TSTP Solution File: SEU248+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:25:35 EDT 2024
% Result : Theorem 3.19s 0.79s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1306
% Syntax : Number of formulae : 4083 ( 784 unt; 0 def)
% Number of atoms : 13926 (1725 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 16191 (6348 ~;6737 |;1564 &)
% (1166 <=>; 375 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 966 ( 964 usr; 887 prp; 0-4 aty)
% Number of functors : 154 ( 154 usr; 15 con; 0-4 aty)
% Number of variables : 6960 (6526 !; 434 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14928,plain,
$false,
inference(avatar_sat_refutation,[],[f2024,f2029,f2034,f2039,f2044,f2049,f2054,f2059,f2064,f2069,f2074,f2079,f2084,f2089,f2094,f2099,f2104,f2109,f2114,f2119,f2124,f2129,f2134,f2139,f2144,f2149,f2154,f2159,f2164,f2169,f2174,f2179,f2184,f2189,f2194,f2199,f2204,f2209,f2214,f2219,f2224,f2229,f2234,f2238,f2242,f2246,f2250,f2254,f2258,f2262,f2266,f2271,f2276,f2280,f2284,f2299,f2304,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2384,f2389,f2393,f2397,f2401,f2405,f2410,f2414,f2418,f2431,f2466,f2570,f2574,f2578,f2582,f2586,f2590,f2595,f2599,f2603,f2608,f2613,f2617,f2621,f2625,f2629,f2633,f2637,f2641,f2645,f2649,f2653,f2658,f2662,f2666,f2670,f2674,f2678,f2682,f2686,f2690,f2697,f2755,f2794,f2800,f2804,f2809,f2814,f2819,f2823,f2835,f2847,f2852,f2856,f2860,f2864,f2868,f2872,f2876,f2881,f2885,f2889,f2893,f2898,f2902,f2906,f2910,f2914,f2918,f2922,f2926,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2967,f2971,f2975,f2979,f2983,f2987,f2991,f2995,f2999,f3003,f3007,f3011,f3015,f3019,f3029,f3140,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3252,f3262,f3267,f3297,f3301,f3305,f3309,f3313,f3317,f3321,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3370,f3375,f3379,f3383,f3387,f3394,f3399,f3400,f3401,f3402,f3436,f3440,f3444,f3448,f3452,f3461,f3465,f3469,f3473,f3477,f3549,f3619,f3643,f3647,f3651,f3655,f3659,f3663,f3667,f3671,f3675,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3708,f3713,f3717,f3721,f3725,f3729,f3733,f3737,f3741,f3750,f3754,f3758,f3878,f3882,f3947,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4032,f4036,f4040,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4216,f4241,f4342,f4431,f4512,f4524,f4528,f4533,f4537,f4543,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4582,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4666,f4670,f4674,f4833,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4884,f4956,f4960,f4966,f4972,f4976,f4980,f4984,f4988,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5040,f5045,f5050,f5054,f5141,f5335,f5339,f5377,f5381,f5385,f5390,f5396,f5400,f5404,f5408,f5412,f5416,f5420,f5424,f5428,f5432,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5472,f5512,f5613,f5617,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5650,f5654,f5658,f5662,f5666,f5971,f5975,f5979,f5984,f5988,f5992,f5996,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6039,f6043,f6047,f6051,f6055,f6059,f6063,f6067,f6076,f6192,f6201,f6205,f6209,f6213,f6217,f6221,f6225,f6229,f6233,f6237,f6241,f6246,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6495,f6499,f6503,f6507,f6511,f6515,f6519,f6523,f6527,f6576,f6606,f6610,f6614,f6618,f6622,f6628,f6632,f6663,f6667,f6671,f6675,f6680,f6684,f6688,f6692,f6792,f6812,f6914,f7017,f7021,f7025,f7029,f7033,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7086,f7090,f7094,f7098,f7102,f7107,f7111,f7118,f7243,f7291,f7350,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7393,f7397,f7401,f7405,f7409,f7717,f7722,f7727,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7949,f7953,f7957,f7961,f7965,f7985,f7990,f7995,f8031,f8035,f8039,f8043,f8047,f8051,f8055,f8059,f8063,f8167,f8171,f8213,f8342,f8346,f8363,f8367,f8371,f8375,f8379,f8383,f8402,f8418,f8422,f8426,f8430,f8434,f8438,f8445,f8449,f8453,f8627,f8672,f8677,f8682,f8686,f8690,f8694,f8698,f8702,f8707,f8711,f8715,f8719,f8723,f8727,f8731,f8735,f8739,f8743,f8747,f8754,f8758,f8762,f8766,f9464,f9468,f9472,f9477,f9482,f9487,f9493,f9497,f9502,f9506,f9510,f9514,f9519,f9584,f9588,f9593,f9598,f9602,f9606,f9653,f9764,f9876,f9880,f9884,f9888,f9892,f9896,f9901,f10135,f10140,f10144,f10148,f10155,f10160,f10164,f10168,f10172,f10177,f10317,f10357,f10375,f10545,f10549,f10553,f10557,f10561,f10566,f10732,f10736,f10741,f10745,f10750,f10755,f10760,f10765,f10845,f10871,f10897,f10943,f10989,f10993,f10997,f11002,f11007,f11012,f11017,f11023,f11027,f11032,f11037,f11118,f11122,f11126,f11130,f11134,f11138,f11143,f11148,f11337,f11342,f11349,f11355,f11377,f11383,f11405,f11410,f11454,f11459,f11502,f11506,f11510,f11514,f11597,f11601,f11605,f11609,f11613,f11821,f11825,f11830,f11835,f11839,f11995,f12010,f12014,f12020,f12024,f12029,f12033,f12049,f12053,f12143,f12147,f12151,f12155,f12160,f12164,f12168,f12173,f12177,f12293,f12297,f12342,f12453,f12457,f12462,f12480,f12484,f12489,f12541,f12586,f12591,f12605,f12650,f12655,f12660,f12664,f12668,f12672,f12684,f12780,f12785,f12798,f12802,f12831,f12836,f12840,f12844,f12848,f12853,f12857,f12862,f12867,f13072,f13101,f13124,f13128,f13296,f13301,f13306,f13310,f13359,f13364,f13370,f13375,f13380,f13384,f13454,f13485,f13491,f13497,f13501,f13516,f13613,f13619,f13625,f13629,f13730,f13736,f13742,f13749,f13753,f13757,f13761,f13765,f14095,f14101,f14106,f14110,f14144,f14149,f14168,f14174,f14180,f14186,f14191,f14197,f14202,f14207,f14212,f14217,f14223,f14229,f14235,f14240,f14246,f14251,f14256,f14261,f14266,f14272,f14278,f14284,f14289,f14295,f14300,f14305,f14310,f14315,f14321,f14327,f14333,f14338,f14344,f14349,f14354,f14359,f14364,f14370,f14376,f14382,f14387,f14393,f14398,f14403,f14408,f14413,f14419,f14425,f14431,f14436,f14442,f14447,f14452,f14457,f14462,f14468,f14474,f14480,f14485,f14491,f14496,f14501,f14506,f14511,f14517,f14559,f14574,f14589,f14594,f14599,f14604,f14609,f14614,f14619,f14627,f14631,f14649,f14668,f14674,f14678,f14682,f14762,f14800,f14804,f14808,f14918,f14922,f14926,f14927]) ).
fof(f14927,plain,
( ~ spl171_1
| ~ spl171_176
| spl171_877 ),
inference(avatar_split_clause,[],[f14670,f14665,f3228,f2021]) ).
fof(f2021,plain,
( spl171_1
<=> relation(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_1])]) ).
fof(f3228,plain,
( spl171_176
<=> ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_176])]) ).
fof(f14665,plain,
( spl171_877
<=> subset(relation_rng_restriction(sK50,sK51),sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_877])]) ).
fof(f14670,plain,
( ~ relation(sK51)
| ~ spl171_176
| spl171_877 ),
inference(resolution,[],[f14667,f3229]) ).
fof(f3229,plain,
( ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) )
| ~ spl171_176 ),
inference(avatar_component_clause,[],[f3228]) ).
fof(f14667,plain,
( ~ subset(relation_rng_restriction(sK50,sK51),sK51)
| spl171_877 ),
inference(avatar_component_clause,[],[f14665]) ).
fof(f14926,plain,
( spl171_886
| ~ spl171_12
| ~ spl171_44
| ~ spl171_105
| ~ spl171_122 ),
inference(avatar_split_clause,[],[f2830,f2802,f2639,f2236,f2076,f14924]) ).
fof(f14924,plain,
( spl171_886
<=> ! [X0] : ~ proper_subset(X0,sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_886])]) ).
fof(f2076,plain,
( spl171_12
<=> empty(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_12])]) ).
fof(f2236,plain,
( spl171_44
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_44])]) ).
fof(f2639,plain,
( spl171_105
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_105])]) ).
fof(f2802,plain,
( spl171_122
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_122])]) ).
fof(f2830,plain,
( ! [X0] : ~ proper_subset(X0,sK160)
| ~ spl171_12
| ~ spl171_44
| ~ spl171_105
| ~ spl171_122 ),
inference(forward_demodulation,[],[f2826,f2706]) ).
fof(f2706,plain,
( empty_set = sK160
| ~ spl171_12
| ~ spl171_105 ),
inference(resolution,[],[f2640,f2078]) ).
fof(f2078,plain,
( empty(sK160)
| ~ spl171_12 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f2640,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl171_105 ),
inference(avatar_component_clause,[],[f2639]) ).
fof(f2826,plain,
( ! [X0] : ~ proper_subset(X0,empty_set)
| ~ spl171_44
| ~ spl171_122 ),
inference(resolution,[],[f2803,f2237]) ).
fof(f2237,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl171_44 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f2803,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl171_122 ),
inference(avatar_component_clause,[],[f2802]) ).
fof(f14922,plain,
( spl171_885
| ~ spl171_55
| ~ spl171_117 ),
inference(avatar_split_clause,[],[f2788,f2688,f2282,f14920]) ).
fof(f14920,plain,
( spl171_885
<=> ! [X0] : ~ empty(sK67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_885])]) ).
fof(f2282,plain,
( spl171_55
<=> ! [X0] : in(X0,sK67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_55])]) ).
fof(f2688,plain,
( spl171_117
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_117])]) ).
fof(f2788,plain,
( ! [X0] : ~ empty(sK67(X0))
| ~ spl171_55
| ~ spl171_117 ),
inference(resolution,[],[f2689,f2283]) ).
fof(f2283,plain,
( ! [X0] : in(X0,sK67(X0))
| ~ spl171_55 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f2689,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl171_117 ),
inference(avatar_component_clause,[],[f2688]) ).
fof(f14918,plain,
( spl171_884
| ~ spl171_46
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2285,f2278,f2244,f14916]) ).
fof(f14916,plain,
( spl171_884
<=> ! [X0] : sP1(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_884])]) ).
fof(f2244,plain,
( spl171_46
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_46])]) ).
fof(f2278,plain,
( spl171_54
<=> ! [X0] :
( sP1(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_54])]) ).
fof(f2285,plain,
( ! [X0] : sP1(identity_relation(X0))
| ~ spl171_46
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2245]) ).
fof(f2245,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl171_46 ),
inference(avatar_component_clause,[],[f2244]) ).
fof(f2279,plain,
( ! [X0] :
( ~ relation(X0)
| sP1(X0) )
| ~ spl171_54 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f14808,plain,
( spl171_883
| ~ spl171_1
| ~ spl171_552 ),
inference(avatar_split_clause,[],[f8012,f7993,f2021,f14806]) ).
fof(f14806,plain,
( spl171_883
<=> ! [X0] : relation_image(sK51,X0) = relation_image(sK51,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(sK51))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_883])]) ).
fof(f7993,plain,
( spl171_552
<=> ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1)))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_552])]) ).
fof(f8012,plain,
( ! [X0] : relation_image(sK51,X0) = relation_image(sK51,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(sK51)))))
| ~ spl171_1
| ~ spl171_552 ),
inference(resolution,[],[f7994,f2023]) ).
fof(f2023,plain,
( relation(sK51)
| ~ spl171_1 ),
inference(avatar_component_clause,[],[f2021]) ).
