(f1088,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X1,hAPP_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,[],[f751]) ).
fof(f751,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(minus_minus_nat(X2),X0))) ) ),
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X38,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(minus_minus_nat(X15),X38))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4049,plain,
spl17_349,
inference(avatar_split_clause,[],[f1730,f4047]) ).
fof(f1730,plain,
! [X2,X0,X1] :
( image_pname_a(X1,sK10(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,[],[f1240]) ).
fof(f4045,plain,
spl17_348,
inference(avatar_split_clause,[],[f1722,f4043]) ).
fof(f1722,plain,
! [X2,X0,X1] :
( hAPP_pname_a(X1,sK8(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,[],[f1234]) ).
fof(f4041,plain,
spl17_347,
inference(avatar_split_clause,[],[f1718,f4039]) ).
fof(f1718,plain,
! [X2,X0,X1] :
( hAPP_pname_a(X1,sK7(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,[],[f1230]) ).
fof(f4037,plain,
spl17_346,
inference(avatar_split_clause,[],[f1457,f4035]) ).
fof(f1457,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(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,[],[f1188]) ).
fof(f4011,plain,
spl17_345,
inference(avatar_split_clause,[],[f2009,f4009]) ).
fof(f4009,plain,
( spl17_345
<=> ! [X2,X1] :
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X2))
| ~ is_a(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_345])]) ).
fof(f2009,plain,
! [X2,X1] :
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X2))
| ~ is_a(X2) ),
inference(duplicate_literal_removal,[],[f1991]) ).
fof(f1991,plain,
! [X2,X1] :
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X2))
| ~ is_a(X2)
| ~ is_a(X2) ),
inference(equality_resolution,[],[f1923]) ).
fof(f1923,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(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))),X2))
| X0 != X2
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(definition_unfolding,[],[f1781,f1386]) ).
fof(f1781,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| X0 != X2
| ~ is_a(X2)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f1250]) ).
fof(f4007,plain,
spl17_344,
inference(avatar_split_clause,[],[f2007,f4005]) ).
fof(f4005,plain,
( spl17_344
<=> ! [X2,X1] :
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X2))
| ~ is_pname(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_344])]) ).
fof(f2007,plain,
! [X2,X1] :
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X2))
| ~ is_pname(X2) ),
inference(duplicate_literal_removal,[],[f1993]) ).
fof(f1993,plain,
! [X2,X1] :
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X2))
| ~ is_pname(X2)
| ~ is_pname(X2) ),
inference(equality_resolution,[],[f1930]) ).
fof(f1930,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(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))),X2))
| X0 != X2
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(definition_unfolding,[],[f1788,f1384]) ).
fof(f1788,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| X0 != X2
| ~ is_pname(X2)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f4003,plain,
spl17_343,
inference(avatar_split_clause,[],[f1885,f4001]) ).
fof(f1885,plain,
! [X0,X1] :
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(definition_unfolding,[],[f1598,f1378]) ).
fof(f1598,plain,
! [X0,X1] :
( is_fun1661590463l_bool(insert1325755072e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,plain,
! [X0,X1] :
( is_fun1661590463l_bool(insert1325755072e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f1059]) ).
fof(f1059,plain,
! [X0,X1] :
( is_fun1661590463l_bool(insert1325755072e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( ( is_fun1661590463l_bool(X1)
& is_fun_pname_bool(X0) )
=> is_fun1661590463l_bool(insert1325755072e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3999,plain,
spl17_342,
inference(avatar_split_clause,[],[f1884,f3997]) ).
fof(f1884,plain,
! [X0,X1] :
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(definition_unfolding,[],[f1590,f1380]) ).
fof(f1590,plain,
! [X0,X1] :
( is_fun949378684l_bool(insert_fun_a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,plain,
! [X0,X1] :
( is_fun949378684l_bool(insert_fun_a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f1047]) ).
fof(f1047,plain,
! [X0,X1] :
( is_fun949378684l_bool(insert_fun_a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( ( is_fun949378684l_bool(X1)
& is_fun_a_bool(X0) )
=> is_fun949378684l_bool(insert_fun_a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3995,plain,
spl17_341,
inference(avatar_split_clause,[],[f1883,f3993]) ).
fof(f1883,plain,
! [X0,X1] :
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) ),
inference(definition_unfolding,[],[f1586,f1384]) ).
fof(f1586,plain,
! [X0,X1] :
( is_fun_pname_bool(insert_pname(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,plain,
! [X0,X1] :
( is_fun_pname_bool(insert_pname(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) ),
inference(flattening,[],[f1039]) ).
fof(f1039,plain,
! [X0,X1] :
( is_fun_pname_bool(insert_pname(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( ( is_fun_pname_bool(X1)
& is_pname(X0) )
=> is_fun_pname_bool(insert_pname(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3991,plain,
spl17_340,
inference(avatar_split_clause,[],[f1834,f3989]) ).
fof(f1834,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0))))),
inference(definition_unfolding,[],[f1370,f1384]) ).
fof(f1370,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),insert_pname(X1,X0))),
inference(cnf_transformation,[],[f487]) ).
fof(f487,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),insert_pname(X1,X0))),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X9,X7] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),insert_pname(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3987,plain,
spl17_339,
inference(avatar_split_clause,[],[f1833,f3985]) ).
fof(f1833,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),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(definition_unfolding,[],[f1369,f1384]) ).
fof(f1369,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1))),
inference(cnf_transformation,[],[f486]) ).
fof(f486,plain,
! [X0,X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1))),
inference(rectify,[],[f272]) ).
fof(f272,axiom,
! [X7,X9] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X7),insert_pname(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3983,plain,
spl17_338,
inference(avatar_split_clause,[],[f1832,f3981]) ).
fof(f1832,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0))))),
inference(definition_unfolding,[],[f1368,f1386]) ).
fof(f1368,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0))),
inference(cnf_transformation,[],[f485]) ).
fof(f485,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0))),
inference(rectify,[],[f353]) ).
fof(f353,axiom,
! [X9,X7] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),insert_a(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3979,plain,
spl17_337,
inference(avatar_split_clause,[],[f1831,f3977]) ).
fof(f1831,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),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(definition_unfolding,[],[f1367,f1386]) ).
fof(f1367,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X0,X1))),
inference(cnf_transformation,[],[f484]) ).
fof(f484,plain,
! [X0,X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X0,X1))),
inference(rectify,[],[f273]) ).
fof(f273,axiom,
! [X7,X9] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X7),insert_a(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3975,plain,
spl17_336,
inference(avatar_split_clause,[],[f1808,f3973]) ).
fof(f1808,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,sK16(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f3971,plain,
spl17_335,
inference(avatar_split_clause,[],[f1340,f3969]) ).
fof(f1340,plain,
! [X0,X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,plain,
! [X0] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(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,[sK0,sK1])],[f1183,f1185,f1184]) ).
fof(f1184,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,sK0(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1185,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),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1183,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,[],[f1182]) ).
fof(f1182,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,[],[f841]) ).
fof(f841,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,[],[f481]) ).
fof(f481,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,[],[f381]) ).
fof(f381,axiom,
! [X42] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X42))
<=> ? [X40] :
! [X29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X42))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3965,plain,
( ~ spl17_8
| spl17_334
| ~ spl17_100
| ~ spl17_325 ),
inference(avatar_split_clause,[],[f3929,f3795,f2550,f3962,f2128]) ).
fof(f3929,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_100
| ~ spl17_325 ),
inference(resolution,[],[f3796,f2552]) ).
fof(f3960,plain,
spl17_333,
inference(avatar_split_clause,[],[f1828,f3958]) ).
fof(f1828,plain,
! [X0,X1] :
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) ),
inference(definition_unfolding,[],[f1296,f1386]) ).
fof(f1296,plain,
! [X0,X1] :
( is_fun_a_bool(insert_a(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) ),
inference(cnf_transformation,[],[f819]) ).
fof(f819,plain,
! [X0,X1] :
( is_fun_a_bool(insert_a(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) ),
inference(flattening,[],[f818]) ).
fof(f818,plain,
! [X0,X1] :
( is_fun_a_bool(insert_a(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_a(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( ( is_fun_a_bool(X1)
& is_a(X0) )
=> is_fun_a_bool(insert_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3853,plain,
spl17_332,
inference(avatar_split_clause,[],[f2058,f3851]) ).
fof(f2058,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,[],[f2057,f1307]) ).
fof(f2057,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,[],[f2056,f1307]) ).
fof(f2056,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,[],[f1664,f1307]) ).
fof(f1664,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,[],[f1223]) ).
fof(f1223,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,[],[f1222]) ).
fof(f1222,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,[],[f698]) ).
fof(f698,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,[],[f215]) ).
fof(f215,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(f3849,plain,
spl17_331,
inference(avatar_split_clause,[],[f2051,f3847]) ).
fof(f2051,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f2050,f1306]) ).
fof(f2050,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(forward_demodulation,[],[f2049,f1306]) ).
fof(f2049,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_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(forward_demodulation,[],[f1655,f1306]) ).
fof(f1655,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,[],[f1217]) ).
fof(f1217,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,[],[f1216]) ).
fof(f1216,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,[],[f695]) ).
fof(f695,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,[],[f212]) ).
fof(f212,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(f3845,plain,
spl17_330,
inference(avatar_split_clause,[],[f2020,f3843]) ).
fof(f2020,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)))),
inference(forward_demodulation,[],[f1830,f1307]) ).
fof(f1830,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0))))),
inference(definition_unfolding,[],[f1366,f1382]) ).
fof(f1366,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),insert_nat(X1,X0))),
inference(cnf_transformation,[],[f483]) ).
fof(f483,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),insert_nat(X1,X0))),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X9,X7] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),insert_nat(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3813,plain,
spl17_329,
inference(avatar_split_clause,[],[f2019,f3811]) ).
fof(f2019,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),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(forward_demodulation,[],[f1829,f1307]) ).
fof(f1829,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),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(definition_unfolding,[],[f1365,f1382]) ).
fof(f1365,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X0,X1))),
inference(cnf_transformation,[],[f482]) ).
fof(f482,plain,
! [X0,X1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X0,X1))),
inference(rectify,[],[f271]) ).
fof(f271,axiom,
! [X7,X9] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X7),insert_nat(X7,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3809,plain,
spl17_328,
inference(avatar_split_clause,[],[f1772,f3807]) ).
fof(f1772,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,[],[f1137]) ).
fof(f1137,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,[],[f783]) ).
fof(f783,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,[],[f369]) ).
fof(f369,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(f3805,plain,
spl17_327,
inference(avatar_split_clause,[],[f1768,f3803]) ).
fof(f1768,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,[],[f1132]) ).
fof(f1132,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,[],[f779]) ).
fof(f779,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,[],[f343]) ).
fof(f343,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(f3801,plain,
spl17_326,
inference(avatar_split_clause,[],[f1734,f3799]) ).
fof(f1734,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK11(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f3797,plain,
spl17_325,
inference(avatar_split_clause,[],[f1732,f3795]) ).
fof(f1732,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,[],[f1087]) ).
fof(f1087,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,[],[f1086]) ).
fof(f1086,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,[],[f750]) ).
fof(f750,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,[],[f251]) ).
fof(f251,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(f3793,plain,
spl17_324,
inference(avatar_split_clause,[],[f1672,f3791]) ).
fof(f1672,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1228,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,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_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ) ),
inference(nnf_transformation,[],[f701]) ).
fof(f701,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f238]) ).
fof(f238,axiom,
! [X16,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X16)),hAPP_nat_nat(suc,X24)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3789,plain,
spl17_323,
inference(avatar_split_clause,[],[f1671,f3787]) ).
fof(f1671,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,X0)),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f3785,plain,
spl17_322,
inference(avatar_split_clause,[],[f1561,f3783]) ).
fof(f1561,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,[],[f1001]) ).
fof(f1001,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,[],[f639]) ).
fof(f639,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,[],[f143]) ).
fof(f143,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(f3781,plain,
spl17_321,
inference(avatar_split_clause,[],[f1560,f3779]) ).
fof(f1560,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,[],[f1000]) ).
fof(f1000,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,[],[f638]) ).
fof(f638,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,[],[f151]) ).
fof(f151,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(f3777,plain,
spl17_320,
inference(avatar_split_clause,[],[f1559,f3775]) ).
fof(f1559,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,[],[f999]) ).
fof(f999,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,[],[f637]) ).
fof(f637,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,[],[f136]) ).
fof(f136,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(f3772,plain,
spl17_319,
inference(avatar_split_clause,[],[f1558,f3770]) ).
fof(f1558,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f998]) ).
fof(f998,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f636]) ).
fof(f636,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3768,plain,
spl17_318,
inference(avatar_split_clause,[],[f1557,f3766]) ).
fof(f1557,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f997]) ).
fof(f997,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f635]) ).
fof(f635,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3764,plain,
spl17_317,
inference(avatar_split_clause,[],[f1556,f3762]) ).
fof(f1556,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f996]) ).
fof(f996,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f634]) ).
fof(f634,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X8,X4))),hAPP_f921600141ol_nat(finite_card_pname,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3760,plain,
spl17_316,
inference(avatar_split_clause,[],[f1539,f3758]) ).
fof(f1539,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,[],[f977]) ).
fof(f977,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,[],[f618]) ).
fof(f618,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,[],[f150]) ).
fof(f150,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(f3756,plain,
spl17_315,
inference(avatar_split_clause,[],[f1538,f3754]) ).
fof(f1538,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,[],[f976]) ).
fof(f976,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,[],[f617]) ).
fof(f617,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,[],[f141]) ).
fof(f141,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(f3752,plain,
spl17_314,
inference(avatar_split_clause,[],[f1537,f3750]) ).
fof(f1537,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,[],[f975]) ).
fof(f975,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,[],[f616]) ).
fof(f616,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,[],[f137]) ).
fof(f137,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(f3748,plain,
spl17_313,
inference(avatar_split_clause,[],[f1525,f3746]) ).
fof(f1525,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f960]) ).
fof(f960,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f605]) ).
fof(f605,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f155]) ).
fof(f155,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3744,plain,
spl17_312,
inference(avatar_split_clause,[],[f1524,f3742]) ).
fof(f1524,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,[],[f959]) ).
fof(f959,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,[],[f604]) ).
fof(f604,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,[],[f142]) ).