fof(f7994,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1))))) )
| ~ spl171_552 ),
inference(avatar_component_clause,[],[f7993]) ).
fof(f14804,plain,
( spl171_882
| ~ spl171_1
| ~ spl171_527 ),
inference(avatar_split_clause,[],[f7549,f7382,f2021,f14802]) ).
fof(f14802,plain,
( spl171_882
<=> ! [X0] : relation_dom(relation_dom_restriction(sK51,X0)) = set_difference(relation_dom(sK51),set_difference(relation_dom(sK51),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_882])]) ).
fof(f7382,plain,
( spl171_527
<=> ! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_527])]) ).
fof(f7549,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK51,X0)) = set_difference(relation_dom(sK51),set_difference(relation_dom(sK51),X0))
| ~ spl171_1
| ~ spl171_527 ),
inference(resolution,[],[f7383,f2023]) ).
fof(f7383,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) )
| ~ spl171_527 ),
inference(avatar_component_clause,[],[f7382]) ).
fof(f14800,plain,
( spl171_881
| ~ spl171_1
| ~ spl171_526 ),
inference(avatar_split_clause,[],[f7500,f7378,f2021,f14798]) ).
fof(f14798,plain,
( spl171_881
<=> ! [X0] : relation_rng(relation_rng_restriction(X0,sK51)) = set_difference(relation_rng(sK51),set_difference(relation_rng(sK51),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_881])]) ).
fof(f7378,plain,
( spl171_526
<=> ! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_526])]) ).
fof(f7500,plain,
( ! [X0] : relation_rng(relation_rng_restriction(X0,sK51)) = set_difference(relation_rng(sK51),set_difference(relation_rng(sK51),X0))
| ~ spl171_1
| ~ spl171_526 ),
inference(resolution,[],[f7379,f2023]) ).
fof(f7379,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0)) )
| ~ spl171_526 ),
inference(avatar_component_clause,[],[f7378]) ).
fof(f14762,plain,
( ~ spl171_1
| ~ spl171_160
| spl171_876 ),
inference(avatar_split_clause,[],[f14669,f14661,f2977,f2021]) ).
fof(f2977,plain,
( spl171_160
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_160])]) ).
fof(f14661,plain,
( spl171_876
<=> relation(relation_rng_restriction(sK50,sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_876])]) ).
fof(f14669,plain,
( ~ relation(sK51)
| ~ spl171_160
| spl171_876 ),
inference(resolution,[],[f14663,f2978]) ).
fof(f2978,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl171_160 ),
inference(avatar_component_clause,[],[f2977]) ).
fof(f14663,plain,
( ~ relation(relation_rng_restriction(sK50,sK51))
| spl171_876 ),
inference(avatar_component_clause,[],[f14661]) ).
fof(f14682,plain,
( spl171_880
| ~ spl171_1
| ~ spl171_488 ),
inference(avatar_split_clause,[],[f6985,f6686,f2021,f14680]) ).
fof(f14680,plain,
( spl171_880
<=> ! [X0] : relation_restriction(sK51,X0) = set_difference(sK51,set_difference(sK51,cartesian_product2(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_880])]) ).
fof(f6686,plain,
( spl171_488
<=> ! [X0,X1] :
( relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_488])]) ).
fof(f6985,plain,
( ! [X0] : relation_restriction(sK51,X0) = set_difference(sK51,set_difference(sK51,cartesian_product2(X0,X0)))
| ~ spl171_1
| ~ spl171_488 ),
inference(resolution,[],[f6687,f2023]) ).
fof(f6687,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) )
| ~ spl171_488 ),
inference(avatar_component_clause,[],[f6686]) ).
fof(f14678,plain,
( spl171_879
| ~ spl171_1
| ~ spl171_480 ),
inference(avatar_split_clause,[],[f6829,f6626,f2021,f14676]) ).
fof(f14676,plain,
( spl171_879
<=> ! [X0,X1] : relation_dom_restriction(relation_rng_restriction(X0,sK51),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK51,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_879])]) ).
fof(f6626,plain,
( spl171_480
<=> ! [X2,X0,X1] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_480])]) ).
fof(f6829,plain,
( ! [X0,X1] : relation_dom_restriction(relation_rng_restriction(X0,sK51),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK51,X1))
| ~ spl171_1
| ~ spl171_480 ),
inference(resolution,[],[f6627,f2023]) ).
fof(f6627,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) )
| ~ spl171_480 ),
inference(avatar_component_clause,[],[f6626]) ).
fof(f14674,plain,
( spl171_878
| ~ spl171_1
| ~ spl171_476 ),
inference(avatar_split_clause,[],[f6775,f6608,f2021,f14672]) ).
fof(f14672,plain,
( spl171_878
<=> ! [X0] :
( relation_rng(relation_composition(X0,sK51)) = relation_image(sK51,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_878])]) ).
fof(f6608,plain,
( spl171_476
<=> ! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_476])]) ).
fof(f6775,plain,
( ! [X0] :
( relation_rng(relation_composition(X0,sK51)) = relation_image(sK51,relation_rng(X0))
| ~ relation(X0) )
| ~ spl171_1
| ~ spl171_476 ),
inference(resolution,[],[f6609,f2023]) ).
fof(f6609,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl171_476 ),
inference(avatar_component_clause,[],[f6608]) ).
fof(f14668,plain,
( ~ spl171_876
| ~ spl171_1
| ~ spl171_877
| spl171_2
| ~ spl171_444 ),
inference(avatar_split_clause,[],[f6247,f6190,f2026,f14665,f2021,f14661]) ).
fof(f2026,plain,
( spl171_2
<=> subset(relation_dom(relation_rng_restriction(sK50,sK51)),relation_dom(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_2])]) ).
fof(f6190,plain,
( spl171_444
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_444])]) ).
fof(f6247,plain,
( ~ subset(relation_rng_restriction(sK50,sK51),sK51)
| ~ relation(sK51)
| ~ relation(relation_rng_restriction(sK50,sK51))
| spl171_2
| ~ spl171_444 ),
inference(resolution,[],[f6191,f2028]) ).
fof(f2028,plain,
( ~ subset(relation_dom(relation_rng_restriction(sK50,sK51)),relation_dom(sK51))
| spl171_2 ),
inference(avatar_component_clause,[],[f2026]) ).
fof(f6191,plain,
( ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_444 ),
inference(avatar_component_clause,[],[f6190]) ).
fof(f14649,plain,
( ~ spl171_874
| spl171_875
| ~ spl171_166
| ~ spl171_316 ),
inference(avatar_split_clause,[],[f4264,f4213,f3001,f14646,f14642]) ).
fof(f14642,plain,
( spl171_874
<=> sP30(relation_inverse(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_874])]) ).
fof(f14646,plain,
( spl171_875
<=> sP29(relation_inverse(sK51),relation_dom(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_875])]) ).
fof(f3001,plain,
( spl171_166
<=> ! [X0] :
( sP29(X0,relation_rng(X0))
| ~ sP30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_166])]) ).
fof(f4213,plain,
( spl171_316
<=> relation_dom(sK51) = relation_rng(relation_inverse(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_316])]) ).
fof(f4264,plain,
( sP29(relation_inverse(sK51),relation_dom(sK51))
| ~ sP30(relation_inverse(sK51))
| ~ spl171_166
| ~ spl171_316 ),
inference(superposition,[],[f3002,f4215]) ).
fof(f4215,plain,
( relation_dom(sK51) = relation_rng(relation_inverse(sK51))
| ~ spl171_316 ),
inference(avatar_component_clause,[],[f4213]) ).
fof(f3002,plain,
( ! [X0] :
( sP29(X0,relation_rng(X0))
| ~ sP30(X0) )
| ~ spl171_166 ),
inference(avatar_component_clause,[],[f3001]) ).
fof(f14631,plain,
( spl171_873
| ~ spl171_1
| ~ spl171_411 ),
inference(avatar_split_clause,[],[f5769,f5627,f2021,f14629]) ).
fof(f14629,plain,
( spl171_873
<=> ! [X0] : relation_restriction(sK51,X0) = relation_dom_restriction(relation_rng_restriction(X0,sK51),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_873])]) ).
fof(f5627,plain,
( spl171_411
<=> ! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_411])]) ).
fof(f5769,plain,
( ! [X0] : relation_restriction(sK51,X0) = relation_dom_restriction(relation_rng_restriction(X0,sK51),X0)
| ~ spl171_1
| ~ spl171_411 ),
inference(resolution,[],[f5628,f2023]) ).
fof(f5628,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) )
| ~ spl171_411 ),
inference(avatar_component_clause,[],[f5627]) ).
fof(f14627,plain,
( spl171_872
| ~ spl171_1
| ~ spl171_410 ),
inference(avatar_split_clause,[],[f5740,f5623,f2021,f14625]) ).
fof(f14625,plain,
( spl171_872
<=> ! [X0] : relation_restriction(sK51,X0) = relation_rng_restriction(X0,relation_dom_restriction(sK51,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_872])]) ).
fof(f5623,plain,
( spl171_410
<=> ! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_410])]) ).
fof(f5740,plain,
( ! [X0] : relation_restriction(sK51,X0) = relation_rng_restriction(X0,relation_dom_restriction(sK51,X0))
| ~ spl171_1
| ~ spl171_410 ),
inference(resolution,[],[f5624,f2023]) ).
fof(f5624,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) )
| ~ spl171_410 ),
inference(avatar_component_clause,[],[f5623]) ).
fof(f14619,plain,
( spl171_871
| ~ spl171_12
| ~ spl171_105
| ~ spl171_854 ),
inference(avatar_split_clause,[],[f14475,f14471,f2639,f2076,f14616]) ).
fof(f14616,plain,
( spl171_871
<=> sP26(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_871])]) ).
fof(f14471,plain,
( spl171_854
<=> sP26(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_854])]) ).
fof(f14475,plain,
( sP26(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_854 ),
inference(forward_demodulation,[],[f14473,f2706]) ).
fof(f14473,plain,
( sP26(empty_set)
| ~ spl171_854 ),
inference(avatar_component_clause,[],[f14471]) ).
fof(f14614,plain,
( spl171_870
| ~ spl171_12
| ~ spl171_105
| ~ spl171_845 ),
inference(avatar_split_clause,[],[f14426,f14422,f2639,f2076,f14611]) ).
fof(f14611,plain,
( spl171_870
<=> sP24(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_870])]) ).
fof(f14422,plain,
( spl171_845
<=> sP24(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_845])]) ).
fof(f14426,plain,
( sP24(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_845 ),
inference(forward_demodulation,[],[f14424,f2706]) ).
fof(f14424,plain,
( sP24(empty_set)
| ~ spl171_845 ),
inference(avatar_component_clause,[],[f14422]) ).
fof(f14609,plain,
( spl171_869
| ~ spl171_12
| ~ spl171_105
| ~ spl171_836 ),
inference(avatar_split_clause,[],[f14377,f14373,f2639,f2076,f14606]) ).
fof(f14606,plain,
( spl171_869
<=> sP20(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_869])]) ).
fof(f14373,plain,
( spl171_836
<=> sP20(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_836])]) ).
fof(f14377,plain,
( sP20(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_836 ),
inference(forward_demodulation,[],[f14375,f2706]) ).
fof(f14375,plain,
( sP20(empty_set)
| ~ spl171_836 ),
inference(avatar_component_clause,[],[f14373]) ).
fof(f14604,plain,
( spl171_868
| ~ spl171_12
| ~ spl171_105
| ~ spl171_827 ),
inference(avatar_split_clause,[],[f14328,f14324,f2639,f2076,f14601]) ).
fof(f14601,plain,
( spl171_868
<=> sP18(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_868])]) ).
fof(f14324,plain,
( spl171_827
<=> sP18(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_827])]) ).
fof(f14328,plain,
( sP18(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_827 ),
inference(forward_demodulation,[],[f14326,f2706]) ).
fof(f14326,plain,
( sP18(empty_set)
| ~ spl171_827 ),
inference(avatar_component_clause,[],[f14324]) ).
fof(f14599,plain,
( spl171_867
| ~ spl171_12
| ~ spl171_105
| ~ spl171_818 ),
inference(avatar_split_clause,[],[f14279,f14275,f2639,f2076,f14596]) ).