fof(f142,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(f3740,plain,
spl17_311,
inference(avatar_split_clause,[],[f1523,f3738]) ).
fof(f1523,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f958]) ).
fof(f958,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f603]) ).
fof(f603,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3736,plain,
spl17_310,
inference(avatar_split_clause,[],[f1522,f3734]) ).
fof(f1522,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f957]) ).
fof(f957,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f602]) ).
fof(f602,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3732,plain,
( ~ spl17_3
| spl17_309
| ~ spl17_100
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f3673,f3633,f2550,f3729,f2103]) ).
fof(f3673,plain,
( is_fun_pname_bool(sK10(g,mgt_call,u))
| ~ is_fun_a_bool(g)
| ~ spl17_100
| ~ spl17_294 ),
inference(resolution,[],[f3634,f2552]) ).
fof(f3727,plain,
spl17_308,
inference(avatar_split_clause,[],[f1521,f3725]) ).
fof(f1521,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f956]) ).
fof(f956,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f601]) ).
fof(f601,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f156]) ).
fof(f156,axiom,
! [X8,X4] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X8,X4))),hAPP_f22106695ol_nat(finite_card_nat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3723,plain,
spl17_307,
inference(avatar_split_clause,[],[f1494,f3721]) ).
fof(f1494,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,[],[f922]) ).
fof(f922,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,[],[f577]) ).
fof(f577,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,[],[f149]) ).
fof(f149,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(f3719,plain,
spl17_306,
inference(avatar_split_clause,[],[f1493,f3717]) ).
fof(f1493,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,[],[f921]) ).
fof(f921,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,[],[f576]) ).
fof(f576,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,[],[f148]) ).
fof(f148,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(f3715,plain,
spl17_305,
inference(avatar_split_clause,[],[f1492,f3713]) ).
fof(f1492,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,[],[f920]) ).
fof(f920,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,[],[f575]) ).
fof(f575,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,[],[f147]) ).
fof(f147,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(f3711,plain,
spl17_304,
inference(avatar_split_clause,[],[f1491,f3709]) ).
fof(f1491,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f919]) ).
fof(f919,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f574]) ).
fof(f574,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X8,X4] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X8,X4))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3707,plain,
spl17_303,
inference(avatar_split_clause,[],[f1490,f3705]) ).
fof(f1490,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f918]) ).
fof(f918,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f573]) ).
fof(f573,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X8,X4))),hAPP_f696928925ol_nat(finite346522414t_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3703,plain,
spl17_302,
inference(avatar_split_clause,[],[f1489,f3701]) ).
fof(f1489,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f917]) ).
fof(f917,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f572]) ).
fof(f572,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X8,X4] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X8,X4))),hAPP_f55526627ol_nat(finite1340463720e_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3699,plain,
spl17_301,
inference(avatar_split_clause,[],[f1488,f3697]) ).
fof(f1488,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,[],[f916]) ).
fof(f916,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,[],[f571]) ).
fof(f571,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,[],[f139]) ).
fof(f139,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(f3695,plain,
spl17_300,
inference(avatar_split_clause,[],[f1487,f3693]) ).
fof(f1487,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,[],[f915]) ).
fof(f915,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,[],[f570]) ).
fof(f570,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,[],[f140]) ).
fof(f140,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(f3691,plain,
spl17_299,
inference(avatar_split_clause,[],[f1486,f3689]) ).
fof(f1486,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,[],[f914]) ).
fof(f914,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,[],[f569]) ).
fof(f569,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,[],[f138]) ).
fof(f138,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(f3686,plain,
spl17_298,
inference(avatar_split_clause,[],[f1470,f3684]) ).
fof(f1470,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f898]) ).
fof(f898,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f553]) ).
fof(f553,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1))) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X8,X4] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X8,X4))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3682,plain,
spl17_297,
inference(avatar_split_clause,[],[f1469,f3680]) ).
fof(f1469,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f897]) ).
fof(f897,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f552]) ).
fof(f552,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1))) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X8,X4] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X8,X4))),hAPP_f98387925ol_nat(finite269641166l_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3678,plain,
spl17_296,
inference(avatar_split_clause,[],[f1468,f3676]) ).
fof(f1468,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f896]) ).
fof(f896,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f551]) ).
fof(f551,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1))) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X8,X4] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X8,X4))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3640,plain,
( spl17_295
| ~ spl17_3
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f3607,f2807,f2103,f3637]) ).
fof(f3637,plain,
( spl17_295
<=> p(g) = collect_fun_a_bool(p(g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_295])]) ).
fof(f3607,plain,
( p(g) = collect_fun_a_bool(p(g))
| ~ spl17_3
| ~ spl17_163 ),
inference(resolution,[],[f2808,f2105]) ).
fof(f3635,plain,
spl17_294,
inference(avatar_split_clause,[],[f1728,f3633]) ).
fof(f1728,plain,
! [X2,X0,X1] :
( is_fun_pname_bool(sK10(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,[],[f1240]) ).
fof(f3631,plain,
spl17_293,
inference(avatar_split_clause,[],[f1720,f3629]) ).
fof(f1720,plain,
! [X2,X0,X1] :
( is_pname(sK8(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,[],[f1234]) ).
fof(f3627,plain,
spl17_292,
inference(avatar_split_clause,[],[f1717,f3625]) ).
fof(f1717,plain,
! [X2,X0,X1] :
( is_pname(sK7(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,[],[f1230]) ).
fof(f3623,plain,
spl17_291,
inference(avatar_split_clause,[],[f1715,f3621]) ).
fof(f1715,plain,
! [X2,X0,X1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
inference(cnf_transformation,[],[f744]) ).
fof(f744,plain,
! [X0,X1,X2] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X22,X23,X21] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X22),X23)),X21) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X22),X21)),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3619,plain,
spl17_290,
inference(avatar_split_clause,[],[f1576,f3617]) ).
fof(f1576,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,[],[f1024]) ).
fof(f1024,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,[],[f1023]) ).
fof(f1023,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,[],[f653]) ).
fof(f653,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,[],[f259]) ).
fof(f259,axiom,
! [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),X4))
=> X4 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3615,plain,
spl17_289,
inference(avatar_split_clause,[],[f1573,f3613]) ).
fof(f1573,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,[],[f1019]) ).
fof(f1019,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,[],[f1018]) ).
fof(f1018,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,[],[f650]) ).
fof(f650,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,[],[f205]) ).
fof(f205,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,X13),X14))
=> X13 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3611,plain,
spl17_288,
inference(avatar_split_clause,[],[f1571,f3609]) ).
fof(f1571,plain,
! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1016]) ).
fof(f1016,plain,
! [X0,X1] :
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f648]) ).
fof(f648,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X22,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X13))
=> hAPP_nat_nat(minus_minus_nat(X13),hAPP_nat_nat(minus_minus_nat(X13),X22)) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3532,plain,
spl17_287,
inference(avatar_split_clause,[],[f2084,f3530]) ).
fof(f2084,plain,
! [X2,X1] : hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),X2)),
inference(forward_demodulation,[],[f2000,f1307]) ).
fof(f2000,plain,
! [X2,X1] : hBOOL(hAPP_nat_bool(collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X2)),
inference(equality_resolution,[],[f1946]) ).
fof(f1946,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(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))),X2))
| X0 != X2 ),
inference(definition_unfolding,[],[f1811,f1382]) ).
fof(f1811,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f1270]) ).
fof(f3528,plain,
spl17_286,
inference(avatar_split_clause,[],[f1669,f3526]) ).
fof(f1669,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,[],[f1227]) ).
fof(f3524,plain,
spl17_285,
inference(avatar_split_clause,[],[f1668,f3522]) ).
fof(f1668,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,[],[f1227]) ).
fof(f3520,plain,
spl17_284,
inference(avatar_split_clause,[],[f1666,f3518]) ).
fof(f1666,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,[],[f1225]) ).
fof(f3516,plain,
spl17_283,
inference(avatar_split_clause,[],[f1665,f3514]) ).
fof(f1665,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,[],[f1225]) ).
fof(f3512,plain,
spl17_282,
inference(avatar_split_clause,[],[f1660,f3510]) ).
fof(f1660,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,[],[f1221]) ).
fof(f3508,plain,
spl17_281,
inference(avatar_split_clause,[],[f1659,f3506]) ).
fof(f1659,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,[],[f1221]) ).
fof(f3504,plain,
spl17_280,
inference(avatar_split_clause,[],[f1657,f3502]) ).
fof(f1657,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,[],[f1219]) ).
fof(f3487,plain,
spl17_279,
inference(avatar_split_clause,[],[f1656,f3485]) ).
fof(f1656,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,[],[f1219]) ).
fof(f3483,plain,
spl17_278,
inference(avatar_split_clause,[],[f1629,f3481]) ).
fof(f1629,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,[],[f1203]) ).
fof(f1203,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,[],[f683]) ).
fof(f683,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,[],[f240]) ).
fof(f240,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(f3479,plain,
spl17_277,
inference(avatar_split_clause,[],[f1628,f3477]) ).
fof(f1628,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,[],[f1203]) ).
fof(f3475,plain,
spl17_276,
inference(avatar_split_clause,[],[f1624,f3473]) ).
fof(f1624,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f1079,f1199]) ).
fof(f1199,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,sK6(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1079,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,[],[f681]) ).
fof(f681,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,[],[f371]) ).
fof(f371,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(f3471,plain,
spl17_275,
inference(avatar_split_clause,[],[f1623,f3469]) ).
fof(f1623,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK6(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1200]) ).
fof(f3467,plain,
spl17_274,
inference(avatar_split_clause,[],[f1622,f3465]) ).
fof(f1622,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f1198,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X1))
& is_pname(sK5(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f1078,f1197]) ).
fof(f1197,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,sK5(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X1))
& is_pname(sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1078,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,[],[f1077]) ).
fof(f1077,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,[],[f680]) ).
fof(f680,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,[],[f373]) ).
fof(f373,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(f3463,plain,
spl17_273,
inference(avatar_split_clause,[],[f1621,f3461]) ).
fof(f1621,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK5(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f3459,plain,
spl17_272,
inference(avatar_split_clause,[],[f1619,f3457]) ).
fof(f1619,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,sK4(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,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,sK4(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(X0,X1)),X1))
& is_a(sK4(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1076,f1195]) ).
fof(f1195,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,sK4(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK4(X0,X1)),X1))
& is_a(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1076,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,[],[f1075]) ).
fof(f1075,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,[],[f679]) ).
fof(f679,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,[],[f372]) ).
fof(f372,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(f3455,plain,
spl17_271,
inference(avatar_split_clause,[],[f1618,f3453]) ).
fof(f1618,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,sK4(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f3451,plain,
spl17_270,
inference(avatar_split_clause,[],[f1616,f3449]) ).
fof(f1616,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,[],[f1074]) ).
fof(f1074,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,[],[f678]) ).
fof(f678,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,[],[f196]) ).
fof(f196,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(f3447,plain,
( spl17_269
| ~ spl17_33
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2496,f2335,f2229,f3445]) ).
fof(f3445,plain,
( spl17_269
<=> ! [X0,X1] : hAPP_n1025906991e_bool(X0,X1) = collect_pname(hAPP_n1025906991e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_269])]) ).
fof(f2229,plain,
( spl17_33
<=> ! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f2496,plain,
( ! [X0,X1] : hAPP_n1025906991e_bool(X0,X1) = collect_pname(hAPP_n1025906991e_bool(X0,X1))
| ~ spl17_33
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2230]) ).
fof(f2230,plain,
( ! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1))
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f2229]) ).
fof(f3443,plain,
spl17_268,
inference(avatar_split_clause,[],[f1615,f3441]) ).
fof(f1615,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,[],[f1074]) ).
fof(f3439,plain,
spl17_267,
inference(avatar_split_clause,[],[f1614,f3437]) ).
fof(f3437,plain,
( spl17_267
<=> ! [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,[spl17_267])]) ).
fof(f1614,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,[],[f1073]) ).
fof(f1073,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,[],[f677]) ).
fof(f677,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,[],[f195]) ).
fof(f195,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(f3435,plain,
spl17_266,
inference(avatar_split_clause,[],[f1613,f3433]) ).
fof(f3433,plain,
( spl17_266
<=> ! [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,[spl17_266])]) ).
fof(f1613,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,[],[f1073]) ).
fof(f3431,plain,
spl17_265,
inference(avatar_split_clause,[],[f1610,f3429]) ).
fof(f3429,plain,
( spl17_265
<=> ! [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,[spl17_265])]) ).
fof(f1610,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,[],[f1071]) ).
fof(f1071,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,[],[f675]) ).
fof(f675,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,[],[f194]) ).
fof(f194,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(f3427,plain,
spl17_264,
inference(avatar_split_clause,[],[f1609,f3425]) ).
fof(f3425,plain,
( spl17_264
<=> ! [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,[spl17_264])]) ).
fof(f1609,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,[],[f1071]) ).
fof(f3423,plain,
spl17_263,
inference(avatar_split_clause,[],[f1608,f3421]) ).
fof(f3421,plain,
( spl17_263
<=> ! [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,[spl17_263])]) ).
fof(f1608,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,[],[f1070]) ).
fof(f1070,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,[],[f674]) ).
fof(f674,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,[],[f193]) ).
fof(f193,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(f3419,plain,
spl17_262,
inference(avatar_split_clause,[],[f1607,f3417]) ).
fof(f3417,plain,
( spl17_262
<=> ! [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,[spl17_262])]) ).
fof(f1607,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,[],[f1070]) ).
fof(f3415,plain,
spl17_261,
inference(avatar_split_clause,[],[f1583,f3413]) ).
fof(f1583,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK3(X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,sK3(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,[sK3])],[f1034,f1189]) ).
fof(f1189,plain,
! [X1] :
( ? [X2] : hAPP_nat_nat(suc,X2) = X1
=> hAPP_nat_nat(suc,sK3(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f1034,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,[],[f660]) ).
fof(f660,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,[],[f375]) ).
fof(f375,axiom,
! [X13,X39] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X13)),X39))
=> ? [X40] : hAPP_nat_nat(suc,X40) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3411,plain,
spl17_260,
inference(avatar_split_clause,[],[f1582,f3409]) ).
fof(f1582,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,X0)),X1)) ),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,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,X0)),X1)) ),
inference(ennf_transformation,[],[f659]) ).