fof(f14596,plain,
( spl171_867
<=> sP16(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_867])]) ).
fof(f14275,plain,
( spl171_818
<=> sP16(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_818])]) ).
fof(f14279,plain,
( sP16(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_818 ),
inference(forward_demodulation,[],[f14277,f2706]) ).
fof(f14277,plain,
( sP16(empty_set)
| ~ spl171_818 ),
inference(avatar_component_clause,[],[f14275]) ).
fof(f14594,plain,
( spl171_866
| ~ spl171_12
| ~ spl171_105
| ~ spl171_809 ),
inference(avatar_split_clause,[],[f14230,f14226,f2639,f2076,f14591]) ).
fof(f14591,plain,
( spl171_866
<=> sP14(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_866])]) ).
fof(f14226,plain,
( spl171_809
<=> sP14(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_809])]) ).
fof(f14230,plain,
( sP14(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_809 ),
inference(forward_demodulation,[],[f14228,f2706]) ).
fof(f14228,plain,
( sP14(empty_set)
| ~ spl171_809 ),
inference(avatar_component_clause,[],[f14226]) ).
fof(f14589,plain,
( spl171_865
| ~ spl171_12
| ~ spl171_105
| ~ spl171_800 ),
inference(avatar_split_clause,[],[f14181,f14177,f2639,f2076,f14586]) ).
fof(f14586,plain,
( spl171_865
<=> sP12(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_865])]) ).
fof(f14177,plain,
( spl171_800
<=> sP12(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_800])]) ).
fof(f14181,plain,
( sP12(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_800 ),
inference(forward_demodulation,[],[f14179,f2706]) ).
fof(f14179,plain,
( sP12(empty_set)
| ~ spl171_800 ),
inference(avatar_component_clause,[],[f14177]) ).
fof(f14574,plain,
( spl171_864
| ~ spl171_12
| ~ spl171_105
| ~ spl171_751 ),
inference(avatar_split_clause,[],[f12832,f12828,f2639,f2076,f14571]) ).
fof(f14571,plain,
( spl171_864
<=> sP8(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_864])]) ).
fof(f12828,plain,
( spl171_751
<=> sP8(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_751])]) ).
fof(f12832,plain,
( sP8(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_751 ),
inference(forward_demodulation,[],[f12830,f2706]) ).
fof(f12830,plain,
( sP8(empty_set)
| ~ spl171_751 ),
inference(avatar_component_clause,[],[f12828]) ).
fof(f14559,plain,
( spl171_863
| ~ spl171_12
| ~ spl171_105
| ~ spl171_693 ),
inference(avatar_split_clause,[],[f11455,f11451,f2639,f2076,f14556]) ).
fof(f14556,plain,
( spl171_863
<=> sP6(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_863])]) ).
fof(f11451,plain,
( spl171_693
<=> sP6(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_693])]) ).
fof(f11455,plain,
( sP6(sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_693 ),
inference(forward_demodulation,[],[f11453,f2706]) ).
fof(f11453,plain,
( sP6(empty_set)
| ~ spl171_693 ),
inference(avatar_component_clause,[],[f11451]) ).
fof(f14517,plain,
( spl171_862
| ~ spl171_41
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2565,f2391,f2221,f14514]) ).
fof(f14514,plain,
( spl171_862
<=> sP26(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_862])]) ).
fof(f2221,plain,
( spl171_41
<=> relation(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_41])]) ).
fof(f2391,plain,
( spl171_79
<=> ! [X0] :
( sP26(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_79])]) ).
fof(f2565,plain,
( sP26(sK170)
| ~ spl171_41
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2223]) ).
fof(f2223,plain,
( relation(sK170)
| ~ spl171_41 ),
inference(avatar_component_clause,[],[f2221]) ).
fof(f2392,plain,
( ! [X0] :
( ~ relation(X0)
| sP26(X0) )
| ~ spl171_79 ),
inference(avatar_component_clause,[],[f2391]) ).
fof(f14511,plain,
( spl171_861
| ~ spl171_34
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2564,f2391,f2186,f14508]) ).
fof(f14508,plain,
( spl171_861
<=> sP26(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_861])]) ).
fof(f2186,plain,
( spl171_34
<=> relation(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_34])]) ).
fof(f2564,plain,
( sP26(sK169)
| ~ spl171_34
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2188]) ).
fof(f2188,plain,
( relation(sK169)
| ~ spl171_34 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f14506,plain,
( spl171_860
| ~ spl171_31
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2563,f2391,f2171,f14503]) ).
fof(f14503,plain,
( spl171_860
<=> sP26(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_860])]) ).
fof(f2171,plain,
( spl171_31
<=> relation(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_31])]) ).
fof(f2563,plain,
( sP26(sK168)
| ~ spl171_31
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2173]) ).
fof(f2173,plain,
( relation(sK168)
| ~ spl171_31 ),
inference(avatar_component_clause,[],[f2171]) ).
fof(f14501,plain,
( spl171_859
| ~ spl171_29
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2562,f2391,f2161,f14498]) ).
fof(f14498,plain,
( spl171_859
<=> sP26(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_859])]) ).
fof(f2161,plain,
( spl171_29
<=> relation(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_29])]) ).
fof(f2562,plain,
( sP26(sK167)
| ~ spl171_29
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2163]) ).
fof(f2163,plain,
( relation(sK167)
| ~ spl171_29 ),
inference(avatar_component_clause,[],[f2161]) ).
fof(f14496,plain,
( spl171_858
| ~ spl171_26
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2561,f2391,f2146,f14493]) ).
fof(f14493,plain,
( spl171_858
<=> sP26(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_858])]) ).
fof(f2146,plain,
( spl171_26
<=> relation(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_26])]) ).
fof(f2561,plain,
( sP26(sK166)
| ~ spl171_26
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2148]) ).
fof(f2148,plain,
( relation(sK166)
| ~ spl171_26 ),
inference(avatar_component_clause,[],[f2146]) ).
fof(f14491,plain,
( spl171_857
| ~ spl171_24
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2560,f2391,f2136,f14488]) ).
fof(f14488,plain,
( spl171_857
<=> sP26(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_857])]) ).
fof(f2136,plain,
( spl171_24
<=> relation(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_24])]) ).
fof(f2560,plain,
( sP26(sK165)
| ~ spl171_24
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2138]) ).
fof(f2138,plain,
( relation(sK165)
| ~ spl171_24 ),
inference(avatar_component_clause,[],[f2136]) ).
fof(f14485,plain,
( spl171_856
| ~ spl171_23
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2559,f2391,f2131,f14482]) ).
fof(f14482,plain,
( spl171_856
<=> sP26(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_856])]) ).
fof(f2131,plain,
( spl171_23
<=> relation(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_23])]) ).
fof(f2559,plain,
( sP26(sK164)
| ~ spl171_23
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2133]) ).
fof(f2133,plain,
( relation(sK164)
| ~ spl171_23 ),
inference(avatar_component_clause,[],[f2131]) ).
fof(f14480,plain,
( spl171_855
| ~ spl171_18
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2558,f2391,f2106,f14477]) ).
fof(f14477,plain,
( spl171_855
<=> sP26(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_855])]) ).
fof(f2106,plain,
( spl171_18
<=> relation(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_18])]) ).
fof(f2558,plain,
( sP26(sK162)
| ~ spl171_18
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2108]) ).
fof(f2108,plain,
( relation(sK162)
| ~ spl171_18 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f14474,plain,
( spl171_854
| ~ spl171_4
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2556,f2391,f2036,f14471]) ).
fof(f2036,plain,
( spl171_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_4])]) ).
fof(f2556,plain,
( sP26(empty_set)
| ~ spl171_4
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2038]) ).
fof(f2038,plain,
( relation(empty_set)
| ~ spl171_4 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f14468,plain,
( spl171_853
| ~ spl171_41
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2554,f2382,f2221,f14465]) ).
fof(f14465,plain,
( spl171_853
<=> sP24(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_853])]) ).
fof(f2382,plain,
( spl171_77
<=> ! [X0] :
( sP24(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_77])]) ).
fof(f2554,plain,
( sP24(sK170)
| ~ spl171_41
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2223]) ).
fof(f2383,plain,
( ! [X0] :
( ~ relation(X0)
| sP24(X0) )
| ~ spl171_77 ),
inference(avatar_component_clause,[],[f2382]) ).
fof(f14462,plain,
( spl171_852
| ~ spl171_34
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2553,f2382,f2186,f14459]) ).
fof(f14459,plain,
( spl171_852
<=> sP24(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_852])]) ).
fof(f2553,plain,
( sP24(sK169)
| ~ spl171_34
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2188]) ).
fof(f14457,plain,
( spl171_851
| ~ spl171_31
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2552,f2382,f2171,f14454]) ).
fof(f14454,plain,
( spl171_851
<=> sP24(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_851])]) ).
fof(f2552,plain,
( sP24(sK168)
| ~ spl171_31
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2173]) ).
fof(f14452,plain,
( spl171_850
| ~ spl171_29
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2551,f2382,f2161,f14449]) ).
fof(f14449,plain,
( spl171_850
<=> sP24(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_850])]) ).
fof(f2551,plain,
( sP24(sK167)
| ~ spl171_29
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2163]) ).
fof(f14447,plain,
( spl171_849
| ~ spl171_26
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2550,f2382,f2146,f14444]) ).
fof(f14444,plain,
( spl171_849
<=> sP24(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_849])]) ).
fof(f2550,plain,
( sP24(sK166)
| ~ spl171_26
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2148]) ).
fof(f14442,plain,
( spl171_848
| ~ spl171_24
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2549,f2382,f2136,f14439]) ).
fof(f14439,plain,
( spl171_848
<=> sP24(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_848])]) ).
fof(f2549,plain,
( sP24(sK165)
| ~ spl171_24
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2138]) ).
fof(f14436,plain,
( spl171_847
| ~ spl171_23
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2548,f2382,f2131,f14433]) ).
fof(f14433,plain,
( spl171_847
<=> sP24(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_847])]) ).
fof(f2548,plain,
( sP24(sK164)
| ~ spl171_23
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2133]) ).
fof(f14431,plain,
( spl171_846
| ~ spl171_18
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2547,f2382,f2106,f14428]) ).
fof(f14428,plain,
( spl171_846
<=> sP24(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_846])]) ).
fof(f2547,plain,
( sP24(sK162)
| ~ spl171_18
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2108]) ).
fof(f14425,plain,
( spl171_845
| ~ spl171_4
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2545,f2382,f2036,f14422]) ).
fof(f2545,plain,
( sP24(empty_set)
| ~ spl171_4
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2038]) ).
fof(f14419,plain,
( spl171_844
| ~ spl171_41
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2543,f2378,f2221,f14416]) ).
fof(f14416,plain,
( spl171_844
<=> sP20(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_844])]) ).
fof(f2378,plain,
( spl171_76
<=> ! [X0] :
( sP20(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_76])]) ).
fof(f2543,plain,
( sP20(sK170)
| ~ spl171_41
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2223]) ).
fof(f2379,plain,
( ! [X0] :
( ~ relation(X0)
| sP20(X0) )
| ~ spl171_76 ),
inference(avatar_component_clause,[],[f2378]) ).
fof(f14413,plain,
( spl171_843
| ~ spl171_34
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2542,f2378,f2186,f14410]) ).
fof(f14410,plain,
( spl171_843
<=> sP20(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_843])]) ).
fof(f2542,plain,
( sP20(sK169)
| ~ spl171_34
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2188]) ).
fof(f14408,plain,
( spl171_842
| ~ spl171_31
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2541,f2378,f2171,f14405]) ).
fof(f14405,plain,
( spl171_842
<=> sP20(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_842])]) ).
fof(f2541,plain,
( sP20(sK168)
| ~ spl171_31
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2173]) ).
fof(f14403,plain,
( spl171_841
| ~ spl171_29
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2540,f2378,f2161,f14400]) ).
fof(f14400,plain,
( spl171_841
<=> sP20(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_841])]) ).
fof(f2540,plain,
( sP20(sK167)
| ~ spl171_29
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2163]) ).
fof(f14398,plain,
( spl171_840
| ~ spl171_26
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2539,f2378,f2146,f14395]) ).