fof(f659,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f235]) ).
fof(f235,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3407,plain,
spl17_259,
inference(avatar_split_clause,[],[f1570,f3405]) ).
fof(f1570,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,[],[f1015]) ).
fof(f1015,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,[],[f647]) ).
fof(f647,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,[],[f237]) ).
fof(f237,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(f3403,plain,
( spl17_258
| ~ spl17_30
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2495,f2335,f2217,f3401]) ).
fof(f3401,plain,
( spl17_258
<=> ! [X0,X1] : image_1604018183_pname(X0,X1) = collect_pname(image_1604018183_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_258])]) ).
fof(f2217,plain,
( spl17_30
<=> ! [X0,X1] : is_fun_pname_bool(image_1604018183_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f2495,plain,
( ! [X0,X1] : image_1604018183_pname(X0,X1) = collect_pname(image_1604018183_pname(X0,X1))
| ~ spl17_30
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2218]) ).
fof(f2218,plain,
( ! [X0,X1] : is_fun_pname_bool(image_1604018183_pname(X0,X1))
| ~ spl17_30 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f3399,plain,
spl17_257,
inference(avatar_split_clause,[],[f1565,f3397]) ).
fof(f1565,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,[],[f1006]) ).
fof(f1006,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,[],[f1005]) ).
fof(f1005,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,[],[f642]) ).
fof(f642,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,[],[f234]) ).
fof(f234,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(f3395,plain,
spl17_256,
inference(avatar_split_clause,[],[f1543,f3393]) ).
fof(f1543,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,[],[f982]) ).
fof(f982,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,[],[f981]) ).
fof(f981,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,[],[f621]) ).
fof(f621,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,[],[f231]) ).
fof(f231,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(f3391,plain,
spl17_255,
inference(avatar_split_clause,[],[f1529,f3389]) ).
fof(f1529,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,[],[f965]) ).
fof(f965,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,[],[f964]) ).
fof(f964,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,[],[f608]) ).
fof(f608,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,[],[f233]) ).
fof(f233,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(f3387,plain,
spl17_254,
inference(avatar_split_clause,[],[f1506,f3385]) ).
fof(f3385,plain,
( spl17_254
<=> ! [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,[spl17_254])]) ).
fof(f1506,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,[],[f937]) ).
fof(f937,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,[],[f936]) ).
fof(f936,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,[],[f586]) ).
fof(f586,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,[],[f230]) ).
fof(f230,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(f3383,plain,
spl17_253,
inference(avatar_split_clause,[],[f1505,f3381]) ).
fof(f3381,plain,
( spl17_253
<=> ! [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,[spl17_253])]) ).
fof(f1505,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,[],[f935]) ).
fof(f935,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,[],[f934]) ).
fof(f934,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,[],[f585]) ).
fof(f585,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,[],[f232]) ).
fof(f232,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(f3379,plain,
spl17_252,
inference(avatar_split_clause,[],[f1504,f3377]) ).
fof(f3377,plain,
( spl17_252
<=> ! [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,[spl17_252])]) ).
fof(f1504,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,[],[f933]) ).
fof(f933,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,[],[f932]) ).
fof(f932,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,[],[f584]) ).
fof(f584,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,[],[f229]) ).
fof(f229,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(f3375,plain,
spl17_251,
inference(avatar_split_clause,[],[f1456,f3373]) ).
fof(f3373,plain,
( spl17_251
<=> ! [X0,X1] :
( is_pname(sK2(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,[spl17_251])]) ).
fof(f1456,plain,
! [X0,X1] :
( is_pname(sK2(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,[],[f1188]) ).
fof(f3370,plain,
spl17_250,
inference(avatar_split_clause,[],[f1289,f3367]) ).
fof(f1289,plain,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_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,[],[f446]) ).
fof(f446,axiom,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_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(f3326,plain,
( spl17_249
| ~ spl17_100
| ~ spl17_177 ),
inference(avatar_split_clause,[],[f2942,f2876,f2550,f3323]) ).
fof(f3323,plain,
( spl17_249
<=> hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(mgt_call,u)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_249])]) ).
fof(f2942,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(mgt_call,u)),g))
| ~ spl17_100
| ~ spl17_177 ),
inference(resolution,[],[f2877,f2552]) ).
fof(f3320,plain,
spl17_248,
inference(avatar_split_clause,[],[f1807,f3318]) ).
fof(f1807,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| is_pname(sK16(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f3316,plain,
spl17_247,
inference(avatar_split_clause,[],[f1714,f3314]) ).
fof(f1714,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,[],[f743]) ).
fof(f743,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,[],[f426]) ).
fof(f426,axiom,
! [X43,X44,X45] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_f1476298914l_bool(X43,X45),hAPP_f1664156314l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3312,plain,
spl17_246,
inference(avatar_split_clause,[],[f1713,f3310]) ).
fof(f1713,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,[],[f742]) ).
fof(f742,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,[],[f419]) ).
fof(f419,axiom,
! [X43,X44,X45] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_f198738859l_bool(X43,X45),hAPP_fun_a_bool_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3308,plain,
spl17_245,
inference(avatar_split_clause,[],[f1712,f3306]) ).
fof(f1712,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,[],[f741]) ).
fof(f741,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,[],[f423]) ).
fof(f423,axiom,
! [X43,X44,X45] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_f1748468828l_bool(X43,X45),hAPP_f54304608l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3304,plain,
spl17_244,
inference(avatar_split_clause,[],[f1711,f3302]) ).
fof(f1711,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,[],[f740]) ).
fof(f740,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,[],[f411]) ).
fof(f411,axiom,
! [X43,X44,X45] : hAPP_nat_bool(cOMBS_nat_bool_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_n1006566506l_bool(X43,X45),hAPP_nat_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3300,plain,
spl17_243,
inference(avatar_split_clause,[],[f1709,f3298]) ).
fof(f1709,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,[],[f738]) ).
fof(f738,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,[],[f413]) ).
fof(f413,axiom,
! [X43,X44,X45] : hAPP_pname_bool(cOMBS_568398431l_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_p393069232l_bool(X43,X45),hAPP_pname_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3296,plain,
spl17_242,
inference(avatar_split_clause,[],[f1708,f3294]) ).
fof(f1708,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,[],[f737]) ).
fof(f737,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,[],[f403]) ).
fof(f403,axiom,
! [X43,X44,X45] : hAPP_a_bool(cOMBS_a_bool_bool(X43,X44),X45) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X43,X45),hAPP_a_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3292,plain,
spl17_241,
inference(avatar_split_clause,[],[f1599,f3290]) ).
fof(f3290,plain,
( spl17_241
<=> ! [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,[spl17_241])]) ).
fof(f1599,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,[],[f1062]) ).
fof(f1062,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,[],[f1061]) ).
fof(f1061,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,[],[f669]) ).
fof(f669,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,[],[f407]) ).
fof(f407,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(f3288,plain,
spl17_240,
inference(avatar_split_clause,[],[f1591,f3286]) ).
fof(f3286,plain,
( spl17_240
<=> ! [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,[spl17_240])]) ).
fof(f1591,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,[],[f1050]) ).
fof(f1050,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,[],[f1049]) ).
fof(f1049,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,[],[f665]) ).
fof(f665,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,[],[f400]) ).
fof(f400,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(f3281,plain,
spl17_239,
inference(avatar_split_clause,[],[f1585,f3279]) ).
fof(f3279,plain,
( spl17_239
<=> ! [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,[spl17_239])]) ).
fof(f1585,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,[],[f1038]) ).
fof(f1038,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ~ is_pname(X1)
| ~ is_pname(X0) ),
inference(flattening,[],[f1037]) ).
fof(f1037,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,[],[f662]) ).
fof(f662,plain,
! [X0,X1] :
( ( is_pname(X1)
& is_pname(X0) )
=> ( X0 = X1
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ) ),
inference(rectify,[],[f397]) ).
fof(f397,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(f3277,plain,
spl17_238,
inference(avatar_split_clause,[],[f1584,f3275]) ).
fof(f1584,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,[],[f1036]) ).
fof(f1036,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,[],[f1035]) ).
fof(f1035,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,[],[f661]) ).
fof(f661,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,[],[f393]) ).
fof(f393,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(f3273,plain,
spl17_237,
inference(avatar_split_clause,[],[f1375,f3271]) ).
fof(f1375,plain,
! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)),
inference(cnf_transformation,[],[f492]) ).
fof(f492,plain,
! [X0,X1] : hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X14,X13] : hAPP_nat_nat(minus_minus_nat(X14),X13) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X14)),hAPP_nat_nat(suc,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3269,plain,
( spl17_236
| ~ spl17_21
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f3031,f2925,f2181,f3267]) ).
fof(f2181,plain,
( spl17_21
<=> ! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f3031,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)))
| ~ spl17_21
| ~ spl17_189 ),
inference(superposition,[],[f2182,f2926]) ).
fof(f2182,plain,
( ! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1))
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f3205,plain,
( spl17_235
| ~ spl17_9
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f3029,f2921,f2133,f3203]) ).
fof(f2133,plain,
( spl17_9
<=> ! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f3029,plain,
( ! [X2,X0,X1] : is_bool(hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)))
| ~ spl17_9
| ~ spl17_188 ),
inference(superposition,[],[f2134,f2922]) ).
fof(f2134,plain,
( ! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1))
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f2133]) ).
fof(f3201,plain,
spl17_234,
inference(avatar_split_clause,[],[f2062,f3199]) ).
fof(f2062,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,[],[f2061,f1307]) ).
fof(f2061,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,[],[f1662,f1307]) ).
fof(f1662,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,[],[f1223]) ).
fof(f3197,plain,
spl17_233,
inference(avatar_split_clause,[],[f2060,f3195]) ).
fof(f2060,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,[],[f2059,f1307]) ).
fof(f2059,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,[],[f1663,f1307]) ).
fof(f1663,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,[],[f1223]) ).
fof(f3193,plain,
spl17_232,
inference(avatar_split_clause,[],[f2055,f3191]) ).
fof(f2055,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(forward_demodulation,[],[f2054,f1306]) ).
fof(f2054,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1653,f1306]) ).
fof(f1653,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,[],[f1217]) ).
fof(f3189,plain,
spl17_231,
inference(avatar_split_clause,[],[f2053,f3187]) ).
fof(f2053,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f2052,f1306]) ).
fof(f2052,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1654,f1306]) ).
fof(f1654,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,[],[f1217]) ).
fof(f3185,plain,
spl17_230,
inference(avatar_split_clause,[],[f2044,f3183]) ).
fof(f3183,plain,
( spl17_230
<=> ! [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,[spl17_230])]) ).
fof(f2044,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,[],[f2043,f1307]) ).
fof(f2043,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,[],[f1611,f1307]) ).
fof(f1611,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,[],[f1072]) ).
fof(f1072,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,[],[f676]) ).
fof(f676,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,[],[f197]) ).
fof(f197,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(f3181,plain,
spl17_229,
inference(avatar_split_clause,[],[f2042,f3179]) ).
fof(f3179,plain,
( spl17_229
<=> ! [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,[spl17_229])]) ).
fof(f2042,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,[],[f2041,f1307]) ).
fof(f2041,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,[],[f1612,f1307]) ).
fof(f1612,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,[],[f1072]) ).
fof(f3177,plain,
spl17_228,
inference(avatar_split_clause,[],[f2040,f3175]) ).
fof(f3175,plain,
( spl17_228
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_228])]) ).
fof(f2040,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f2039,f1306]) ).
fof(f2039,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(forward_demodulation,[],[f1605,f1306]) ).
fof(f1605,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,[],[f1069]) ).
fof(f1069,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,[],[f673]) ).
fof(f673,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,[],[f192]) ).
fof(f192,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(f3173,plain,
spl17_227,
inference(avatar_split_clause,[],[f2038,f3171]) ).
fof(f3171,plain,
( spl17_227
<=> ! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_227])]) ).
fof(f2038,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f2037,f1306]) ).
fof(f2037,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(forward_demodulation,[],[f1606,f1306]) ).
fof(f1606,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,[],[f1069]) ).
fof(f3169,plain,
spl17_226,
inference(avatar_split_clause,[],[f1707,f3167]) ).
fof(f1707,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,[],[f736]) ).
fof(f736,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,[],[f433]) ).
fof(f433,axiom,
! [X43,X44,X45] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X43),X44),X45) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3165,plain,
( ~ spl17_225
| spl17_99
| ~ spl17_168 ),
inference(avatar_split_clause,[],[f2871,f2827,f2545,f3162]) ).
fof(f3162,plain,
( spl17_225
<=> hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_225])]) ).
fof(f2871,plain,
( ~ hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn)))
| spl17_99
| ~ spl17_168 ),
inference(resolution,[],[f2828,f2547]) ).
fof(f3160,plain,
spl17_224,
inference(avatar_split_clause,[],[f1706,f3158]) ).
fof(f1706,plain,
! [X2,X0,X1] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f735]) ).
fof(f735,plain,
! [X0,X1,X2] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X43,X44,X45] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X43),X44),X45) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3156,plain,
spl17_223,
inference(avatar_split_clause,[],[f1705,f3154]) ).
fof(f1705,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,[],[f734]) ).
fof(f734,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,[],[f428]) ).
fof(f428,axiom,
! [X43,X44,X45] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X43),X44),X45) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3152,plain,
spl17_222,
inference(avatar_split_clause,[],[f1704,f3150]) ).
fof(f1704,plain,
! [X2,X0,X1] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f733]) ).
fof(f733,plain,
! [X0,X1,X2] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X43,X44,X45] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X43),X44),X45) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3148,plain,
spl17_221,
inference(avatar_split_clause,[],[f1703,f3146]) ).
fof(f1703,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,[],[f732]) ).
fof(f732,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,[],[f430]) ).
fof(f430,axiom,
! [X43,X44,X45] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X43),X44),X45) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3144,plain,
spl17_220,
inference(avatar_split_clause,[],[f1702,f3142]) ).
fof(f1702,plain,
! [X2,X0,X1] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f731]) ).
fof(f731,plain,
! [X0,X1,X2] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X43,X44,X45] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X43),X44),X45) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3140,plain,
spl17_219,
inference(avatar_split_clause,[],[f1701,f3138]) ).
fof(f1701,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,[],[f730]) ).
fof(f730,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,[],[f409]) ).
fof(f409,axiom,
! [X43,X44,X45] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X43),X44),X45) = hAPP_nat_bool(hAPP_n1699378549t_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3136,plain,
spl17_218,
inference(avatar_split_clause,[],[f1700,f3134]) ).
fof(f1700,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,[],[f729]) ).
fof(f729,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,[],[f420]) ).
fof(f420,axiom,
! [X43,X44,X45] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X43),X44),X45) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3132,plain,
spl17_217,
inference(avatar_split_clause,[],[f1699,f3130]) ).
fof(f3130,plain,
( spl17_217
<=> ! [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,[spl17_217])]) ).
fof(f1699,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,[],[f728]) ).
fof(f728,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,[],[f438]) ).
fof(f438,axiom,
! [X43,X44,X45] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X43),X44),X45) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3128,plain,
spl17_216,
inference(avatar_split_clause,[],[f1698,f3126]) ).
fof(f1698,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,[],[f727]) ).
fof(f727,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,[],[f437]) ).
fof(f437,axiom,
! [X43,X44,X45] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X43),X44),X45) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3124,plain,
spl17_215,
inference(avatar_split_clause,[],[f1697,f3122]) ).
fof(f1697,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,[],[f726]) ).
fof(f726,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,[],[f439]) ).
fof(f439,axiom,
! [X43,X44,X45] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X43),X44),X45) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3120,plain,
spl17_214,
inference(avatar_split_clause,[],[f1696,f3118]) ).
fof(f1696,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,[],[f725]) ).
fof(f725,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,[],[f399]) ).
fof(f399,axiom,
! [X43,X44,X45] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X43),X44),X45) = hAPP_a_bool(hAPP_a_fun_a_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3116,plain,
spl17_213,
inference(avatar_split_clause,[],[f1695,f3114]) ).
fof(f1695,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,[],[f724]) ).
fof(f724,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,[],[f414]) ).
fof(f414,axiom,
! [X43,X44,X45] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X43),X44),X45) = hAPP_pname_bool(hAPP_p61793385e_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3112,plain,
spl17_212,
inference(avatar_split_clause,[],[f1694,f3110]) ).
fof(f1694,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,[],[f723]) ).
fof(f723,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,[],[f427]) ).
fof(f427,axiom,
! [X43,X44,X45] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X43),X44),X45) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3108,plain,
spl17_211,
inference(avatar_split_clause,[],[f1693,f3106]) ).
fof(f1693,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,[],[f722]) ).
fof(f722,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,[],[f415]) ).
fof(f415,axiom,
! [X43,X44,X45] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X43),X44),X45) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3104,plain,
spl17_210,
inference(avatar_split_clause,[],[f1692,f3102]) ).
fof(f1692,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,[],[f721]) ).
fof(f721,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,[],[f404]) ).
fof(f404,axiom,
! [X43,X44,X45] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X43),X44),X45) = hAPP_a_bool(hAPP_p1534023578a_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3100,plain,
spl17_209,
inference(avatar_split_clause,[],[f1691,f3098]) ).
fof(f3098,plain,
( spl17_209
<=> ! [X2,X0,X1] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_209])]) ).
fof(f1691,plain,
! [X2,X0,X1] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f720]) ).
fof(f720,plain,
! [X0,X1,X2] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X43,X44,X45] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X43),X44),X45) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3096,plain,
spl17_208,
inference(avatar_split_clause,[],[f1690,f3094]) ).
fof(f3094,plain,
( spl17_208
<=> ! [X2,X0,X1] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_208])]) ).
fof(f1690,plain,
! [X2,X0,X1] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f719]) ).
fof(f719,plain,
! [X0,X1,X2] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X43,X44,X45] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X43),X44),X45) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3092,plain,
spl17_207,
inference(avatar_split_clause,[],[f1689,f3090]) ).
fof(f3090,plain,
( spl17_207
<=> ! [X2,X0,X1] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_207])]) ).
fof(f1689,plain,
! [X2,X0,X1] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1),
inference(cnf_transformation,[],[f718]) ).
fof(f718,plain,
! [X0,X1,X2] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X43,X44,X45] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X43),X44),X45) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X43,X45),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3088,plain,
spl17_206,
inference(avatar_split_clause,[],[f1411,f3086]) ).
fof(f1411,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,[],[f528]) ).
fof(f528,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,[],[f208]) ).
fof(f208,axiom,
! [X14,X13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X13),X14))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3084,plain,
spl17_205,
inference(avatar_split_clause,[],[f1342,f3082]) ).
fof(f1342,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f3080,plain,
( spl17_204
| ~ spl17_52
| ~ spl17_177 ),
inference(avatar_split_clause,[],[f2940,f2876,f2311,f3078]) ).
fof(f3078,plain,
( spl17_204
<=> ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_204])]) ).
fof(f2940,plain,
( ! [X0] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0))
| ~ spl17_52
| ~ spl17_177 ),
inference(resolution,[],[f2877,f2312]) ).
fof(f3076,plain,
spl17_203,
inference(avatar_split_clause,[],[f1341,f3074]) ).
fof(f1341,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f3072,plain,
spl17_202,
inference(avatar_split_clause,[],[f1339,f3070]) ).
fof(f1339,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,[],[f840]) ).
fof(f840,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,[],[f480]) ).
fof(f480,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,[],[f84]) ).
fof(f84,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(f3068,plain,
spl17_201,
inference(avatar_split_clause,[],[f1338,f3066]) ).
fof(f1338,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,[],[f839]) ).
fof(f839,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,[],[f479]) ).
fof(f479,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,[],[f85]) ).
fof(f85,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(f3064,plain,
spl17_200,
inference(avatar_split_clause,[],[f1336,f3062]) ).
fof(f3062,plain,
( spl17_200
<=> ! [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,[spl17_200])]) ).
fof(f1336,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,[],[f837]) ).
fof(f837,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,[],[f477]) ).
fof(f477,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,[],[f90]) ).
fof(f90,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(f3060,plain,
spl17_199,
inference(avatar_split_clause,[],[f1335,f3058]) ).
fof(f3058,plain,
( spl17_199
<=> ! [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,[spl17_199])]) ).
fof(f1335,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,[],[f836]) ).
fof(f836,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,[],[f476]) ).
fof(f476,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,[],[f89]) ).
fof(f89,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(f3056,plain,
spl17_198,
inference(avatar_split_clause,[],[f1334,f3054]) ).
fof(f3054,plain,
( spl17_198
<=> ! [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,[spl17_198])]) ).
fof(f1334,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,[],[f835]) ).
fof(f835,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,[],[f475]) ).
fof(f475,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,[],[f91]) ).
fof(f91,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(f3052,plain,
spl17_197,
inference(avatar_split_clause,[],[f1333,f3050]) ).
fof(f3050,plain,
( spl17_197
<=> ! [X0] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_197])]) ).
fof(f1333,plain,
! [X0] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f834,plain,
! [X0] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ),
inference(ennf_transformation,[],[f474]) ).
fof(f474,plain,
! [X0] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0)))) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X4] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X4))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3048,plain,
spl17_196,
inference(avatar_split_clause,[],[f1332,f3046]) ).
fof(f3046,plain,
( spl17_196
<=> ! [X0] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_196])]) ).
fof(f1332,plain,
! [X0] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ),
inference(cnf_transformation,[],[f833]) ).
fof(f833,plain,
! [X0] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ),
inference(ennf_transformation,[],[f473]) ).
fof(f473,plain,
! [X0] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0)))) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X4] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X4))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3044,plain,
spl17_195,
inference(avatar_split_clause,[],[f1331,f3042]) ).
fof(f3042,plain,
( spl17_195
<=> ! [X0] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_195])]) ).
fof(f1331,plain,
! [X0] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ),
inference(cnf_transformation,[],[f832]) ).
fof(f832,plain,
! [X0] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ),
inference(ennf_transformation,[],[f472]) ).
fof(f472,plain,
! [X0] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0)))) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X4] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X4))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3040,plain,
spl17_194,
inference(avatar_split_clause,[],[f1288,f3037]) ).
fof(f1288,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,[],[f445]) ).
fof(f445,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(f2992,plain,
( spl17_193
| spl17_43
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f2869,f2803,f2273,f2989]) ).
fof(f2869,plain,
( is_a(sK4(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))))
| spl17_43
| ~ spl17_162 ),
inference(resolution,[],[f2804,f2275]) ).
fof(f2939,plain,
spl17_192,
inference(avatar_split_clause,[],[f2018,f2937]) ).
fof(f2018,plain,
! [X0] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(forward_demodulation,[],[f1337,f1306]) ).
fof(f1337,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,[],[f838]) ).
fof(f838,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,[],[f478]) ).
fof(f478,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,[],[f83]) ).
fof(f83,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(f2935,plain,
spl17_191,
inference(avatar_split_clause,[],[f1688,f2933]) ).
fof(f1688,plain,
! [X2,X0,X1] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)),
inference(cnf_transformation,[],[f717]) ).
fof(f717,plain,
! [X0,X1,X2] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X43,X44,X45] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_f1664156314l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2931,plain,
spl17_190,
inference(avatar_split_clause,[],[f1687,f2929]) ).
fof(f1687,plain,
! [X2,X0,X1] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)),
inference(cnf_transformation,[],[f716]) ).
fof(f716,plain,
! [X0,X1,X2] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X43,X44,X45] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_fun_a_bool_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2927,plain,
spl17_189,
inference(avatar_split_clause,[],[f1686,f2925]) ).
fof(f1686,plain,
! [X2,X0,X1] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)),
inference(cnf_transformation,[],[f715]) ).
fof(f715,plain,
! [X0,X1,X2] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)),
inference(rectify,[],[f421]) ).
fof(f421,axiom,
! [X43,X44,X45] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_f54304608l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2923,plain,
spl17_188,
inference(avatar_split_clause,[],[f1685,f2921]) ).
fof(f1685,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,[],[f714]) ).
fof(f714,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,[],[f410]) ).
fof(f410,axiom,
! [X43,X44,X45] : hAPP_nat_bool(cOMBB_bool_bool_nat(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_nat_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2919,plain,
spl17_187,
inference(avatar_split_clause,[],[f1681,f2917]) ).
fof(f1681,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,[],[f710]) ).
fof(f710,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,[],[f402]) ).
fof(f402,axiom,
! [X43,X44,X45] : hAPP_a_bool(cOMBB_bool_bool_a(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_a_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2915,plain,
spl17_186,
inference(avatar_split_clause,[],[f1680,f2913]) ).
fof(f1680,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,[],[f709]) ).
fof(f709,plain,
! [X0,X1,X2] : hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X43,X44,X45] : hAPP_pname_bool(cOMBB_647938656_pname(X43,X44),X45) = hAPP_bool_bool(X43,hAPP_pname_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2911,plain,
spl17_185,
inference(avatar_split_clause,[],[f1679,f2909]) ).
fof(f2907,plain,
spl17_184,
inference(avatar_split_clause,[],[f1678,f2905]) ).
fof(f1678,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,[],[f707]) ).
fof(f707,plain,
! [X0,X1,X2] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X43,X44,X45] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_pname_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2903,plain,
spl17_183,
inference(avatar_split_clause,[],[f1677,f2901]) ).
fof(f1677,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,[],[f706]) ).
fof(f706,plain,
! [X0,X1,X2] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X43,X44,X45] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_f1664156314l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2899,plain,
spl17_182,
inference(avatar_split_clause,[],[f1676,f2897]) ).
fof(f1676,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,[],[f705]) ).
fof(f705,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,[],[f429]) ).
fof(f429,axiom,
! [X43,X44,X45] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_fun_a_bool_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2895,plain,
spl17_181,
inference(avatar_split_clause,[],[f1675,f2893]) ).
fof(f1675,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,[],[f704]) ).
fof(f704,plain,
! [X0,X1,X2] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X43,X44,X45] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_f54304608l_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2891,plain,
spl17_180,
inference(avatar_split_clause,[],[f1674,f2889]) ).
fof(f1674,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,[],[f703]) ).
fof(f703,plain,
! [X0,X1,X2] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)),
inference(rectify,[],[f422]) ).
fof(f422,axiom,
! [X43,X44,X45] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_nat_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2887,plain,
spl17_179,
inference(avatar_split_clause,[],[f1673,f2885]) ).
fof(f1673,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,[],[f702]) ).
fof(f702,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,[],[f418]) ).
fof(f418,axiom,
! [X43,X44,X45] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X43,X44),X45) = hAPP_b589554111l_bool(X43,hAPP_a_bool(X44,X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2883,plain,
( spl17_178
| ~ spl17_44
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f2873,f2831,f2278,f2880]) ).
fof(f2880,plain,
( spl17_178
<=> hBOOL(hAPP_pname_bool(u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_178])]) ).
fof(f2873,plain,
( hBOOL(hAPP_pname_bool(u,pn))
| ~ spl17_44
| ~ spl17_169 ),
inference(resolution,[],[f2832,f2280]) ).
fof(f2878,plain,
spl17_177,
inference(avatar_split_clause,[],[f1577,f2876]) ).
fof(f1577,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,[],[f1025]) ).
fof(f1025,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,[],[f654]) ).
fof(f654,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,[],[f82]) ).
fof(f82,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(f2868,plain,
( spl17_176
| ~ spl17_28
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2494,f2335,f2209,f2866]) ).
fof(f2866,plain,
( spl17_176
<=> ! [X0,X1] : image_1705983821_pname(X0,X1) = collect_pname(image_1705983821_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_176])]) ).
fof(f2209,plain,
( spl17_28
<=> ! [X0,X1] : is_fun_pname_bool(image_1705983821_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f2494,plain,
( ! [X0,X1] : image_1705983821_pname(X0,X1) = collect_pname(image_1705983821_pname(X0,X1))
| ~ spl17_28
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2210]) ).
fof(f2210,plain,
( ! [X0,X1] : is_fun_pname_bool(image_1705983821_pname(X0,X1))
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f2209]) ).
fof(f2863,plain,
( spl17_175
| ~ spl17_29
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2493,f2335,f2213,f2861]) ).
fof(f2861,plain,
( spl17_175
<=> ! [X0,X1] : image_990671762_pname(X0,X1) = collect_pname(image_990671762_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_175])]) ).