fof(f14395,plain,
( spl171_840
<=> sP20(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_840])]) ).
fof(f2539,plain,
( sP20(sK166)
| ~ spl171_26
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2148]) ).
fof(f14393,plain,
( spl171_839
| ~ spl171_24
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2538,f2378,f2136,f14390]) ).
fof(f14390,plain,
( spl171_839
<=> sP20(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_839])]) ).
fof(f2538,plain,
( sP20(sK165)
| ~ spl171_24
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2138]) ).
fof(f14387,plain,
( spl171_838
| ~ spl171_23
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2537,f2378,f2131,f14384]) ).
fof(f14384,plain,
( spl171_838
<=> sP20(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_838])]) ).
fof(f2537,plain,
( sP20(sK164)
| ~ spl171_23
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2133]) ).
fof(f14382,plain,
( spl171_837
| ~ spl171_18
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2536,f2378,f2106,f14379]) ).
fof(f14379,plain,
( spl171_837
<=> sP20(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_837])]) ).
fof(f2536,plain,
( sP20(sK162)
| ~ spl171_18
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2108]) ).
fof(f14376,plain,
( spl171_836
| ~ spl171_4
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2534,f2378,f2036,f14373]) ).
fof(f2534,plain,
( sP20(empty_set)
| ~ spl171_4
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2038]) ).
fof(f14370,plain,
( spl171_835
| ~ spl171_41
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2532,f2374,f2221,f14367]) ).
fof(f14367,plain,
( spl171_835
<=> sP18(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_835])]) ).
fof(f2374,plain,
( spl171_75
<=> ! [X0] :
( sP18(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_75])]) ).
fof(f2532,plain,
( sP18(sK170)
| ~ spl171_41
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2223]) ).
fof(f2375,plain,
( ! [X0] :
( ~ relation(X0)
| sP18(X0) )
| ~ spl171_75 ),
inference(avatar_component_clause,[],[f2374]) ).
fof(f14364,plain,
( spl171_834
| ~ spl171_34
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2531,f2374,f2186,f14361]) ).
fof(f14361,plain,
( spl171_834
<=> sP18(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_834])]) ).
fof(f2531,plain,
( sP18(sK169)
| ~ spl171_34
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2188]) ).
fof(f14359,plain,
( spl171_833
| ~ spl171_31
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2530,f2374,f2171,f14356]) ).
fof(f14356,plain,
( spl171_833
<=> sP18(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_833])]) ).
fof(f2530,plain,
( sP18(sK168)
| ~ spl171_31
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2173]) ).
fof(f14354,plain,
( spl171_832
| ~ spl171_29
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2529,f2374,f2161,f14351]) ).
fof(f14351,plain,
( spl171_832
<=> sP18(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_832])]) ).
fof(f2529,plain,
( sP18(sK167)
| ~ spl171_29
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2163]) ).
fof(f14349,plain,
( spl171_831
| ~ spl171_26
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2528,f2374,f2146,f14346]) ).
fof(f14346,plain,
( spl171_831
<=> sP18(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_831])]) ).
fof(f2528,plain,
( sP18(sK166)
| ~ spl171_26
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2148]) ).
fof(f14344,plain,
( spl171_830
| ~ spl171_24
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2527,f2374,f2136,f14341]) ).
fof(f14341,plain,
( spl171_830
<=> sP18(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_830])]) ).
fof(f2527,plain,
( sP18(sK165)
| ~ spl171_24
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2138]) ).
fof(f14338,plain,
( spl171_829
| ~ spl171_23
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2526,f2374,f2131,f14335]) ).
fof(f14335,plain,
( spl171_829
<=> sP18(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_829])]) ).
fof(f2526,plain,
( sP18(sK164)
| ~ spl171_23
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2133]) ).
fof(f14333,plain,
( spl171_828
| ~ spl171_18
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2525,f2374,f2106,f14330]) ).
fof(f14330,plain,
( spl171_828
<=> sP18(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_828])]) ).
fof(f2525,plain,
( sP18(sK162)
| ~ spl171_18
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2108]) ).
fof(f14327,plain,
( spl171_827
| ~ spl171_4
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2523,f2374,f2036,f14324]) ).
fof(f2523,plain,
( sP18(empty_set)
| ~ spl171_4
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2038]) ).
fof(f14321,plain,
( spl171_826
| ~ spl171_41
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2521,f2370,f2221,f14318]) ).
fof(f14318,plain,
( spl171_826
<=> sP16(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_826])]) ).
fof(f2370,plain,
( spl171_74
<=> ! [X0] :
( sP16(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_74])]) ).
fof(f2521,plain,
( sP16(sK170)
| ~ spl171_41
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2223]) ).
fof(f2371,plain,
( ! [X0] :
( ~ relation(X0)
| sP16(X0) )
| ~ spl171_74 ),
inference(avatar_component_clause,[],[f2370]) ).
fof(f14315,plain,
( spl171_825
| ~ spl171_34
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2520,f2370,f2186,f14312]) ).
fof(f14312,plain,
( spl171_825
<=> sP16(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_825])]) ).
fof(f2520,plain,
( sP16(sK169)
| ~ spl171_34
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2188]) ).
fof(f14310,plain,
( spl171_824
| ~ spl171_31
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2519,f2370,f2171,f14307]) ).
fof(f14307,plain,
( spl171_824
<=> sP16(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_824])]) ).
fof(f2519,plain,
( sP16(sK168)
| ~ spl171_31
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2173]) ).
fof(f14305,plain,
( spl171_823
| ~ spl171_29
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2518,f2370,f2161,f14302]) ).
fof(f14302,plain,
( spl171_823
<=> sP16(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_823])]) ).
fof(f2518,plain,
( sP16(sK167)
| ~ spl171_29
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2163]) ).
fof(f14300,plain,
( spl171_822
| ~ spl171_26
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2517,f2370,f2146,f14297]) ).
fof(f14297,plain,
( spl171_822
<=> sP16(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_822])]) ).
fof(f2517,plain,
( sP16(sK166)
| ~ spl171_26
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2148]) ).
fof(f14295,plain,
( spl171_821
| ~ spl171_24
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2516,f2370,f2136,f14292]) ).
fof(f14292,plain,
( spl171_821
<=> sP16(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_821])]) ).
fof(f2516,plain,
( sP16(sK165)
| ~ spl171_24
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2138]) ).
fof(f14289,plain,
( spl171_820
| ~ spl171_23
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2515,f2370,f2131,f14286]) ).
fof(f14286,plain,
( spl171_820
<=> sP16(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_820])]) ).
fof(f2515,plain,
( sP16(sK164)
| ~ spl171_23
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2133]) ).
fof(f14284,plain,
( spl171_819
| ~ spl171_18
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2514,f2370,f2106,f14281]) ).
fof(f14281,plain,
( spl171_819
<=> sP16(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_819])]) ).
fof(f2514,plain,
( sP16(sK162)
| ~ spl171_18
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2108]) ).
fof(f14278,plain,
( spl171_818
| ~ spl171_4
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2512,f2370,f2036,f14275]) ).
fof(f2512,plain,
( sP16(empty_set)
| ~ spl171_4
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2038]) ).
fof(f14272,plain,
( spl171_817
| ~ spl171_41
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2510,f2366,f2221,f14269]) ).
fof(f14269,plain,
( spl171_817
<=> sP14(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_817])]) ).
fof(f2366,plain,
( spl171_73
<=> ! [X0] :
( sP14(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_73])]) ).
fof(f2510,plain,
( sP14(sK170)
| ~ spl171_41
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2223]) ).
fof(f2367,plain,
( ! [X0] :
( ~ relation(X0)
| sP14(X0) )
| ~ spl171_73 ),
inference(avatar_component_clause,[],[f2366]) ).
fof(f14266,plain,
( spl171_816
| ~ spl171_34
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2509,f2366,f2186,f14263]) ).
fof(f14263,plain,
( spl171_816
<=> sP14(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_816])]) ).
fof(f2509,plain,
( sP14(sK169)
| ~ spl171_34
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2188]) ).
fof(f14261,plain,
( spl171_815
| ~ spl171_31
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2508,f2366,f2171,f14258]) ).
fof(f14258,plain,
( spl171_815
<=> sP14(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_815])]) ).
fof(f2508,plain,
( sP14(sK168)
| ~ spl171_31
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2173]) ).
fof(f14256,plain,
( spl171_814
| ~ spl171_29
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2507,f2366,f2161,f14253]) ).
fof(f14253,plain,
( spl171_814
<=> sP14(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_814])]) ).
fof(f2507,plain,
( sP14(sK167)
| ~ spl171_29
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2163]) ).
fof(f14251,plain,
( spl171_813
| ~ spl171_26
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2506,f2366,f2146,f14248]) ).
fof(f14248,plain,
( spl171_813
<=> sP14(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_813])]) ).
fof(f2506,plain,
( sP14(sK166)
| ~ spl171_26
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2148]) ).
fof(f14246,plain,
( spl171_812
| ~ spl171_24
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2505,f2366,f2136,f14243]) ).
fof(f14243,plain,
( spl171_812
<=> sP14(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_812])]) ).
fof(f2505,plain,
( sP14(sK165)
| ~ spl171_24
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2138]) ).
fof(f14240,plain,
( spl171_811
| ~ spl171_23
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2504,f2366,f2131,f14237]) ).
fof(f14237,plain,
( spl171_811
<=> sP14(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_811])]) ).
fof(f2504,plain,
( sP14(sK164)
| ~ spl171_23
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2133]) ).
fof(f14235,plain,
( spl171_810
| ~ spl171_18
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2503,f2366,f2106,f14232]) ).
fof(f14232,plain,
( spl171_810
<=> sP14(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_810])]) ).
fof(f2503,plain,
( sP14(sK162)
| ~ spl171_18
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2108]) ).
fof(f14229,plain,
( spl171_809
| ~ spl171_4
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2501,f2366,f2036,f14226]) ).
fof(f2501,plain,
( sP14(empty_set)
| ~ spl171_4
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2038]) ).
fof(f14223,plain,
( spl171_808
| ~ spl171_41
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2499,f2362,f2221,f14220]) ).
fof(f14220,plain,
( spl171_808
<=> sP12(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_808])]) ).
fof(f2362,plain,
( spl171_72
<=> ! [X0] :
( sP12(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_72])]) ).
fof(f2499,plain,
( sP12(sK170)
| ~ spl171_41
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2223]) ).
fof(f2363,plain,
( ! [X0] :
( ~ relation(X0)
| sP12(X0) )
| ~ spl171_72 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f14217,plain,
( spl171_807
| ~ spl171_34
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2498,f2362,f2186,f14214]) ).
fof(f14214,plain,
( spl171_807
<=> sP12(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_807])]) ).
fof(f2498,plain,
( sP12(sK169)
| ~ spl171_34
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2188]) ).
fof(f14212,plain,
( spl171_806
| ~ spl171_31
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2497,f2362,f2171,f14209]) ).
fof(f14209,plain,
( spl171_806
<=> sP12(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_806])]) ).
fof(f2497,plain,
( sP12(sK168)
| ~ spl171_31
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2173]) ).
fof(f14207,plain,
( spl171_805
| ~ spl171_29
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2496,f2362,f2161,f14204]) ).
fof(f14204,plain,
( spl171_805
<=> sP12(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_805])]) ).
fof(f2496,plain,
( sP12(sK167)
| ~ spl171_29
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2163]) ).
fof(f14202,plain,
( spl171_804
| ~ spl171_26
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2495,f2362,f2146,f14199]) ).
fof(f14199,plain,
( spl171_804
<=> sP12(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_804])]) ).
fof(f2495,plain,
( sP12(sK166)
| ~ spl171_26
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2148]) ).
fof(f14197,plain,
( spl171_803
| ~ spl171_24
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2494,f2362,f2136,f14194]) ).
fof(f14194,plain,
( spl171_803
<=> sP12(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_803])]) ).
fof(f2494,plain,
( sP12(sK165)
| ~ spl171_24
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2138]) ).
fof(f14191,plain,
( spl171_802
| ~ spl171_23
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2493,f2362,f2131,f14188]) ).
fof(f14188,plain,
( spl171_802
<=> sP12(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_802])]) ).