fof(f2213,plain,
( spl17_29
<=> ! [X0,X1] : is_fun_pname_bool(image_990671762_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f2493,plain,
( ! [X0,X1] : image_990671762_pname(X0,X1) = collect_pname(image_990671762_pname(X0,X1))
| ~ spl17_29
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2214]) ).
fof(f2214,plain,
( ! [X0,X1] : is_fun_pname_bool(image_990671762_pname(X0,X1))
| ~ spl17_29 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f2859,plain,
( spl17_174
| ~ spl17_32
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2492,f2335,f2225,f2857]) ).
fof(f2857,plain,
( spl17_174
<=> ! [X0,X1] : image_1921560913_pname(X0,X1) = collect_pname(image_1921560913_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_174])]) ).
fof(f2225,plain,
( spl17_32
<=> ! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f2492,plain,
( ! [X0,X1] : image_1921560913_pname(X0,X1) = collect_pname(image_1921560913_pname(X0,X1))
| ~ spl17_32
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2226]) ).
fof(f2226,plain,
( ! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1))
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f2225]) ).
fof(f2855,plain,
( spl17_173
| ~ spl17_31
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2491,f2335,f2221,f2853]) ).
fof(f2853,plain,
( spl17_173
<=> ! [X0,X1] : image_nat_pname(X0,X1) = collect_pname(image_nat_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_173])]) ).
fof(f2221,plain,
( spl17_31
<=> ! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f2491,plain,
( ! [X0,X1] : image_nat_pname(X0,X1) = collect_pname(image_nat_pname(X0,X1))
| ~ spl17_31
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2222]) ).
fof(f2222,plain,
( ! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1))
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f2221]) ).
fof(f2849,plain,
( spl17_172
| ~ spl17_41
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2490,f2335,f2263,f2847]) ).
fof(f2490,plain,
( ! [X0] :
( collect_pname(X0) = collect_pname(collect_pname(X0))
| ~ is_fun_pname_bool(X0) )
| ~ spl17_41
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2264]) ).
fof(f2841,plain,
spl17_171,
inference(avatar_split_clause,[],[f2017,f2839]) ).
fof(f2017,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,[],[f1320,f1307]) ).
fof(f1320,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,[],[f466]) ).
fof(f466,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,[],[f200]) ).
fof(f200,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(f2837,plain,
spl17_170,
inference(avatar_split_clause,[],[f1647,f2835]) ).
fof(f1647,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1212,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,[],[f692]) ).
fof(f692,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
<=> hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(rectify,[],[f336]) ).
fof(f336,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(f2833,plain,
spl17_169,
inference(avatar_split_clause,[],[f1646,f2831]) ).
fof(f1646,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f2829,plain,
spl17_168,
inference(avatar_split_clause,[],[f1643,f2827]) ).
fof(f1643,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,[],[f1210]) ).
fof(f1210,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,[],[f690]) ).
fof(f690,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
<=> hBOOL(hAPP_a_bool(X1,X0)) ),
inference(rectify,[],[f335]) ).
fof(f335,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(f2825,plain,
spl17_167,
inference(avatar_split_clause,[],[f1642,f2823]) ).
fof(f1642,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,[],[f1210]) ).
fof(f2821,plain,
spl17_166,
inference(avatar_split_clause,[],[f1639,f2819]) ).
fof(f1639,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,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,[],[f688]) ).
fof(f688,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(rectify,[],[f334]) ).
fof(f334,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(f2817,plain,
spl17_165,
inference(avatar_split_clause,[],[f1638,f2815]) ).
fof(f1638,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1208]) ).
fof(f2813,plain,
spl17_164,
inference(avatar_split_clause,[],[f1620,f2811]) ).
fof(f1620,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| is_pname(sK5(X0,X1)) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f2809,plain,
( spl17_163
| ~ spl17_39
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2488,f2331,f2255,f2807]) ).
fof(f2488,plain,
( ! [X0] :
( p(X0) = collect_fun_a_bool(p(X0))
| ~ is_fun_a_bool(X0) )
| ~ spl17_39
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2256]) ).
fof(f2805,plain,
spl17_162,
inference(avatar_split_clause,[],[f1617,f2803]) ).
fof(f1617,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| is_a(sK4(X0,X1)) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f2801,plain,
spl17_161,
inference(avatar_split_clause,[],[f1580,f2799]) ).
fof(f2799,plain,
( spl17_161
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_161])]) ).
fof(f1580,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ),
inference(ennf_transformation,[],[f657]) ).
fof(f657,plain,
! [X0,X1] :
( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1)
=> X0 = X1 ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X17,X18] :
( hAPP_nat_nat(suc,X17) = hAPP_nat_nat(suc,X18)
=> X17 = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2797,plain,
spl17_160,
inference(avatar_split_clause,[],[f1553,f2795]) ).
fof(f2795,plain,
( spl17_160
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_160])]) ).
fof(f1553,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f993]) ).
fof(f993,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f631]) ).
fof(f631,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1))) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2793,plain,
spl17_159,
inference(avatar_split_clause,[],[f1552,f2791]) ).
fof(f1552,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,[],[f992]) ).
fof(f992,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,[],[f630]) ).
fof(f630,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,[],[f92]) ).
fof(f92,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(f2789,plain,
spl17_158,
inference(avatar_split_clause,[],[f1551,f2787]) ).
fof(f2787,plain,
( spl17_158
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_158])]) ).
fof(f1551,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f991]) ).
fof(f991,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f629]) ).
fof(f629,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1))) ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2785,plain,
spl17_157,
inference(avatar_split_clause,[],[f1550,f2783]) ).
fof(f2783,plain,
( spl17_157
<=> ! [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,[spl17_157])]) ).
fof(f1550,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,[],[f990]) ).
fof(f990,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,[],[f628]) ).
fof(f628,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(f2781,plain,
spl17_156,
inference(avatar_split_clause,[],[f1549,f2779]) ).
fof(f2779,plain,
( spl17_156
<=> ! [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,[spl17_156])]) ).
fof(f1549,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,[],[f989]) ).
fof(f989,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,[],[f627]) ).
fof(f627,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1))) ),
inference(rectify,[],[f117]) ).
fof(f117,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(f2777,plain,
spl17_155,
inference(avatar_split_clause,[],[f1548,f2775]) ).
fof(f1548,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,[],[f988]) ).
fof(f988,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,[],[f626]) ).
fof(f626,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1))) ),
inference(rectify,[],[f119]) ).
fof(f119,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(f2773,plain,
spl17_154,
inference(avatar_split_clause,[],[f1547,f2771]) ).
fof(f2771,plain,
( spl17_154
<=> ! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_154])]) ).
fof(f1547,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f987]) ).
fof(f987,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1))) ),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2769,plain,
spl17_153,
inference(avatar_split_clause,[],[f1546,f2767]) ).
fof(f2767,plain,
( spl17_153
<=> ! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_153])]) ).
fof(f1546,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f986]) ).
fof(f986,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f624]) ).
fof(f624,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1))) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2765,plain,
( spl17_152
| ~ spl17_13
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2485,f2331,f2149,f2763]) ).
fof(f2763,plain,
( spl17_152
<=> ! [X0,X1] : image_nat_fun_a_bool(X0,X1) = collect_fun_a_bool(image_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_152])]) ).
fof(f2149,plain,
( spl17_13
<=> ! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f2485,plain,
( ! [X0,X1] : image_nat_fun_a_bool(X0,X1) = collect_fun_a_bool(image_nat_fun_a_bool(X0,X1))
| ~ spl17_13
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2150]) ).
fof(f2150,plain,
( ! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1))
| ~ spl17_13 ),
inference(avatar_component_clause,[],[f2149]) ).
fof(f2761,plain,
spl17_151,
inference(avatar_split_clause,[],[f1545,f2759]) ).
fof(f2759,plain,
( spl17_151
<=> ! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_151])]) ).
fof(f1545,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f985]) ).
fof(f985,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1))) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2757,plain,
spl17_150,
inference(avatar_split_clause,[],[f1535,f2755]) ).
fof(f2755,plain,
( spl17_150
<=> ! [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,[spl17_150])]) ).
fof(f1535,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,[],[f973]) ).
fof(f973,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,[],[f614]) ).
fof(f614,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,[],[f106]) ).
fof(f106,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(f2753,plain,
spl17_149,
inference(avatar_split_clause,[],[f1533,f2751]) ).
fof(f2751,plain,
( spl17_149
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_149])]) ).
fof(f1533,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f971]) ).
fof(f971,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1))) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X5,X6] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2749,plain,
spl17_148,
inference(avatar_split_clause,[],[f1532,f2747]) ).
fof(f2747,plain,
( spl17_148
<=> ! [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,[spl17_148])]) ).
fof(f1532,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,[],[f970]) ).
fof(f970,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,[],[f611]) ).
fof(f611,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,[],[f99]) ).
fof(f99,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(f2745,plain,
spl17_147,
inference(avatar_split_clause,[],[f1519,f2743]) ).
fof(f2743,plain,
( spl17_147
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_147])]) ).
fof(f1519,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f954]) ).
fof(f954,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f599]) ).
fof(f599,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1))) ),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2741,plain,
spl17_146,
inference(avatar_split_clause,[],[f1518,f2739]) ).
fof(f2739,plain,
( spl17_146
<=> ! [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,[spl17_146])]) ).
fof(f1518,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,[],[f953]) ).
fof(f953,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,[],[f598]) ).
fof(f598,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,[],[f113]) ).
fof(f113,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(f2737,plain,
spl17_145,
inference(avatar_split_clause,[],[f1516,f2735]) ).
fof(f2735,plain,
( spl17_145
<=> ! [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,[spl17_145])]) ).
fof(f1516,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,[],[f951]) ).
fof(f951,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,[],[f596]) ).
fof(f596,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,[],[f110]) ).
fof(f110,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(f2733,plain,
spl17_144,
inference(avatar_split_clause,[],[f1515,f2731]) ).
fof(f1515,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,[],[f950]) ).
fof(f950,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,[],[f595]) ).
fof(f595,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1))) ),
inference(rectify,[],[f111]) ).
fof(f111,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(f2729,plain,
spl17_143,
inference(avatar_split_clause,[],[f1514,f2727]) ).
fof(f2727,plain,
( spl17_143
<=> ! [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,[spl17_143])]) ).
fof(f1514,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,[],[f949]) ).
fof(f949,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,[],[f594]) ).
fof(f594,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1))) ),
inference(rectify,[],[f112]) ).
fof(f112,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(f2725,plain,
spl17_142,
inference(avatar_split_clause,[],[f1513,f2723]) ).
fof(f2723,plain,
( spl17_142
<=> ! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_142])]) ).
fof(f1513,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f948]) ).
fof(f948,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f593]) ).
fof(f593,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1))) ),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2721,plain,
( spl17_141
| ~ spl17_38
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2484,f2331,f2251,f2719]) ).
fof(f2484,plain,
( ! [X0] :
( collect_fun_a_bool(X0) = collect_fun_a_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) )
| ~ spl17_38
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2252]) ).
fof(f2717,plain,
spl17_140,
inference(avatar_split_clause,[],[f1512,f2715]) ).
fof(f2715,plain,
( spl17_140
<=> ! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_140])]) ).
fof(f1512,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f947]) ).
fof(f947,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f592]) ).
fof(f592,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1))) ),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2713,plain,
spl17_139,
inference(avatar_split_clause,[],[f1511,f2711]) ).
fof(f2711,plain,
( spl17_139
<=> ! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_139])]) ).
fof(f1511,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f946]) ).
fof(f946,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f591]) ).
fof(f591,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1))) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X5,X6] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2709,plain,
spl17_138,
inference(avatar_split_clause,[],[f1482,f2707]) ).
fof(f2707,plain,
( spl17_138
<=> ! [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,[spl17_138])]) ).
fof(f1482,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,[],[f910]) ).
fof(f910,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,[],[f565]) ).
fof(f565,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1))) ),
inference(rectify,[],[f103]) ).
fof(f103,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(f2705,plain,
spl17_137,
inference(avatar_split_clause,[],[f1481,f2703]) ).
fof(f2703,plain,
( spl17_137
<=> ! [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,[spl17_137])]) ).
fof(f1481,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,[],[f909]) ).
fof(f909,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,[],[f564]) ).
fof(f564,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1))) ),
inference(rectify,[],[f104]) ).
fof(f104,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(f2701,plain,
spl17_136,
inference(avatar_split_clause,[],[f1480,f2699]) ).
fof(f2699,plain,
( spl17_136
<=> ! [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,[spl17_136])]) ).
fof(f1480,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,[],[f908]) ).
fof(f908,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,[],[f563]) ).
fof(f563,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1))) ),
inference(rectify,[],[f105]) ).
fof(f105,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(f2697,plain,
spl17_135,
inference(avatar_split_clause,[],[f1479,f2695]) ).
fof(f2695,plain,
( spl17_135
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_135])]) ).
fof(f1479,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f907]) ).
fof(f907,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f562]) ).
fof(f562,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1))) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2693,plain,
spl17_134,
inference(avatar_split_clause,[],[f1478,f2691]) ).
fof(f2691,plain,
( spl17_134
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_134])]) ).
fof(f1478,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f906]) ).
fof(f906,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f561]) ).
fof(f561,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1))) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X5,X6] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2689,plain,
spl17_133,
inference(avatar_split_clause,[],[f1477,f2687]) ).
fof(f2687,plain,
( spl17_133
<=> ! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_133])]) ).
fof(f1477,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f905]) ).
fof(f905,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f560]) ).
fof(f560,plain,
! [X0,X1] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1))) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X5,X6] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X6))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2685,plain,
spl17_132,
inference(avatar_split_clause,[],[f1476,f2683]) ).
fof(f2683,plain,
( spl17_132
<=> ! [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,[spl17_132])]) ).
fof(f1476,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,[],[f904]) ).
fof(f904,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,[],[f559]) ).
fof(f559,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,[],[f96]) ).
fof(f96,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(f2681,plain,
spl17_131,
inference(avatar_split_clause,[],[f1475,f2679]) ).
fof(f2679,plain,
( spl17_131
<=> ! [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,[spl17_131])]) ).
fof(f1475,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,[],[f903]) ).
fof(f903,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,[],[f558]) ).
fof(f558,plain,
! [X0,X1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1))) ),
inference(rectify,[],[f97]) ).
fof(f97,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(f2677,plain,
( spl17_130
| ~ spl17_12
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f2481,f2327,f2145,f2675]) ).