fof(f2493,plain,
( sP12(sK164)
| ~ spl171_23
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2133]) ).
fof(f14186,plain,
( spl171_801
| ~ spl171_18
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2492,f2362,f2106,f14183]) ).
fof(f14183,plain,
( spl171_801
<=> sP12(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_801])]) ).
fof(f2492,plain,
( sP12(sK162)
| ~ spl171_18
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2108]) ).
fof(f14180,plain,
( spl171_800
| ~ spl171_4
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2490,f2362,f2036,f14177]) ).
fof(f2490,plain,
( sP12(empty_set)
| ~ spl171_4
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2038]) ).
fof(f14174,plain,
( spl171_799
| ~ spl171_41
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2488,f2358,f2221,f14171]) ).
fof(f14171,plain,
( spl171_799
<=> sP8(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_799])]) ).
fof(f2358,plain,
( spl171_71
<=> ! [X0] :
( sP8(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_71])]) ).
fof(f2488,plain,
( sP8(sK170)
| ~ spl171_41
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2223]) ).
fof(f2359,plain,
( ! [X0] :
( ~ relation(X0)
| sP8(X0) )
| ~ spl171_71 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f14168,plain,
( spl171_798
| ~ spl171_34
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2487,f2358,f2186,f14165]) ).
fof(f14165,plain,
( spl171_798
<=> sP8(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_798])]) ).
fof(f2487,plain,
( sP8(sK169)
| ~ spl171_34
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2188]) ).
fof(f14149,plain,
( spl171_797
| ~ spl171_203
| ~ spl171_796 ),
inference(avatar_split_clause,[],[f14145,f14142,f3373,f14147]) ).
fof(f14147,plain,
( spl171_797
<=> ! [X0,X5,X2,X1] :
( ~ in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| sP9(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK86(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),X5),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_797])]) ).
fof(f3373,plain,
( spl171_203
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_203])]) ).
fof(f14142,plain,
( spl171_796
<=> ! [X0,X5,X2,X1] :
( sP9(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK86(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),X5),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_796])]) ).
fof(f14145,plain,
( ! [X2,X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| sP9(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK86(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),X5),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1) )
| ~ spl171_203
| ~ spl171_796 ),
inference(forward_demodulation,[],[f14143,f3374]) ).
fof(f3374,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl171_203 ),
inference(avatar_component_clause,[],[f3373]) ).
fof(f14143,plain,
( ! [X2,X0,X1,X5] :
( sP9(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK86(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),X5),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) )
| ~ spl171_796 ),
inference(avatar_component_clause,[],[f14142]) ).
fof(f14144,plain,
spl171_796,
inference(avatar_split_clause,[],[f1859,f14142]) ).
fof(f1859,plain,
! [X2,X0,X1,X5] :
( sP9(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK86(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),X5),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1386,f1762,f1762,f1762]) ).
fof(f1762,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1558,f1065]) ).
fof(f1065,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f283]) ).
fof(f283,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f1558,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f1386,plain,
! [X2,X0,X1,X5] :
( sP9(X0,X1,X2)
| ~ in(ordered_pair(X5,sK86(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK85(X0,X1,X2),X5),X1)
| ~ in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f818,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK86(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK85(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),X0)
& in(ordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),X1) )
| in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ( in(ordered_pair(sK88(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK88(X0,X1,X7,X8)),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87,sK88])],[f814,f817,f816,f815]) ).
fof(f815,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK86(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK85(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK86(X0,X1,X2)),X0)
& in(ordered_pair(sK85(X0,X1,X2),X6),X1) )
| in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f816,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK86(X0,X1,X2)),X0)
& in(ordered_pair(sK85(X0,X1,X2),X6),X1) )
=> ( in(ordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),X0)
& in(ordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f817,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
=> ( in(ordered_pair(sK88(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK88(X0,X1,X7,X8)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f814,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f813]) ).
fof(f813,plain,
! [X1,X0,X2] :
( ( sP9(X1,X0,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP9(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f617]) ).
fof(f617,plain,
! [X1,X0,X2] :
( sP9(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f14110,plain,
( spl171_795
| ~ spl171_203
| ~ spl171_792 ),
inference(avatar_split_clause,[],[f14097,f14093,f3373,f14108]) ).
fof(f14108,plain,
( spl171_795
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2)
| ~ in(sK105(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_795])]) ).
fof(f14093,plain,
( spl171_792
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_792])]) ).
fof(f14097,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2)
| ~ in(sK105(X0,X1,X2),X1) )
| ~ spl171_203
| ~ spl171_792 ),
inference(forward_demodulation,[],[f14096,f3374]) ).
fof(f14096,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) )
| ~ spl171_203
| ~ spl171_792 ),
inference(forward_demodulation,[],[f14094,f3374]) ).
fof(f14094,plain,
( ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) )
| ~ spl171_792 ),
inference(avatar_component_clause,[],[f14093]) ).
fof(f14106,plain,
( spl171_794
| ~ spl171_31
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2486,f2358,f2171,f14103]) ).
fof(f14103,plain,
( spl171_794
<=> sP8(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_794])]) ).
fof(f2486,plain,
( sP8(sK168)
| ~ spl171_31
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2173]) ).
fof(f14101,plain,
spl171_793,
inference(avatar_split_clause,[],[f2008,f14099]) ).
fof(f14099,plain,
( spl171_793
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2)
| ~ in(sK139(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_793])]) ).
fof(f2008,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2)
| ~ in(sK139(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f2007,f1555]) ).
fof(f1555,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f2007,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2)
| ~ in(sK139(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1912,f1555]) ).
fof(f1912,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| ~ in(sK139(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1595,f1762,f1762]) ).
fof(f1595,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
| ~ in(sK139(X0,X1,X2),X1)
| ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f958,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
| ~ in(sK139(X0,X1,X2),X1)
| ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
& in(sK139(X0,X1,X2),X1) )
| in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138,sK139])],[f956,f957]) ).
fof(f957,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
| ~ in(sK139(X0,X1,X2),X1)
| ~ in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
& in(sK139(X0,X1,X2),X1) )
| in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f956,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X6,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(rectify,[],[f955]) ).
fof(f955,plain,
! [X1,X0,X2] :
( ( sP39(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP39(X1,X0,X2) ) ),
inference(flattening,[],[f954]) ).
fof(f954,plain,
! [X1,X0,X2] :
( ( sP39(X1,X0,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP39(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f662]) ).
fof(f662,plain,
! [X1,X0,X2] :
( sP39(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f14095,plain,
spl171_792,
inference(avatar_split_clause,[],[f1885,f14093]) ).
fof(f1885,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1451,f1762,f1762]) ).
fof(f1451,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f866,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
& in(sK105(X0,X1,X2),X1) )
| in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106])],[f864,f865]) ).
fof(f865,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
| ~ in(sK105(X0,X1,X2),X1)
| ~ in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
& in(sK105(X0,X1,X2),X1) )
| in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f864,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(rectify,[],[f863]) ).
fof(f863,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(flattening,[],[f862]) ).
fof(f862,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f635]) ).
fof(f635,plain,
! [X0,X1,X2] :
( sP21(X0,X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f13765,plain,
( spl171_791
| ~ spl171_203
| ~ spl171_786 ),
inference(avatar_split_clause,[],[f13744,f13740,f3373,f13763]) ).
fof(f13763,plain,
( spl171_791
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_791])]) ).
fof(f13740,plain,
( spl171_786
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_786])]) ).
fof(f13744,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_786 ),
inference(forward_demodulation,[],[f13743,f3374]) ).
fof(f13743,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| sP21(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) )
| ~ spl171_203
| ~ spl171_786 ),
inference(forward_demodulation,[],[f13741,f3374]) ).
fof(f13741,plain,
( ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) )
| ~ spl171_786 ),
inference(avatar_component_clause,[],[f13740]) ).
fof(f13761,plain,
( spl171_790
| ~ spl171_203
| ~ spl171_785 ),
inference(avatar_split_clause,[],[f13738,f13734,f3373,f13759]) ).
fof(f13759,plain,
( spl171_790
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_790])]) ).
fof(f13734,plain,
( spl171_785
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_785])]) ).
fof(f13738,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| sP9(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_785 ),
inference(forward_demodulation,[],[f13737,f3374]) ).
fof(f13737,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) )
| ~ spl171_203
| ~ spl171_785 ),
inference(forward_demodulation,[],[f13735,f3374]) ).
fof(f13735,plain,
( ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) )
| ~ spl171_785 ),
inference(avatar_component_clause,[],[f13734]) ).
fof(f13757,plain,
( spl171_789
| ~ spl171_203
| ~ spl171_784 ),
inference(avatar_split_clause,[],[f13732,f13728,f3373,f13755]) ).
fof(f13755,plain,
( spl171_789
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2))),X0)
| sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_789])]) ).
fof(f13728,plain,
( spl171_784
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_784])]) ).
fof(f13732,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK86(X0,X1,X2),sK85(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2))),X0)
| sP9(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_784 ),
inference(forward_demodulation,[],[f13731,f3374]) ).
fof(f13731,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2))),X0)
| sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) )
| ~ spl171_203
| ~ spl171_784 ),
inference(forward_demodulation,[],[f13729,f3374]) ).
fof(f13729,plain,
( ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) )
| ~ spl171_784 ),
inference(avatar_component_clause,[],[f13728]) ).
fof(f13753,plain,
spl171_788,
inference(avatar_split_clause,[],[f2010,f13751]) ).
fof(f13751,plain,
( spl171_788
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_788])]) ).
fof(f2010,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2) ),
inference(forward_demodulation,[],[f2009,f1555]) ).
fof(f2009,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| sP39(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f1913,f1555]) ).
fof(f1913,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1594,f1762,f1762]) ).
fof(f1594,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X0)
| in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f13749,plain,
( spl171_787
| ~ spl171_29
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2485,f2358,f2161,f13746]) ).
fof(f13746,plain,
( spl171_787
<=> sP8(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_787])]) ).
fof(f2485,plain,
( sP8(sK167)
| ~ spl171_29
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2163]) ).
fof(f13742,plain,
spl171_786,
inference(avatar_split_clause,[],[f1886,f13740]) ).
fof(f1886,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1450,f1762,f1762]) ).
fof(f1450,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X0)
| in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f13736,plain,
spl171_785,
inference(avatar_split_clause,[],[f1861,f13734]) ).
fof(f1861,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1384,f1762,f1762]) ).
fof(f1384,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(ordered_pair(sK85(X0,X1,X2),sK87(X0,X1,X2)),X1)
| in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f13730,plain,
spl171_784,
inference(avatar_split_clause,[],[f1860,f13728]) ).
fof(f1860,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK87(X0,X1,X2),sK87(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),unordered_pair(sK85(X0,X1,X2),sK85(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1385,f1762,f1762]) ).
fof(f1385,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| in(ordered_pair(sK87(X0,X1,X2),sK86(X0,X1,X2)),X0)
| in(ordered_pair(sK85(X0,X1,X2),sK86(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f13629,plain,
( spl171_783
| ~ spl171_203
| ~ spl171_781 ),
inference(avatar_split_clause,[],[f13621,f13617,f3373,f13627]) ).
fof(f13627,plain,
( spl171_783
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1),sK83(X0,X1)),unordered_pair(sK83(X0,X1),sK84(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_783])]) ).
fof(f13617,plain,
( spl171_781
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_781])]) ).
fof(f13621,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1),sK83(X0,X1)),unordered_pair(sK83(X0,X1),sK84(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_781 ),
inference(forward_demodulation,[],[f13620,f3374]) ).
fof(f13620,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_781 ),
inference(forward_demodulation,[],[f13618,f3374]) ).
fof(f13618,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_781 ),
inference(avatar_component_clause,[],[f13617]) ).
fof(f13625,plain,
( spl171_782
| ~ spl171_203
| ~ spl171_780 ),
inference(avatar_split_clause,[],[f13615,f13611,f3373,f13623]) ).
fof(f13623,plain,
( spl171_782
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK83(X0,X1)),unordered_pair(sK83(X0,X1),sK84(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_782])]) ).
fof(f13611,plain,
( spl171_780
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_780])]) ).