fof(f2675,plain,
( spl17_130
<=> ! [X0,X1] : image_1655916159e_bool(X0,X1) = collec1974731493e_bool(image_1655916159e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_130])]) ).
fof(f2145,plain,
( spl17_12
<=> ! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f2481,plain,
( ! [X0,X1] : image_1655916159e_bool(X0,X1) = collec1974731493e_bool(image_1655916159e_bool(X0,X1))
| ~ spl17_12
| ~ spl17_56 ),
inference(resolution,[],[f2328,f2146]) ).
fof(f2146,plain,
( ! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1))
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f2145]) ).
fof(f2673,plain,
spl17_129,
inference(avatar_split_clause,[],[f1474,f2671]) ).
fof(f2671,plain,
( spl17_129
<=> ! [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,[spl17_129])]) ).
fof(f1474,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,[],[f902]) ).
fof(f902,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,[],[f557]) ).
fof(f557,plain,
! [X0,X1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1))) ),
inference(rectify,[],[f98]) ).
fof(f98,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(f2669,plain,
spl17_128,
inference(avatar_split_clause,[],[f1467,f2667]) ).
fof(f2667,plain,
( spl17_128
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_128])]) ).
fof(f1467,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f895]) ).
fof(f895,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f550]) ).
fof(f550,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1))) ),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X5,X6] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2665,plain,
spl17_127,
inference(avatar_split_clause,[],[f1466,f2663]) ).
fof(f2663,plain,
( spl17_127
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_127])]) ).
fof(f1466,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f894]) ).
fof(f894,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f549]) ).
fof(f549,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1))) ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X5,X6] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2661,plain,
spl17_126,
inference(avatar_split_clause,[],[f1465,f2659]) ).
fof(f2659,plain,
( spl17_126
<=> ! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_126])]) ).
fof(f1465,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f893]) ).
fof(f893,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f548]) ).
fof(f548,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1))) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X5,X6] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X6))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2657,plain,
spl17_125,
inference(avatar_split_clause,[],[f1464,f2655]) ).
fof(f2655,plain,
( spl17_125
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).
fof(f1464,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f892]) ).
fof(f892,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f547]) ).
fof(f547,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1))) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X5,X6] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2653,plain,
spl17_124,
inference(avatar_split_clause,[],[f1463,f2651]) ).
fof(f2651,plain,
( spl17_124
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
fof(f1463,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f891]) ).
fof(f891,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f546]) ).
fof(f546,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1))) ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X5,X6] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2649,plain,
spl17_123,
inference(avatar_split_clause,[],[f1462,f2647]) ).
fof(f2647,plain,
( spl17_123
<=> ! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
fof(f1462,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f890]) ).
fof(f890,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f545]) ).
fof(f545,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1))) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X5,X6] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X6))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X5,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2645,plain,
spl17_122,
inference(avatar_split_clause,[],[f1461,f2643]) ).
fof(f2643,plain,
( spl17_122
<=> ! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
fof(f1461,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f889]) ).
fof(f889,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f544]) ).
fof(f544,plain,
! [X0,X1] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1))) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X7,X4] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X4))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2641,plain,
spl17_121,
inference(avatar_split_clause,[],[f1460,f2639]) ).
fof(f2639,plain,
( spl17_121
<=> ! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
fof(f1460,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f888]) ).
fof(f888,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f543]) ).
fof(f543,plain,
! [X0,X1] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1))) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X7,X4] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X4))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2637,plain,
spl17_120,
inference(avatar_split_clause,[],[f1459,f2635]) ).
fof(f2635,plain,
( spl17_120
<=> ! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
fof(f1459,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f887]) ).
fof(f887,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0,X1] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1))) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X7,X4] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X4))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X7,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2633,plain,
( spl17_119
| ~ spl17_37
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f2480,f2327,f2247,f2631]) ).
fof(f2480,plain,
( ! [X0] :
( collec1974731493e_bool(X0) = collec1974731493e_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) )
| ~ spl17_37
| ~ spl17_56 ),
inference(resolution,[],[f2328,f2248]) ).
fof(f2629,plain,
spl17_118,
inference(avatar_split_clause,[],[f1408,f2627]) ).
fof(f1408,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f525]) ).
fof(f525,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(rectify,[],[f389]) ).
fof(f389,axiom,
! [X43,X44] :
( hBOOL(X44)
| hBOOL(X43)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X43),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2625,plain,
spl17_117,
inference(avatar_split_clause,[],[f1405,f2623]) ).
fof(f1405,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f522]) ).
fof(f522,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X43,X44] :
( hBOOL(X44)
| ~ hBOOL(X43)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X43),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2621,plain,
spl17_116,
inference(avatar_split_clause,[],[f1394,f2619]) ).
fof(f1394,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f511]) ).
fof(f511,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X44,X43] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X43),X44))
| ~ hBOOL(X44)
| ~ hBOOL(X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2615,plain,
spl17_115,
inference(avatar_split_clause,[],[f1410,f2613]) ).
fof(f2613,plain,
( spl17_115
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
fof(f1410,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(cnf_transformation,[],[f527]) ).
fof(f527,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(rectify,[],[f405]) ).
fof(f405,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(f2611,plain,
spl17_114,
inference(avatar_split_clause,[],[f1409,f2609]) ).
fof(f1409,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(cnf_transformation,[],[f526]) ).
fof(f526,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(rectify,[],[f395]) ).
fof(f395,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(f2607,plain,
spl17_113,
inference(avatar_split_clause,[],[f1374,f2605]) ).
fof(f1374,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
inference(cnf_transformation,[],[f491]) ).
fof(f491,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X14,X13] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X14),X13)),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2603,plain,
spl17_112,
inference(avatar_split_clause,[],[f1597,f2601]) ).
fof(f1597,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(flattening,[],[f1057]) ).
fof(f1057,plain,
! [X0,X1] :
( is_bool(hAPP_pname_bool(X0,X1))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,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(f2599,plain,
spl17_111,
inference(avatar_split_clause,[],[f1589,f2597]) ).
fof(f1589,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(flattening,[],[f1045]) ).
fof(f1045,plain,
! [X0,X1] :
( is_bool(hAPP_a_bool(X0,X1))
| ~ is_a(X1)
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,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(f2595,plain,
spl17_110,
inference(avatar_split_clause,[],[f1407,f2593]) ).
fof(f1407,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f524]) ).
fof(f524,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f385]) ).
fof(f385,axiom,
! [X43,X44] :
( hBOOL(X43)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X43),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2590,plain,
spl17_109,
inference(avatar_split_clause,[],[f1406,f2588]) ).
fof(f1406,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f523]) ).
fof(f523,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X43,X44] :
( hBOOL(X44)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X43),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2586,plain,
spl17_108,
inference(avatar_split_clause,[],[f1398,f2584]) ).
fof(f1398,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f515]) ).
fof(f515,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f390]) ).
fof(f390,axiom,
! [X44,X43] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X43),X44))
| hBOOL(X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2582,plain,
spl17_107,
inference(avatar_split_clause,[],[f1397,f2580]) ).
fof(f1397,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f514]) ).
fof(f514,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X43,X44] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X43),X44))
| ~ hBOOL(X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2578,plain,
spl17_106,
inference(avatar_split_clause,[],[f1396,f2576]) ).
fof(f1396,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f513]) ).
fof(f513,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X44,X43] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X43),X44))
| ~ hBOOL(X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2574,plain,
spl17_105,
inference(avatar_split_clause,[],[f1395,f2572]) ).
fof(f1395,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f512,plain,
! [X0,X1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X43,X44] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X43),X44))
| ~ hBOOL(X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2570,plain,
spl17_104,
inference(avatar_split_clause,[],[f1318,f2568]) ).
fof(f1318,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(cnf_transformation,[],[f464]) ).
fof(f464,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(rectify,[],[f241]) ).
fof(f241,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(f2566,plain,
( spl17_103
| ~ spl17_5
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f2483,f2331,f2113,f2563]) ).
fof(f2563,plain,
( spl17_103
<=> finite_finite_a = collect_fun_a_bool(finite_finite_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f2483,plain,
( finite_finite_a = collect_fun_a_bool(finite_finite_a)
| ~ spl17_5
| ~ spl17_57 ),
inference(resolution,[],[f2332,f2115]) ).
fof(f2561,plain,
spl17_102,
inference(avatar_split_clause,[],[f1298,f2559]) ).
fof(f1298,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f823]) ).
fof(f823,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(flattening,[],[f822]) ).
fof(f822,plain,
! [X0,X1] :
( is_bool(hAPP_fun_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,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(f2557,plain,
spl17_101,
inference(avatar_split_clause,[],[f1297,f2555]) ).
fof(f1297,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f821]) ).
fof(f821,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(flattening,[],[f820]) ).
fof(f820,plain,
! [X0,X1] :
( is_bool(hAPP_f1664156314l_bool(X0,X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,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(f2553,plain,
spl17_100,
inference(avatar_split_clause,[],[f1287,f2550]) ).
fof(f1287,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f444]) ).
fof(f444,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(f2548,plain,
~ spl17_99,
inference(avatar_split_clause,[],[f1286,f2545]) ).
fof(f1286,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(cnf_transformation,[],[f448]) ).
fof(f448,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(f2541,plain,
spl17_98,
inference(avatar_split_clause,[],[f2016,f2539]) ).
fof(f2016,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
inference(forward_demodulation,[],[f1319,f1307]) ).
fof(f1319,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,[],[f465]) ).
fof(f465,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,[],[f199]) ).
fof(f199,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(f2537,plain,
spl17_97,
inference(avatar_split_clause,[],[f1305,f2534]) ).
fof(f1305,plain,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2532,plain,
spl17_96,
inference(avatar_split_clause,[],[f1304,f2529]) ).
fof(f1304,plain,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2516,plain,
( spl17_95
| ~ spl17_4
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f2497,f2335,f2108,f2513]) ).
fof(f2497,plain,
( u = collect_pname(u)
| ~ spl17_4
| ~ spl17_58 ),
inference(resolution,[],[f2336,f2110]) ).
fof(f2505,plain,
( spl17_94
| ~ spl17_2
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f2479,f2327,f2098,f2502]) ).
fof(f2502,plain,
( spl17_94
<=> finite_finite_pname = collec1974731493e_bool(finite_finite_pname) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
fof(f2479,plain,
( finite_finite_pname = collec1974731493e_bool(finite_finite_pname)
| ~ spl17_2
| ~ spl17_56 ),
inference(resolution,[],[f2328,f2100]) ).
fof(f2477,plain,
spl17_93,
inference(avatar_split_clause,[],[f1965,f2475]) ).
fof(f2475,plain,
( spl17_93
<=> ! [X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
fof(f1965,plain,
! [X1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
inference(equality_resolution,[],[f1404]) ).
fof(f1404,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f521]) ).
fof(f521,plain,
! [X0,X1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f408]) ).
fof(f408,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(f2473,plain,
spl17_92,
inference(avatar_split_clause,[],[f1964,f2471]) ).
fof(f2471,plain,
( spl17_92
<=> ! [X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
fof(f1964,plain,
! [X1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
inference(equality_resolution,[],[f1403]) ).
fof(f1403,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f520]) ).
fof(f520,plain,
! [X0,X1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f401]) ).
fof(f401,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(f2469,plain,
spl17_91,
inference(avatar_split_clause,[],[f1963,f2467]) ).
fof(f2467,plain,
( spl17_91
<=> ! [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
fof(f1963,plain,
! [X1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
inference(equality_resolution,[],[f1402]) ).
fof(f1402,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f519]) ).
fof(f519,plain,
! [X0,X1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f406]) ).
fof(f406,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(f2465,plain,
spl17_90,
inference(avatar_split_clause,[],[f1962,f2463]) ).
fof(f2463,plain,
( spl17_90
<=> ! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
fof(f1962,plain,
! [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(equality_resolution,[],[f1401]) ).
fof(f1401,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f518]) ).
fof(f518,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f396]) ).
fof(f396,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(f2461,plain,
spl17_89,
inference(avatar_split_clause,[],[f1961,f2459]) ).
fof(f1961,plain,
! [X1] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
inference(equality_resolution,[],[f1400]) ).
fof(f1400,plain,
! [X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f517]) ).
fof(f517,plain,
! [X0,X1] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f394]) ).
fof(f394,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(f2457,plain,
spl17_88,
inference(avatar_split_clause,[],[f1960,f2455]) ).
fof(f2455,plain,
( spl17_88
<=> ! [X1] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
fof(f1960,plain,
! [X1] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
inference(equality_resolution,[],[f1399]) ).
fof(f1399,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f516]) ).
fof(f516,plain,
! [X0,X1] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| X0 != X1 ),
inference(rectify,[],[f398]) ).
fof(f398,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(f2453,plain,
spl17_87,
inference(avatar_split_clause,[],[f1441,f2451]) ).
fof(f1441,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBS_568398431l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f872]) ).
fof(f872,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(f2449,plain,
spl17_86,
inference(avatar_split_clause,[],[f1440,f2447]) ).
fof(f1440,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f871]) ).
fof(f871,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_f759274231e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,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(f2445,plain,
spl17_85,
inference(avatar_split_clause,[],[f1439,f2443]) ).
fof(f1439,plain,
! [X0,X1] :
( is_fun_pname_bool(cOMBB_647938656_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f870]) ).
fof(f870,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(f2441,plain,
spl17_84,
inference(avatar_split_clause,[],[f1438,f2439]) ).
fof(f1438,plain,
! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f869]) ).
fof(f869,plain,
! [X0,X1] :
( is_fun_pname_bool(image_pname_pname(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,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(f2437,plain,
spl17_83,
inference(avatar_split_clause,[],[f1437,f2435]) ).
fof(f1437,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f868]) ).
fof(f868,plain,
! [X0,X1] :
( is_fun949378684l_bool(image_112932426a_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,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(f2433,plain,
spl17_82,
inference(avatar_split_clause,[],[f1436,f2431]) ).
fof(f1436,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f867]) ).
fof(f867,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,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(f2429,plain,
spl17_81,
inference(avatar_split_clause,[],[f1435,f2427]) ).
fof(f1435,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f866]) ).
fof(f866,plain,
! [X0,X1] :
( is_fun1661590463l_bool(image_47868345e_bool(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,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(f2425,plain,
spl17_80,
inference(avatar_split_clause,[],[f1433,f2423]) ).
fof(f1433,plain,
! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f863]) ).
fof(f863,plain,
! [X0,X1] :
( is_fun_pname_bool(image_a_pname(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,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(f2421,plain,
spl17_79,
inference(avatar_split_clause,[],[f1432,f2419]) ).
fof(f2419,plain,
( spl17_79
<=> ! [X0,X1] :
( is_fun_a_bool(cOMBS_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f1432,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBS_a_bool_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f862]) ).
fof(f862,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(f2417,plain,
spl17_78,
inference(avatar_split_clause,[],[f1431,f2415]) ).
fof(f2415,plain,
( spl17_78
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f1431,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f861]) ).
fof(f861,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_f2050579477a_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,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(f2413,plain,
spl17_77,
inference(avatar_split_clause,[],[f1430,f2411]) ).
fof(f2411,plain,
( spl17_77
<=> ! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f1430,plain,
! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f860,plain,
! [X0,X1] :
( is_fun_a_bool(image_a_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,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(f2409,plain,
spl17_76,
inference(avatar_split_clause,[],[f1429,f2407]) ).
fof(f2407,plain,
( spl17_76
<=> ! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f1429,plain,
! [X0,X1] :
( is_fun_a_bool(cOMBB_bool_bool_a(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f859]) ).
fof(f859,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(f2405,plain,
spl17_75,
inference(avatar_split_clause,[],[f1428,f2403]) ).
fof(f1428,plain,
! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ),
inference(cnf_transformation,[],[f858]) ).
fof(f858,plain,
! [X0,X1] :
( is_bool(hAPP_bool_bool(X0,X1))
| ~ is_bool(X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( is_bool(X1)
=> is_bool(hAPP_bool_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2401,plain,
spl17_74,
inference(avatar_split_clause,[],[f1427,f2399]) ).
fof(f1427,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f857]) ).
fof(f857,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1854862208_pname(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,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(f2397,plain,
spl17_73,
inference(avatar_split_clause,[],[f1426,f2395]) ).
fof(f2395,plain,
( spl17_73
<=> ! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f1426,plain,
! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f856]) ).
fof(f856,plain,
! [X0,X1] :
( is_fun_a_bool(image_fun_a_bool_a(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,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(f2393,plain,
spl17_72,
inference(avatar_split_clause,[],[f1425,f2391]) ).
fof(f1425,plain,
! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f855]) ).
fof(f855,plain,
! [X0,X1] :
( is_bool(hAPP_f621171935l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_bool(hAPP_f621171935l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2389,plain,
spl17_71,
inference(avatar_split_clause,[],[f1424,f2387]) ).
fof(f1424,plain,
! [X0,X1] :
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f854]) ).
fof(f854,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(f2385,plain,
spl17_70,
inference(avatar_split_clause,[],[f1423,f2383]) ).
fof(f1423,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f853]) ).
fof(f853,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2381,plain,
spl17_69,
inference(avatar_split_clause,[],[f1422,f2379]) ).
fof(f1422,plain,
! [X0,X1] :
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(cnf_transformation,[],[f852]) ).
fof(f852,plain,
! [X0,X1] :
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(cOMBB_2140588453a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2377,plain,
spl17_68,
inference(avatar_split_clause,[],[f1421,f2375]) ).
fof(f1421,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f851]) ).
fof(f851,plain,
! [X0,X1] :
( is_fun_pname_bool(image_1283814551_pname(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,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(f2373,plain,
spl17_67,
inference(avatar_split_clause,[],[f1420,f2371]) ).
fof(f2371,plain,
( spl17_67
<=> ! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f1420,plain,
! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f850]) ).
fof(f850,plain,
! [X0,X1] :
( is_fun_a_bool(image_876012084bool_a(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,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(f2369,plain,
spl17_66,
inference(avatar_split_clause,[],[f1419,f2367]) ).
fof(f1419,plain,
! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f849]) ).
fof(f849,plain,
! [X0,X1] :
( is_bool(hAPP_f1935102916l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_bool(hAPP_f1935102916l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2365,plain,
spl17_65,
inference(avatar_split_clause,[],[f1418,f2363]) ).
fof(f1418,plain,
! [X0,X1] :
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f848]) ).
fof(f848,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(f2361,plain,
spl17_64,
inference(avatar_split_clause,[],[f1417,f2359]) ).
fof(f1417,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f847]) ).
fof(f847,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2357,plain,
spl17_63,
inference(avatar_split_clause,[],[f1416,f2355]) ).
fof(f1416,plain,
! [X0,X1] :
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(cnf_transformation,[],[f846]) ).
fof(f846,plain,
! [X0,X1] :
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(cOMBB_307249310e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2353,plain,
spl17_62,
inference(avatar_split_clause,[],[f1415,f2351]) ).
fof(f1415,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f845]) ).
fof(f845,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2349,plain,
spl17_61,
inference(avatar_split_clause,[],[f1414,f2347]) ).
fof(f2347,plain,
( spl17_61
<=> ! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f1414,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f844]) ).
fof(f844,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2345,plain,
spl17_60,
inference(avatar_split_clause,[],[f1413,f2343]) ).
fof(f1413,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f843]) ).
fof(f843,plain,
! [X0,X1] :
( is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( is_a(X1)
=> is_fun_pname_bool(hAPP_a93125764e_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2341,plain,
spl17_59,
inference(avatar_split_clause,[],[f1412,f2339]) ).
fof(f1412,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f842]) ).
fof(f842,plain,
! [X0,X1] :
( is_fun_a_bool(hAPP_a_fun_a_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,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(f2337,plain,
spl17_58,
inference(avatar_split_clause,[],[f1330,f2335]) ).
fof(f1330,plain,
! [X0] :
( collect_pname(X0) = X0
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f831]) ).
fof(f831,plain,
! [X0] :
( collect_pname(X0) = X0
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f471]) ).
fof(f471,plain,
! [X0] :
( is_fun_pname_bool(X0)
=> collect_pname(X0) = X0 ),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X12] :
( is_fun_pname_bool(X12)
=> collect_pname(X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2333,plain,
spl17_57,
inference(avatar_split_clause,[],[f1326,f2331]) ).
fof(f1326,plain,
! [X0] :
( collect_fun_a_bool(X0) = X0
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0] :
( collect_fun_a_bool(X0) = X0
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f470]) ).
fof(f470,plain,
! [X0] :
( is_fun949378684l_bool(X0)
=> collect_fun_a_bool(X0) = X0 ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X12] :
( is_fun949378684l_bool(X12)
=> collect_fun_a_bool(X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2329,plain,
spl17_56,
inference(avatar_split_clause,[],[f1324,f2327]) ).
fof(f1324,plain,
! [X0] :
( collec1974731493e_bool(X0) = X0
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f825]) ).
fof(f825,plain,
! [X0] :
( collec1974731493e_bool(X0) = X0
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f469]) ).
fof(f469,plain,
! [X0] :
( is_fun1661590463l_bool(X0)
=> collec1974731493e_bool(X0) = X0 ),
inference(rectify,[],[f339]) ).
fof(f339,axiom,
! [X12] :
( is_fun1661590463l_bool(X12)
=> collec1974731493e_bool(X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2325,plain,
spl17_55,
inference(avatar_split_clause,[],[f1322,f2323]) ).
fof(f1322,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(cnf_transformation,[],[f468]) ).
fof(f468,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X43] :
( ~ hBOOL(X43)
| ~ hBOOL(hAPP_bool_bool(fNot,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2321,plain,
spl17_54,
inference(avatar_split_clause,[],[f1321,f2319]) ).
fof(f1321,plain,
! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f467]) ).
fof(f467,plain,
! [X0] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X43] :
( hBOOL(hAPP_bool_bool(fNot,X43))
| hBOOL(X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2317,plain,
spl17_53,
inference(avatar_split_clause,[],[f1316,f2315]) ).
fof(f2315,plain,
( spl17_53
<=> ! [X0] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f1316,plain,
! [X0] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)),
inference(cnf_transformation,[],[f462]) ).
fof(f462,plain,
! [X0] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X4] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2313,plain,
spl17_52,
inference(avatar_split_clause,[],[f1314,f2311]) ).
fof(f1314,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(cnf_transformation,[],[f460]) ).
fof(f460,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2309,plain,
spl17_51,
inference(avatar_split_clause,[],[f1312,f2307]) ).
fof(f2307,plain,
( spl17_51
<=> ! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f1312,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(cnf_transformation,[],[f458]) ).
fof(f458,plain,
! [X0] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(rectify,[],[f307]) ).
fof(f307,axiom,
! [X4] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2305,plain,
spl17_50,
inference(avatar_split_clause,[],[f1310,f2303]) ).
fof(f1310,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f379]) ).
fof(f379,axiom,
! [X41] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X41),X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2301,plain,
spl17_49,
inference(avatar_split_clause,[],[f1295,f2299]) ).
fof(f1295,plain,
! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(cnf_transformation,[],[f817]) ).
fof(f817,plain,
! [X0,X1] :
( is_fun_a_bool(image_pname_a(X0,X1))
| ~ is_fun_pname_bool(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,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(f2297,plain,
spl17_48,
inference(avatar_split_clause,[],[f1294,f2295]) ).
fof(f1294,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(cnf_transformation,[],[f816]) ).
fof(f816,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X0,X1))
| ~ is_fun_a_bool(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,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(f2293,plain,
spl17_47,
inference(avatar_split_clause,[],[f1293,f2291]) ).
fof(f1293,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f815]) ).
fof(f815,plain,
! [X0,X1] :
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2289,plain,
spl17_46,
inference(avatar_split_clause,[],[f1292,f2287]) ).
fof(f2287,plain,
( spl17_46
<=> ! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f1292,plain,
! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ),
inference(cnf_transformation,[],[f814]) ).
fof(f814,plain,
! [X0,X1] :
( is_a(hAPP_pname_a(X0,X1))
| ~ is_pname(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
( is_pname(X1)
=> is_a(hAPP_pname_a(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2285,plain,
spl17_45,
inference(avatar_split_clause,[],[f1291,f2283]) ).
fof(f1291,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ),
inference(cnf_transformation,[],[f813]) ).
fof(f813,plain,
! [X0,X1] :
( is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1))
| ~ is_a(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( is_a(X1)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2281,plain,
spl17_44,
inference(avatar_split_clause,[],[f1285,f2278]) ).
fof(f1285,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f447]) ).
fof(f447,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2276,plain,
( ~ spl17_43
| spl17_42 ),
inference(avatar_split_clause,[],[f2271,f2267,f2273]) ).
fof(f2267,plain,
( spl17_42
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f2271,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_p1534023578a_bool(cOMBB_1897541054_pname(cOMBC_a_a_bool(fequal_a),mgt_call),pn)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u)))
| spl17_42 ),
inference(forward_demodulation,[],[f2269,f1679]) ).
fof(f2269,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u)))
| spl17_42 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f2270,plain,
~ spl17_42,
inference(avatar_split_clause,[],[f1827,f2267]) ).
fof(f1827,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(definition_unfolding,[],[f1279,f1386]) ).
fof(f1279,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f451]) ).
fof(f451,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(flattening,[],[f450]) ).
fof(f450,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[],[f449]) ).
fof(f449,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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(f2265,plain,
spl17_41,
inference(avatar_split_clause,[],[f1329,f2263]) ).
fof(f1329,plain,
! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ),
inference(cnf_transformation,[],[f830]) ).
fof(f830,plain,
! [X0] :
( is_fun_pname_bool(collect_pname(X0))
| ~ is_fun_pname_bool(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( is_fun_pname_bool(X0)
=> is_fun_pname_bool(collect_pname(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2261,plain,
spl17_40,
inference(avatar_split_clause,[],[f1328,f2259]) ).
fof(f1328,plain,
! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f829]) ).
fof(f829,plain,
! [X0] :
( is_fun_a_bool(collect_a(X0))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( is_fun_a_bool(X0)
=> is_fun_a_bool(collect_a(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2257,plain,
spl17_39,
inference(avatar_split_clause,[],[f1327,f2255]) ).
fof(f1327,plain,
! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ),
inference(cnf_transformation,[],[f828]) ).
fof(f828,plain,
! [X0] :
( is_fun949378684l_bool(p(X0))
| ~ is_fun_a_bool(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( is_fun_a_bool(X0)
=> is_fun949378684l_bool(p(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2253,plain,
spl17_38,
inference(avatar_split_clause,[],[f1325,f2251]) ).
fof(f1325,plain,
! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f826,plain,
! [X0] :
( is_fun949378684l_bool(collect_fun_a_bool(X0))
| ~ is_fun949378684l_bool(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( is_fun949378684l_bool(X0)
=> is_fun949378684l_bool(collect_fun_a_bool(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2249,plain,
spl17_37,
inference(avatar_split_clause,[],[f1323,f2247]) ).
fof(f1323,plain,
! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ),
inference(cnf_transformation,[],[f824]) ).
fof(f824,plain,
! [X0] :
( is_fun1661590463l_bool(collec1974731493e_bool(X0))
| ~ is_fun1661590463l_bool(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( is_fun1661590463l_bool(X0)
=> is_fun1661590463l_bool(collec1974731493e_bool(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2245,plain,
spl17_36,
inference(avatar_split_clause,[],[f1308,f2243]) ).
fof(f1308,plain,
! [X0] : hAPP_nat_nat(suc,X0) != X0,
inference(cnf_transformation,[],[f454]) ).
fof(f454,plain,
! [X0] : hAPP_nat_nat(suc,X0) != X0,
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X13] : hAPP_nat_nat(suc,X13) != X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2241,plain,
spl17_35,
inference(avatar_split_clause,[],[f1303,f2238]) ).
fof(f1303,plain,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2236,plain,
spl17_34,
inference(avatar_split_clause,[],[f1302,f2233]) ).
fof(f2233,plain,
( spl17_34
<=> is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f1302,plain,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2231,plain,
spl17_33,
inference(avatar_split_clause,[],[f1364,f2229]) ).
fof(f1364,plain,
! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] : is_fun_pname_bool(hAPP_n1025906991e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2227,plain,
spl17_32,
inference(avatar_split_clause,[],[f1363,f2225]) ).
fof(f1363,plain,
! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : is_fun_pname_bool(image_1921560913_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2223,plain,
spl17_31,
inference(avatar_split_clause,[],[f1362,f2221]) ).