fof(f13615,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK83(X0,X1)),unordered_pair(sK83(X0,X1),sK84(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_780 ),
inference(forward_demodulation,[],[f13614,f3374]) ).
fof(f13614,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_780 ),
inference(forward_demodulation,[],[f13612,f3374]) ).
fof(f13612,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_780 ),
inference(avatar_component_clause,[],[f13611]) ).
fof(f13619,plain,
spl171_781,
inference(avatar_split_clause,[],[f1856,f13617]) ).
fof(f1856,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1377,f1762,f1762]) ).
fof(f1377,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f810]) ).
fof(f810,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| ~ in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1) )
& ( in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84])],[f808,f809]) ).
fof(f809,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( ~ in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| ~ in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1) )
& ( in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f808,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f807]) ).
fof(f807,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f492]) ).
fof(f492,plain,
! [X0] :
( ! [X1] :
( ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f13613,plain,
spl171_780,
inference(avatar_split_clause,[],[f1855,f13611]) ).
fof(f1855,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK84(X0,X1),sK83(X0,X1)),unordered_pair(sK84(X0,X1),sK84(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK83(X0,X1),sK84(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1378,f1762,f1762]) ).
fof(f1378,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK84(X0,X1),sK83(X0,X1)),X0)
| ~ in(ordered_pair(sK83(X0,X1),sK84(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f810]) ).
fof(f13516,plain,
( spl171_779
| ~ spl171_26
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2484,f2358,f2146,f13513]) ).
fof(f13513,plain,
( spl171_779
<=> sP8(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_779])]) ).
fof(f2484,plain,
( sP8(sK166)
| ~ spl171_26
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2148]) ).
fof(f13501,plain,
( spl171_778
| ~ spl171_203
| ~ spl171_776 ),
inference(avatar_split_clause,[],[f13493,f13489,f3373,f13499]) ).
fof(f13499,plain,
( spl171_778
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_778])]) ).
fof(f13489,plain,
( spl171_776
<=> ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_776])]) ).
fof(f13493,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_776 ),
inference(forward_demodulation,[],[f13492,f3374]) ).
fof(f13492,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_776 ),
inference(forward_demodulation,[],[f13490,f3374]) ).
fof(f13490,plain,
( ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_776 ),
inference(avatar_component_clause,[],[f13489]) ).
fof(f13497,plain,
( spl171_777
| ~ spl171_203
| ~ spl171_775 ),
inference(avatar_split_clause,[],[f13487,f13483,f3373,f13495]) ).
fof(f13495,plain,
( spl171_777
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_777])]) ).
fof(f13483,plain,
( spl171_775
<=> ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_775])]) ).
fof(f13487,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_775 ),
inference(forward_demodulation,[],[f13486,f3374]) ).
fof(f13486,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK80(X0,X1),sK79(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_775 ),
inference(forward_demodulation,[],[f13484,f3374]) ).
fof(f13484,plain,
( ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_775 ),
inference(avatar_component_clause,[],[f13483]) ).
fof(f13491,plain,
spl171_776,
inference(avatar_split_clause,[],[f1849,f13489]) ).
fof(f1849,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1370,f1762,f1762]) ).
fof(f1370,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f802]) ).
fof(f802,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0) )
& ( in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f800,f801]) ).
fof(f801,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
=> ( ( ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0) )
& ( in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f800,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f799]) ).
fof(f799,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f13485,plain,
spl171_775,
inference(avatar_split_clause,[],[f1848,f13483]) ).
fof(f1848,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK79(X0,X1),sK80(X0,X1)),unordered_pair(sK79(X0,X1),sK79(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1371,f1762,f1762]) ).
fof(f1371,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X1)
| ~ in(ordered_pair(sK79(X0,X1),sK80(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f802]) ).
fof(f13454,plain,
spl171_774,
inference(avatar_split_clause,[],[f1876,f13452]) ).
fof(f13452,plain,
( spl171_774
<=> ! [X6,X0,X5,X1,X7] :
( in(unordered_pair(unordered_pair(X5,X7),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_774])]) ).
fof(f1876,plain,
! [X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X5,X7),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP19(X0,X1) ),
inference(definition_unfolding,[],[f1428,f1762,f1762,f1762]) ).
fof(f1428,plain,
! [X0,X1,X6,X7,X5] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f847]) ).
fof(f847,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ( ~ in(ordered_pair(sK96(X0,X1),sK98(X0,X1)),X0)
& in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0)
& in(ordered_pair(sK96(X0,X1),sK97(X0,X1)),X0)
& in(sK98(X0,X1),X1)
& in(sK97(X0,X1),X1)
& in(sK96(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP19(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97,sK98])],[f845,f846]) ).
fof(f846,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK96(X0,X1),sK98(X0,X1)),X0)
& in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0)
& in(ordered_pair(sK96(X0,X1),sK97(X0,X1)),X0)
& in(sK98(X0,X1),X1)
& in(sK97(X0,X1),X1)
& in(sK96(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f845,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP19(X0,X1) ) ),
inference(rectify,[],[f844]) ).
fof(f844,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ sP19(X0,X1) ) ),
inference(nnf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0,X1] :
( sP19(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f13384,plain,
( spl171_773
| ~ spl171_203
| ~ spl171_770 ),
inference(avatar_split_clause,[],[f13371,f13368,f3373,f13382]) ).
fof(f13382,plain,
( spl171_773
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X8,sK88(X0,X1,X7,X8)),unordered_pair(sK88(X0,X1,X7,X8),sK88(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_773])]) ).
fof(f13368,plain,
( spl171_770
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(sK88(X0,X1,X7,X8),X8),unordered_pair(sK88(X0,X1,X7,X8),sK88(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_770])]) ).
fof(f13371,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK88(X0,X1,X7,X8)),unordered_pair(sK88(X0,X1,X7,X8),sK88(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_770 ),
inference(forward_demodulation,[],[f13369,f3374]) ).
fof(f13369,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK88(X0,X1,X7,X8),X8),unordered_pair(sK88(X0,X1,X7,X8),sK88(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) )
| ~ spl171_770 ),
inference(avatar_component_clause,[],[f13368]) ).
fof(f13380,plain,
( spl171_772
| ~ spl171_24
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2483,f2358,f2136,f13377]) ).
fof(f13377,plain,
( spl171_772
<=> sP8(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_772])]) ).
fof(f2483,plain,
( sP8(sK165)
| ~ spl171_24
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2138]) ).
fof(f13375,plain,
spl171_771,
inference(avatar_split_clause,[],[f2015,f13373]) ).
fof(f13373,plain,
( spl171_771
<=> ! [X2,X0,X1] :
( sK150(X0,X1,X2) = unordered_pair(unordered_pair(sK152(X0,X1,X2),sK151(X0,X1,X2)),unordered_pair(sK151(X0,X1,X2),sK151(X0,X1,X2)))
| sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_771])]) ).
fof(f2015,plain,
! [X2,X0,X1] :
( sK150(X0,X1,X2) = unordered_pair(unordered_pair(sK152(X0,X1,X2),sK151(X0,X1,X2)),unordered_pair(sK151(X0,X1,X2),sK151(X0,X1,X2)))
| sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f1926,f1555]) ).
fof(f1926,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| sK150(X0,X1,X2) = unordered_pair(unordered_pair(sK151(X0,X1,X2),sK152(X0,X1,X2)),unordered_pair(sK151(X0,X1,X2),sK151(X0,X1,X2)))
| in(sK150(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1690,f1762]) ).
fof(f1690,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| sK150(X0,X1,X2) = ordered_pair(sK151(X0,X1,X2),sK152(X0,X1,X2))
| in(sK150(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f1006,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK150(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK150(X0,X1,X2),X2) )
& ( ( sK150(X0,X1,X2) = ordered_pair(sK151(X0,X1,X2),sK152(X0,X1,X2))
& in(sK152(X0,X1,X2),X0)
& in(sK151(X0,X1,X2),X1) )
| in(sK150(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK153(X0,X1,X8),sK154(X0,X1,X8)) = X8
& in(sK154(X0,X1,X8),X0)
& in(sK153(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP45(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151,sK152,sK153,sK154])],[f1002,f1005,f1004,f1003]) ).
fof(f1003,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK150(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK150(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK150(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK150(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1004,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK150(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK150(X0,X1,X2) = ordered_pair(sK151(X0,X1,X2),sK152(X0,X1,X2))
& in(sK152(X0,X1,X2),X0)
& in(sK151(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1005,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK153(X0,X1,X8),sK154(X0,X1,X8)) = X8
& in(sK154(X0,X1,X8),X0)
& in(sK153(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP45(X0,X1,X2) ) ),
inference(rectify,[],[f1001]) ).
fof(f1001,plain,
! [X1,X0,X2] :
( ( sP45(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP45(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f672]) ).
fof(f672,plain,
! [X1,X0,X2] :
( sP45(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP45])]) ).
fof(f13370,plain,
spl171_770,
inference(avatar_split_clause,[],[f1863,f13368]) ).
fof(f1863,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK88(X0,X1,X7,X8),X8),unordered_pair(sK88(X0,X1,X7,X8),sK88(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ),
inference(definition_unfolding,[],[f1382,f1762,f1762]) ).
fof(f1382,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK88(X0,X1,X7,X8),X8),X0)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f13364,plain,
( spl171_769
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_768 ),
inference(avatar_split_clause,[],[f13360,f13357,f7378,f2580,f2244,f13362]) ).
fof(f13362,plain,
( spl171_769
<=> ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_769])]) ).
fof(f2580,plain,
( spl171_91
<=> ! [X0] : relation_rng(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_91])]) ).
fof(f13357,plain,
( spl171_768
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_768])]) ).
fof(f13360,plain,
( ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_768 ),
inference(forward_demodulation,[],[f13358,f7509]) ).
fof(f7509,plain,
( ! [X0,X1] : set_difference(X1,set_difference(X1,X0)) = relation_rng(relation_rng_restriction(X0,identity_relation(X1)))
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526 ),
inference(forward_demodulation,[],[f7485,f2581]) ).
fof(f2581,plain,
( ! [X0] : relation_rng(identity_relation(X0)) = X0
| ~ spl171_91 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f7485,plain,
( ! [X0,X1] : relation_rng(relation_rng_restriction(X0,identity_relation(X1))) = set_difference(relation_rng(identity_relation(X1)),set_difference(relation_rng(identity_relation(X1)),X0))
| ~ spl171_46
| ~ spl171_526 ),
inference(resolution,[],[f7379,f2245]) ).
fof(f13358,plain,
( ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl171_768 ),
inference(avatar_component_clause,[],[f13357]) ).
fof(f13359,plain,
spl171_768,
inference(avatar_split_clause,[],[f1797,f13357]) ).
fof(f1797,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1203,f1148]) ).
fof(f1148,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f263]) ).
fof(f263,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f1203,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f743]) ).
fof(f743,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
& in(sK72(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f741,f742]) ).
fof(f742,plain,
! [X1,X2] :
( ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK72(X1,X2)) != apply(X2,sK72(X1,X2))
& in(sK72(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f741,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f740]) ).
fof(f740,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f739]) ).
fof(f739,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f420]) ).
fof(f420,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f419]) ).
fof(f419,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f282]) ).
fof(f282,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f13310,plain,
spl171_767,
inference(avatar_split_clause,[],[f1723,f13308]) ).
fof(f13308,plain,
( spl171_767
<=> ! [X0,X3,X2,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) = X0
| sK158(X0,X1,X2,X3) = X1
| sK158(X0,X1,X2,X3) = X2
| in(sK158(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_767])]) ).
fof(f1723,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) = X0
| sK158(X0,X1,X2,X3) = X1
| sK158(X0,X1,X2,X3) = X2
| in(sK158(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1,X2,X3] :
( ( sP49(X0,X1,X2,X3)
| ( ( ( sK158(X0,X1,X2,X3) != X0
& sK158(X0,X1,X2,X3) != X1
& sK158(X0,X1,X2,X3) != X2 )
| ~ in(sK158(X0,X1,X2,X3),X3) )
& ( sK158(X0,X1,X2,X3) = X0
| sK158(X0,X1,X2,X3) = X1
| sK158(X0,X1,X2,X3) = X2
| in(sK158(X0,X1,X2,X3),X3) ) ) )
& ( ! [X5] :
( ( in(X5,X3)
| ( X0 != X5
& X1 != X5
& X2 != X5 ) )
& ( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3) ) )
| ~ sP49(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f1028,f1029]) ).