fof(f1362,plain,
! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] : is_fun_pname_bool(image_nat_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2219,plain,
spl17_30,
inference(avatar_split_clause,[],[f1361,f2217]) ).
fof(f1361,plain,
! [X0,X1] : is_fun_pname_bool(image_1604018183_pname(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] : is_fun_pname_bool(image_1604018183_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2215,plain,
spl17_29,
inference(avatar_split_clause,[],[f1360,f2213]) ).
fof(f1360,plain,
! [X0,X1] : is_fun_pname_bool(image_990671762_pname(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] : is_fun_pname_bool(image_990671762_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2211,plain,
spl17_28,
inference(avatar_split_clause,[],[f1359,f2209]) ).
fof(f1359,plain,
! [X0,X1] : is_fun_pname_bool(image_1705983821_pname(X0,X1)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] : is_fun_pname_bool(image_1705983821_pname(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2207,plain,
spl17_27,
inference(avatar_split_clause,[],[f1358,f2205]) ).
fof(f1358,plain,
! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] : is_fun_a_bool(hAPP_nat_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2203,plain,
spl17_26,
inference(avatar_split_clause,[],[f1357,f2201]) ).
fof(f1357,plain,
! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : is_fun_a_bool(image_nat_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2199,plain,
spl17_25,
inference(avatar_split_clause,[],[f1356,f2197]) ).
fof(f1356,plain,
! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] : is_fun_a_bool(image_fun_nat_bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2195,plain,
spl17_24,
inference(avatar_split_clause,[],[f1355,f2193]) ).
fof(f1355,plain,
! [X0,X1] : is_fun_a_bool(image_349102846bool_a(X0,X1)),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] : is_fun_a_bool(image_349102846bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2191,plain,
spl17_23,
inference(avatar_split_clause,[],[f1354,f2189]) ).
fof(f1354,plain,
! [X0,X1] : is_fun_a_bool(image_526090948bool_a(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] : is_fun_a_bool(image_526090948bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2187,plain,
spl17_22,
inference(avatar_split_clause,[],[f1353,f2185]) ).
fof(f1353,plain,
! [X0,X1] : is_fun_a_bool(image_573985017bool_a(X0,X1)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] : is_fun_a_bool(image_573985017bool_a(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2183,plain,
spl17_21,
inference(avatar_split_clause,[],[f1352,f2181]) ).
fof(f1352,plain,
! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] : is_bool(hAPP_f54304608l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2179,plain,
spl17_20,
inference(avatar_split_clause,[],[f1351,f2177]) ).
fof(f2177,plain,
( spl17_20
<=> ! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f1351,plain,
! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] : is_bool(hAPP_f1637334154l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2175,plain,
spl17_19,
inference(avatar_split_clause,[],[f1350,f2173]) ).
fof(f2173,plain,
( spl17_19
<=> ! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f1350,plain,
! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1] : is_bool(hAPP_f389811538l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2171,plain,
spl17_18,
inference(avatar_split_clause,[],[f1349,f2169]) ).
fof(f2169,plain,
( spl17_18
<=> ! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f1349,plain,
! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0,X1] : is_bool(hAPP_f937997336l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2167,plain,
spl17_17,
inference(avatar_split_clause,[],[f1348,f2165]) ).
fof(f2165,plain,
( spl17_17
<=> ! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f1348,plain,
! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0,X1] : is_bool(hAPP_f292226953l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2163,plain,
spl17_16,
inference(avatar_split_clause,[],[f1347,f2161]) ).
fof(f2161,plain,
( spl17_16
<=> ! [X0,X1] : is_bool(hAPP_f1363661463l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f1347,plain,
! [X0,X1] : is_bool(hAPP_f1363661463l_bool(X0,X1)),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0,X1] : is_bool(hAPP_f1363661463l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2159,plain,
spl17_15,
inference(avatar_split_clause,[],[f1346,f2157]) ).
fof(f2157,plain,
( spl17_15
<=> ! [X0,X1] : is_bool(hAPP_f595608956l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f1346,plain,
! [X0,X1] : is_bool(hAPP_f595608956l_bool(X0,X1)),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] : is_bool(hAPP_f595608956l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2155,plain,
spl17_14,
inference(avatar_split_clause,[],[f1345,f2153]) ).
fof(f2153,plain,
( spl17_14
<=> ! [X0,X1] : is_bool(hAPP_f1295398978l_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f1345,plain,
! [X0,X1] : is_bool(hAPP_f1295398978l_bool(X0,X1)),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1] : is_bool(hAPP_f1295398978l_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2151,plain,
spl17_13,
inference(avatar_split_clause,[],[f1344,f2149]) ).
fof(f1344,plain,
! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : is_fun949378684l_bool(image_nat_fun_a_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2147,plain,
spl17_12,
inference(avatar_split_clause,[],[f1343,f2145]) ).
fof(f1343,plain,
! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] : is_fun1661590463l_bool(image_1655916159e_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2143,plain,
spl17_11,
inference(avatar_split_clause,[],[f1307,f2141]) ).
fof(f2139,plain,
spl17_10,
inference(avatar_split_clause,[],[f1306,f2137]) ).
fof(f2135,plain,
spl17_9,
inference(avatar_split_clause,[],[f1290,f2133]) ).
fof(f1290,plain,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2131,plain,
spl17_8,
inference(avatar_split_clause,[],[f1284,f2128]) ).
fof(f1284,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(cnf_transformation,[],[f443]) ).
fof(f443,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2126,plain,
spl17_7,
inference(avatar_split_clause,[],[f1301,f2123]) ).
fof(f1301,plain,
is_pname(undefined_pname(pname)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
is_pname(undefined_pname(pname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2121,plain,
spl17_6,
inference(avatar_split_clause,[],[f1300,f2118]) ).
fof(f1300,plain,
is_a(undefined_a(x_a)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
is_a(undefined_a(x_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2116,plain,
spl17_5,
inference(avatar_split_clause,[],[f1299,f2113]) ).
fof(f1299,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(f2111,plain,
spl17_4,
inference(avatar_split_clause,[],[f1283,f2108]) ).
fof(f1283,plain,
is_fun_pname_bool(u),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
is_fun_pname_bool(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2106,plain,
spl17_3,
inference(avatar_split_clause,[],[f1282,f2103]) ).
fof(f1282,plain,
is_fun_a_bool(g),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
is_fun_a_bool(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2101,plain,
spl17_2,
inference(avatar_split_clause,[],[f1281,f2098]) ).
fof(f1281,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(f2096,plain,
spl17_1,
inference(avatar_split_clause,[],[f1280,f2093]) ).
fof(f1280,plain,
is_pname(pn),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
is_pname(pn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW473+1 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.12 % Command : run_vampire %s %d SAT
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 06:14:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.20/0.35 Running first-order model finding
% 0.20/0.35 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (9980)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)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9977)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9978)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)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9983)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)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9979)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9981)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.22/0.44 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (9982)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)
% 0.22/0.49 % (9981)Instruction limit reached!
% 0.22/0.49 % (9981)------------------------------
% 0.22/0.49 % (9981)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.49 % (9981)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.49 % (9981)Termination reason: Time limit
% 0.22/0.49 % (9981)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (9981)Memory used [KB]: 2840
% 0.22/0.49 % (9981)Time elapsed: 0.059 s
% 0.22/0.49 % (9981)Instructions burned: 104 (million)
% 0.22/0.50 % (9983)Instruction limit reached!
% 0.22/0.50 % (9983)------------------------------
% 0.22/0.50 % (9983)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.50 % (9983)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.50 % (9983)Termination reason: Time limit
% 0.22/0.50 % (9983)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (9983)Memory used [KB]: 3348
% 0.22/0.50 % (9983)Time elapsed: 0.062 s
% 0.22/0.50 % (9983)Instructions burned: 117 (million)
% 0.22/0.51 % (9982)Instruction limit reached!
% 0.22/0.51 % (9982)------------------------------
% 0.22/0.51 % (9982)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.51 % (9982)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.51 % (9982)Termination reason: Time limit
% 0.22/0.51 % (9982)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (9982)Memory used [KB]: 2674
% 0.22/0.51 % (9982)Time elapsed: 0.073 s
% 0.22/0.51 % (9982)Instructions burned: 147 (million)
% 0.22/0.53 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.53 % (9984)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)
% 0.22/0.53 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.53 % (9985)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 0.22/0.54 % (9976)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.54 % (9986)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)
% 1.42/0.56 TRYING [1]
% 1.56/0.58 TRYING [2]
% 1.56/0.59 % (9985)Instruction limit reached!
% 1.56/0.59 % (9985)------------------------------
% 1.56/0.59 % (9985)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.56/0.59 % (9985)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.56/0.59 % (9985)Termination reason: Time limit
% 1.56/0.59 % (9985)Termination phase: Saturation
% 1.56/0.59
% 1.56/0.59 % (9985)Memory used [KB]: 3431
% 1.56/0.59 % (9985)Time elapsed: 0.059 s
% 1.56/0.59 % (9985)Instructions burned: 176 (million)
% 1.56/0.63 % (9976)Running in auto input_syntax mode. Trying TPTP
% 1.56/0.63 % (9987)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2998ds/900Mi)
% 1.87/0.64 % (9986)Instruction limit reached!
% 1.87/0.64 % (9986)------------------------------
% 1.87/0.64 % (9986)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.87/0.64 % (9986)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.87/0.64 % (9986)Termination reason: Time limit
% 1.87/0.64 % (9986)Termination phase: Saturation
% 1.87/0.64
% 1.87/0.64 % (9986)Memory used [KB]: 6043
% 1.87/0.64 % (9986)Time elapsed: 0.103 s
% 1.87/0.64 % (9986)Instructions burned: 273 (million)
% 2.01/0.68 % (9984)Instruction limit reached!
% 2.01/0.68 % (9984)------------------------------
% 2.01/0.68 % (9984)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.01/0.68 % (9984)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.01/0.68 % (9984)Termination reason: Time limit
% 2.01/0.68 % (9984)Termination phase: Saturation
% 2.01/0.68
% 2.01/0.68 % (9984)Memory used [KB]: 5565
% 2.01/0.68 % (9984)Time elapsed: 0.149 s
% 2.01/0.68 % (9984)Instructions burned: 404 (million)
% 2.01/0.68 % (9976)Running in auto input_syntax mode. Trying TPTP
% 2.01/0.68 % (9988)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2997ds/7859Mi)
% 2.01/0.71 % (9976)Running in auto input_syntax mode. Trying TPTP
% 2.01/0.71 % (9989)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 (2997ds/2145Mi)
% 2.33/0.72 TRYING [3]
% 2.33/0.74 TRYING [1]
% 2.33/0.75 TRYING [2]
% 2.51/0.81 TRYING [10]
% 2.51/0.82 TRYING [3]
% 3.26/0.96 % (9987)Instruction limit reached!
% 3.26/0.96 % (9987)------------------------------
% 3.26/0.96 % (9987)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 3.26/0.96 % (9987)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 3.26/0.96 % (9987)Termination reason: Time limit
% 3.26/0.96 % (9987)Termination phase: Saturation
% 3.26/0.96
% 3.26/0.96 % (9987)Memory used [KB]: 11596
% 3.26/0.96 % (9987)Time elapsed: 0.333 s
% 3.26/0.96 % (9987)Instructions burned: 900 (million)
% 3.26/1.00 % (9976)Running in auto input_syntax mode. Trying TPTP
% 3.26/1.00 % (10007)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2994ds/1187Mi)
% 3.91/1.05 TRYING [4]
% 3.91/1.05 TRYING [4]
% 7.31/1.42 % (10007)Instruction limit reached!
% 7.31/1.42 % (10007)------------------------------
% 7.31/1.42 % (10007)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 7.31/1.42 % (10007)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 7.31/1.42 % (10007)Termination reason: Time limit
% 7.31/1.42 % (10007)Termination phase: Saturation
% 7.31/1.42
% 7.31/1.42 % (10007)Memory used [KB]: 14898
% 7.31/1.42 % (10007)Time elapsed: 0.429 s
% 7.31/1.42 % (10007)Instructions burned: 1187 (million)
% 7.31/1.46 % (9976)Running in auto input_syntax mode. Trying TPTP
% 7.31/1.46 % (10147)fmb+10_1:1_sil=32000:i=23580:newcnf=on_0 on theBenchmark for (2989ds/23580Mi)
% 7.76/1.55 TRYING [1]
% 7.76/1.56 TRYING [2]
% 7.76/1.56 % (9989)Instruction limit reached!
% 7.76/1.56 % (9989)------------------------------
% 7.76/1.56 % (9989)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 7.76/1.56 % (9989)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 7.76/1.56 % (9989)Termination reason: Time limit
% 7.76/1.56 % (9989)Termination phase: Saturation
% 7.76/1.56
% 7.76/1.56 % (9989)Memory used [KB]: 26715
% 7.76/1.56 % (9989)Time elapsed: 0.851 s
% 7.76/1.56 % (9989)Instructions burned: 2145 (million)
% 8.53/1.60 % (9976)Running in auto input_syntax mode. Trying TPTP
% 8.53/1.60 % (10148)fmb+10_1:1_sil=32000:fmbss=17:fmbsr=2.0:i=2892_0 on theBenchmark for (2988ds/2892Mi)
% 8.70/1.66 TRYING [3]
% 9.19/1.74 TRYING [5]
% 9.19/1.80 % (9978)First to succeed.
% 10.24/1.86 % (9978)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9976"
% 10.24/1.86 % (9976)Running in auto input_syntax mode. Trying TPTP
% 10.24/1.86 % (9978)Refutation found. Thanks to Tanya!
% 10.24/1.86 % SZS status Theorem for theBenchmark
% 10.24/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 10.66/1.89 % (9978)------------------------------
% 10.66/1.89 % (9978)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 10.66/1.89 % (9978)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 10.66/1.89 % (9978)Termination reason: Refutation
% 10.66/1.89
% 10.66/1.89 % (9978)Memory used [KB]: 21108
% 10.66/1.89 % (9978)Time elapsed: 1.420 s
% 10.66/1.89 % (9978)Instructions burned: 3826 (million)
% 10.66/1.89 % (9978)------------------------------
% 10.66/1.89 % (9978)------------------------------
% 10.66/1.89 % (9976)Success in time 1.503 s
%------------------------------------------------------------------------------