fof(f1029,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ( ( X0 != X4
& X1 != X4
& X2 != X4 )
| ~ in(X4,X3) )
& ( X0 = X4
| X1 = X4
| X2 = X4
| in(X4,X3) ) )
=> ( ( ( sK158(X0,X1,X2,X3) != X0
& sK158(X0,X1,X2,X3) != X1
& sK158(X0,X1,X2,X3) != X2 )
| ~ in(sK158(X0,X1,X2,X3),X3) )
& ( sK158(X0,X1,X2,X3) = X0
| sK158(X0,X1,X2,X3) = X1
| sK158(X0,X1,X2,X3) = X2
| in(sK158(X0,X1,X2,X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1028,plain,
! [X0,X1,X2,X3] :
( ( sP49(X0,X1,X2,X3)
| ? [X4] :
( ( ( X0 != X4
& X1 != X4
& X2 != X4 )
| ~ in(X4,X3) )
& ( X0 = X4
| X1 = X4
| X2 = X4
| in(X4,X3) ) ) )
& ( ! [X5] :
( ( in(X5,X3)
| ( X0 != X5
& X1 != X5
& X2 != X5 ) )
& ( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3) ) )
| ~ sP49(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1027]) ).
fof(f1027,plain,
! [X2,X1,X0,X3] :
( ( sP49(X2,X1,X0,X3)
| ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) ) )
& ( ! [X4] :
( ( in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| ~ in(X4,X3) ) )
| ~ sP49(X2,X1,X0,X3) ) ),
inference(flattening,[],[f1026]) ).
fof(f1026,plain,
! [X2,X1,X0,X3] :
( ( sP49(X2,X1,X0,X3)
| ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) ) )
& ( ! [X4] :
( ( in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| ~ in(X4,X3) ) )
| ~ sP49(X2,X1,X0,X3) ) ),
inference(nnf_transformation,[],[f680]) ).
fof(f680,plain,
! [X2,X1,X0,X3] :
( sP49(X2,X1,X0,X3)
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP49])]) ).
fof(f13306,plain,
spl171_766,
inference(avatar_split_clause,[],[f1132,f13304]) ).
fof(f13304,plain,
( spl171_766
<=> ! [X0,X1] :
( sP3(X0,X1)
| sK65(X0,X1) != apply(X0,sK64(X0,X1))
| ~ in(sK64(X0,X1),relation_rng(X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_766])]) ).
fof(f1132,plain,
! [X0,X1] :
( sP3(X0,X1)
| sK65(X0,X1) != apply(X0,sK64(X0,X1))
| ~ in(sK64(X0,X1),relation_rng(X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f718,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( ( sK65(X0,X1) != apply(X0,sK64(X0,X1))
| ~ in(sK64(X0,X1),relation_rng(X1)) )
& sK64(X0,X1) = apply(X1,sK65(X0,X1))
& in(sK65(X0,X1),relation_dom(X1)) )
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP2(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP3(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f716,f717]) ).
fof(f717,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP2(X2,X3,X1,X0) )
=> ( ( ( sK65(X0,X1) != apply(X0,sK64(X0,X1))
| ~ in(sK64(X0,X1),relation_rng(X1)) )
& sK64(X0,X1) = apply(X1,sK65(X0,X1))
& in(sK65(X0,X1),relation_dom(X1)) )
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f716,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP2(X2,X3,X1,X0) )
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP2(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f715]) ).
fof(f715,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP2(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP2(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f714]) ).
fof(f714,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP2(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP2(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f608]) ).
fof(f608,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP2(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f13301,plain,
( spl171_765
| ~ spl171_23
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2482,f2358,f2131,f13298]) ).
fof(f13298,plain,
( spl171_765
<=> sP8(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_765])]) ).
fof(f2482,plain,
( sP8(sK164)
| ~ spl171_23
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2133]) ).
fof(f13296,plain,
spl171_764,
inference(avatar_split_clause,[],[f2004,f13294]) ).
fof(f13294,plain,
( spl171_764
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK137(X0,X1),sK137(X0,X1)),unordered_pair(sK137(X0,X1),sK137(X0,X1))),X1)
| sP37(X0,X1)
| sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK137(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_764])]) ).
fof(f2004,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK137(X0,X1),sK137(X0,X1)),unordered_pair(sK137(X0,X1),sK137(X0,X1))),X1)
| sP37(X0,X1)
| sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK137(X0,X1),X0) ),
inference(inner_rewriting,[],[f2003]) ).
fof(f2003,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK137(X0,X1),sK136(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1)
| sP37(X0,X1)
| sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK136(X0,X1),X0) ),
inference(forward_demodulation,[],[f1906,f1555]) ).
fof(f1906,plain,
! [X0,X1] :
( sP37(X0,X1)
| sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK136(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK136(X0,X1),sK137(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1586,f1762]) ).
fof(f1586,plain,
! [X0,X1] :
( sP37(X0,X1)
| sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK136(X0,X1),X0)
| ~ in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f951,plain,
! [X0,X1] :
( ( sP37(X0,X1)
| ( ( sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK136(X0,X1),X0)
| ~ in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) )
& ( ( sK136(X0,X1) = sK137(X0,X1)
& in(sK136(X0,X1),X0) )
| in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP37(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136,sK137])],[f949,f950]) ).
fof(f950,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK136(X0,X1) != sK137(X0,X1)
| ~ in(sK136(X0,X1),X0)
| ~ in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) )
& ( ( sK136(X0,X1) = sK137(X0,X1)
& in(sK136(X0,X1),X0) )
| in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f949,plain,
! [X0,X1] :
( ( sP37(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP37(X0,X1) ) ),
inference(rectify,[],[f948]) ).
fof(f948,plain,
! [X0,X1] :
( ( sP37(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP37(X0,X1) ) ),
inference(flattening,[],[f947]) ).
fof(f947,plain,
! [X0,X1] :
( ( sP37(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP37(X0,X1) ) ),
inference(nnf_transformation,[],[f659]) ).
fof(f659,plain,
! [X0,X1] :
( sP37(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f13128,plain,
( spl171_763
| ~ spl171_203
| ~ spl171_758 ),
inference(avatar_split_clause,[],[f12863,f12860,f3373,f13126]) ).
fof(f13126,plain,
( spl171_763
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK111(X0,X1,X2),sK111(X0,X1,X2)),unordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2))),X1)
| sP25(X0,X1,X2)
| in(sK110(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_763])]) ).
fof(f12860,plain,
( spl171_758
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),unordered_pair(sK111(X0,X1,X2),sK111(X0,X1,X2))),X1)
| in(sK110(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_758])]) ).
fof(f12863,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK111(X0,X1,X2),sK111(X0,X1,X2)),unordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2))),X1)
| sP25(X0,X1,X2)
| in(sK110(X0,X1,X2),X2) )
| ~ spl171_203
| ~ spl171_758 ),
inference(forward_demodulation,[],[f12861,f3374]) ).
fof(f12861,plain,
( ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),unordered_pair(sK111(X0,X1,X2),sK111(X0,X1,X2))),X1)
| in(sK110(X0,X1,X2),X2) )
| ~ spl171_758 ),
inference(avatar_component_clause,[],[f12860]) ).
fof(f13124,plain,
( spl171_762
| ~ spl171_203
| ~ spl171_757 ),
inference(avatar_split_clause,[],[f12858,f12855,f3373,f13122]) ).
fof(f13122,plain,
( spl171_762
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK108(X0,X1,X2),sK107(X0,X1,X2)),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| sP23(X0,X1,X2)
| in(sK107(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_762])]) ).
fof(f12855,plain,
( spl171_757
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| in(sK107(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_757])]) ).
fof(f12858,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK108(X0,X1,X2),sK107(X0,X1,X2)),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| sP23(X0,X1,X2)
| in(sK107(X0,X1,X2),X2) )
| ~ spl171_203
| ~ spl171_757 ),
inference(forward_demodulation,[],[f12856,f3374]) ).
fof(f12856,plain,
( ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| in(sK107(X0,X1,X2),X2) )
| ~ spl171_757 ),
inference(avatar_component_clause,[],[f12855]) ).
fof(f13101,plain,
( spl171_761
| ~ spl171_203
| ~ spl171_755 ),
inference(avatar_split_clause,[],[f12849,f12846,f3373,f13099]) ).
fof(f13099,plain,
( spl171_761
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_761])]) ).
fof(f12846,plain,
( spl171_755
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_755])]) ).
fof(f12849,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK106(X0,X1,X2),sK105(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2)
| sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1) )
| ~ spl171_203
| ~ spl171_755 ),
inference(forward_demodulation,[],[f12847,f3374]) ).
fof(f12847,plain,
( ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) )
| ~ spl171_755 ),
inference(avatar_component_clause,[],[f12846]) ).
fof(f13072,plain,
( spl171_760
| ~ spl171_18
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2481,f2358,f2106,f13069]) ).
fof(f13069,plain,
( spl171_760
<=> sP8(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_760])]) ).
fof(f2481,plain,
( sP8(sK162)
| ~ spl171_18
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2108]) ).
fof(f12867,plain,
spl171_759,
inference(avatar_split_clause,[],[f2011,f12865]) ).
fof(f12865,plain,
( spl171_759
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| sP39(X0,X1,X2)
| in(sK139(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_759])]) ).
fof(f2011,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK139(X0,X1,X2),sK138(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2)
| sP39(X0,X1,X2)
| in(sK139(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f1914,f1555]) ).
fof(f1914,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK139(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),unordered_pair(sK138(X0,X1,X2),sK138(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1593,f1762]) ).
fof(f1593,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK139(X0,X1,X2),X1)
| in(ordered_pair(sK138(X0,X1,X2),sK139(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f12862,plain,
spl171_758,
inference(avatar_split_clause,[],[f1896,f12860]) ).
fof(f1896,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),unordered_pair(sK111(X0,X1,X2),sK111(X0,X1,X2))),X1)
| in(sK110(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1467,f1762]) ).
fof(f1467,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(ordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),X1)
| in(sK110(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f880,plain,
! [X0,X1,X2] :
( ( sP25(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK110(X0,X1,X2)),X1) )
| ~ in(sK110(X0,X1,X2),X2) )
& ( ( in(sK111(X0,X1,X2),X0)
& in(ordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),X1) )
| in(sK110(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ( in(sK112(X0,X1,X6),X0)
& in(ordered_pair(sK112(X0,X1,X6),X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111,sK112])],[f876,f879,f878,f877]) ).
fof(f877,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK110(X0,X1,X2)),X1) )
| ~ in(sK110(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK110(X0,X1,X2)),X1) )
| in(sK110(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f878,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK110(X0,X1,X2)),X1) )
=> ( in(sK111(X0,X1,X2),X0)
& in(ordered_pair(sK111(X0,X1,X2),sK110(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f879,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
=> ( in(sK112(X0,X1,X6),X0)
& in(ordered_pair(sK112(X0,X1,X6),X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f876,plain,
! [X0,X1,X2] :
( ( sP25(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(rectify,[],[f875]) ).
fof(f875,plain,
! [X1,X0,X2] :
( ( sP25(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| ~ sP25(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f641]) ).
fof(f641,plain,
! [X1,X0,X2] :
( sP25(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f12857,plain,
spl171_757,
inference(avatar_split_clause,[],[f1892,f12855]) ).
fof(f1892,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| in(sK107(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1458,f1762]) ).
fof(f1458,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(ordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),X1)
| in(sK107(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f873,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(sK107(X0,X1,X2),X4),X1) )
| ~ in(sK107(X0,X1,X2),X2) )
& ( ( in(sK108(X0,X1,X2),X0)
& in(ordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),X1) )
| in(sK107(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1) ) )
& ( ( in(sK109(X0,X1,X6),X0)
& in(ordered_pair(X6,sK109(X0,X1,X6)),X1) )
| ~ in(X6,X2) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK107,sK108,sK109])],[f869,f872,f871,f870]) ).
fof(f870,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X3,X5),X1) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(sK107(X0,X1,X2),X4),X1) )
| ~ in(sK107(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK107(X0,X1,X2),X5),X1) )
| in(sK107(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f871,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK107(X0,X1,X2),X5),X1) )
=> ( in(sK108(X0,X1,X2),X0)
& in(ordered_pair(sK107(X0,X1,X2),sK108(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f872,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X6,X8),X1) )
=> ( in(sK109(X0,X1,X6),X0)
& in(ordered_pair(X6,sK109(X0,X1,X6)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f869,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X3,X5),X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1) ) )
& ( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X6,X8),X1) )
| ~ in(X6,X2) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(rectify,[],[f868]) ).
fof(f868,plain,
! [X1,X0,X2] :
( ( sP23(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) ) )
| ~ sP23(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f638]) ).
fof(f638,plain,
! [X1,X0,X2] :
( sP23(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f12853,plain,
spl171_756,
inference(avatar_split_clause,[],[f1891,f12851]) ).
fof(f12851,plain,
( spl171_756
<=> ! [X4,X0,X2,X1] :
( sP23(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK107(X0,X1,X2),X4),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| ~ in(sK107(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_756])]) ).
fof(f1891,plain,
! [X2,X0,X1,X4] :
( sP23(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK107(X0,X1,X2),X4),unordered_pair(sK107(X0,X1,X2),sK107(X0,X1,X2))),X1)
| ~ in(sK107(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1460,f1762]) ).
fof(f1460,plain,
! [X2,X0,X1,X4] :
( sP23(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(sK107(X0,X1,X2),X4),X1)
| ~ in(sK107(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f12848,plain,
spl171_755,
inference(avatar_split_clause,[],[f1887,f12846]) ).
fof(f1887,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),unordered_pair(sK105(X0,X1,X2),sK105(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1449,f1762]) ).
fof(f1449,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| in(sK105(X0,X1,X2),X1)
| in(ordered_pair(sK105(X0,X1,X2),sK106(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f12844,plain,
spl171_754,
inference(avatar_split_clause,[],[f1862,f12842]) ).
fof(f12842,plain,
( spl171_754
<=> ! [X1,X0,X8,X9,X2,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_754])]) ).
fof(f1862,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP9(X0,X1,X2) ),
inference(definition_unfolding,[],[f1383,f1762,f1762,f1762]) ).
fof(f1383,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f12840,plain,
spl171_753,
inference(avatar_split_clause,[],[f1785,f12838]) ).
fof(f12838,plain,
( spl171_753
<=> ! [X5,X4,X0,X6] :
( in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_753])]) ).
fof(f1785,plain,
! [X0,X6,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1104,f1762,f1762,f1762]) ).
fof(f1104,plain,
! [X0,X6,X4,X5] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f710,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK61(X0),sK63(X0)),X0)
& in(ordered_pair(sK62(X0),sK63(X0)),X0)
& in(ordered_pair(sK61(X0),sK62(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62,sK63])],[f708,f709]) ).
fof(f709,plain,
! [X0] :
( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( ~ in(ordered_pair(sK61(X0),sK63(X0)),X0)
& in(ordered_pair(sK62(X0),sK63(X0)),X0)
& in(ordered_pair(sK61(X0),sK62(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f708,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f707]) ).
fof(f707,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f148,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f12836,plain,
spl171_752,
inference(avatar_split_clause,[],[f1781,f12834]) ).
fof(f12834,plain,
( spl171_752
<=> ! [X4,X0,X3] :
( in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_752])]) ).
fof(f1781,plain,
! [X3,X0,X4] :
( in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f1097,f1762,f1762]) ).
fof(f1097,plain,
! [X3,X0,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f706]) ).
fof(f706,plain,
! [X0] :
( ( sP0(X0)
| ( ~ in(ordered_pair(sK60(X0),sK59(X0)),X0)
& ~ in(ordered_pair(sK59(X0),sK60(X0)),X0)
& sK59(X0) != sK60(X0)
& in(sK60(X0),relation_field(X0))
& in(sK59(X0),relation_field(X0)) ) )
& ( ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60])],[f704,f705]) ).
fof(f705,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
=> ( ~ in(ordered_pair(sK60(X0),sK59(X0)),X0)
& ~ in(ordered_pair(sK59(X0),sK60(X0)),X0)
& sK59(X0) != sK60(X0)
& in(sK60(X0),relation_field(X0))
& in(sK59(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f704,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) )
& ( ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f703]) ).
fof(f703,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) )
& ( ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f604]) ).
fof(f604,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f12831,plain,
( spl171_751
| ~ spl171_4
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2479,f2358,f2036,f12828]) ).
fof(f2479,plain,
( sP8(empty_set)
| ~ spl171_4
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2038]) ).
fof(f12802,plain,
spl171_750,
inference(avatar_split_clause,[],[f1872,f12800]) ).
fof(f12800,plain,
( spl171_750
<=> ! [X4,X0,X5,X1] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_750])]) ).
fof(f1872,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP17(X0,X1) ),
inference(definition_unfolding,[],[f1419,f1762,f1762]) ).
fof(f1419,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f842]) ).
fof(f842,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ( ~ in(ordered_pair(sK95(X0,X1),sK94(X0,X1)),X0)
& ~ in(ordered_pair(sK94(X0,X1),sK95(X0,X1)),X0)
& sK94(X0,X1) != sK95(X0,X1)
& in(sK95(X0,X1),X1)
& in(sK94(X0,X1),X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP17(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f840,f841]) ).
fof(f841,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK95(X0,X1),sK94(X0,X1)),X0)
& ~ in(ordered_pair(sK94(X0,X1),sK95(X0,X1)),X0)
& sK94(X0,X1) != sK95(X0,X1)
& in(sK95(X0,X1),X1)
& in(sK94(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f840,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP17(X0,X1) ) ),
inference(rectify,[],[f839]) ).
fof(f839,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ sP17(X0,X1) ) ),
inference(nnf_transformation,[],[f629]) ).
fof(f629,plain,
! [X0,X1] :
( sP17(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f12798,plain,
spl171_749,
inference(avatar_split_clause,[],[f1869,f12796]) ).
fof(f12796,plain,
( spl171_749
<=> ! [X4,X0,X5,X1] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_749])]) ).
fof(f1869,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP15(X0,X1) ),
inference(definition_unfolding,[],[f1410,f1762,f1762]) ).
fof(f1410,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f837]) ).
fof(f837,plain,
! [X0,X1] :
( ( sP15(X0,X1)
| ( sK92(X0,X1) != sK93(X0,X1)
& in(ordered_pair(sK93(X0,X1),sK92(X0,X1)),X0)
& in(ordered_pair(sK92(X0,X1),sK93(X0,X1)),X0)
& in(sK93(X0,X1),X1)
& in(sK92(X0,X1),X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP15(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93])],[f835,f836]) ).
fof(f836,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> ( sK92(X0,X1) != sK93(X0,X1)
& in(ordered_pair(sK93(X0,X1),sK92(X0,X1)),X0)
& in(ordered_pair(sK92(X0,X1),sK93(X0,X1)),X0)
& in(sK93(X0,X1),X1)
& in(sK92(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f835,plain,
! [X0,X1] :
( ( sP15(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP15(X0,X1) ) ),
inference(rectify,[],[f834]) ).
fof(f834,plain,
! [X0,X1] :
( ( sP15(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ sP15(X0,X1) ) ),
inference(nnf_transformation,[],[f626]) ).
fof(f626,plain,
! [X0,X1] :
( sP15(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f12785,plain,
( spl171_748
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_747 ),
inference(avatar_split_clause,[],[f12781,f12778,f7378,f2580,f2244,f12783]) ).
fof(f12783,plain,
( spl171_748
<=> ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_748])]) ).
fof(f12778,plain,
( spl171_747
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_747])]) ).
fof(f12781,plain,
( ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_747 ),
inference(forward_demodulation,[],[f12779,f7509]) ).
fof(f12779,plain,
( ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl171_747 ),
inference(avatar_component_clause,[],[f12778]) ).
fof(f12780,plain,
spl171_747,
inference(avatar_split_clause,[],[f1798,f12778]) ).
fof(f1798,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1202,f1148]) ).
fof(f1202,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK72(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f743]) ).
fof(f12684,plain,
( spl171_746
| ~ spl171_41
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2477,f2354,f2221,f12681]) ).
fof(f12681,plain,
( spl171_746
<=> sP6(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_746])]) ).
fof(f2354,plain,
( spl171_70
<=> ! [X0] :
( sP6(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_70])]) ).
fof(f2477,plain,
( sP6(sK170)
| ~ spl171_41
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2223]) ).
fof(f2355,plain,
( ! [X0] :
( ~ relation(X0)
| sP6(X0) )
| ~ spl171_70 ),
inference(avatar_component_clause,[],[f2354]) ).
fof(f12672,plain,
( spl171_745
| ~ spl171_203
| ~ spl171_741 ),
inference(avatar_split_clause,[],[f12656,f12653,f3373,f12670]) ).
fof(f12670,plain,
( spl171_745
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK103(X0,X1),sK102(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK102(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_745])]) ).
fof(f12653,plain,
( spl171_741
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| in(sK102(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_741])]) ).
fof(f12656,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK103(X0,X1),sK102(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK102(X0,X1),X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_741 ),
inference(forward_demodulation,[],[f12654,f3374]) ).
fof(f12654,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| in(sK102(X0,X1),X1)
| ~ relation(X0) )
| ~ spl171_741 ),
inference(avatar_component_clause,[],[f12653]) ).
fof(f12668,plain,
( spl171_744
| ~ spl171_203
| ~ spl171_740 ),
inference(avatar_split_clause,[],[f12651,f12648,f3373,f12666]) ).
fof(f12666,plain,
( spl171_744
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK100(X0,X1),sK100(X0,X1)),unordered_pair(sK100(X0,X1),sK99(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK99(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_744])]) ).
fof(f12648,plain,
( spl171_740
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK100(X0,X1),sK99(X0,X1)),unordered_pair(sK100(X0,X1),sK100(X0,X1))),X0)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_740])]) ).
fof(f12651,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK100(X0,X1),sK100(X0,X1)),unordered_pair(sK100(X0,X1),sK99(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK99(X0,X1),X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_740 ),
inference(forward_demodulation,[],[f12649,f3374]) ).
fof(f12649,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK100(X0,X1),sK99(X0,X1)),unordered_pair(sK100(X0,X1),sK100(X0,X1))),X0)
| in(sK99(X0,X1),X1)
| ~ relation(X0) )
| ~ spl171_740 ),
inference(avatar_component_clause,[],[f12648]) ).
fof(f12664,plain,
spl171_743,
inference(avatar_split_clause,[],[f2016,f12662]) ).
fof(f12662,plain,
( spl171_743
<=> ! [X0,X8,X2,X1] :
( unordered_pair(unordered_pair(sK154(X0,X1,X8),sK153(X0,X1,X8)),unordered_pair(sK153(X0,X1,X8),sK153(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_743])]) ).
fof(f2016,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK154(X0,X1,X8),sK153(X0,X1,X8)),unordered_pair(sK153(X0,X1,X8),sK153(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ),
inference(forward_demodulation,[],[f1928,f1555]) ).
fof(f1928,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK153(X0,X1,X8),sK154(X0,X1,X8)),unordered_pair(sK153(X0,X1,X8),sK153(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ),
inference(definition_unfolding,[],[f1686,f1762]) ).
fof(f1686,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK153(X0,X1,X8),sK154(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f12660,plain,
spl171_742,
inference(avatar_split_clause,[],[f1925,f12658]) ).
fof(f12658,plain,
( spl171_742
<=> ! [X4,X0,X5,X2,X1] :
( sP45(X0,X1,X2)
| sK150(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK150(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_742])]) ).
fof(f1925,plain,
! [X2,X0,X1,X4,X5] :
( sP45(X0,X1,X2)
| sK150(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK150(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1691,f1762]) ).
fof(f1691,plain,
! [X2,X0,X1,X4,X5] :
( sP45(X0,X1,X2)
| ordered_pair(X4,X5) != sK150(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK150(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f12655,plain,
spl171_741,
inference(avatar_split_clause,[],[f1882,f12653]) ).
fof(f1882,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| in(sK102(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1442,f1762]) ).
fof(f1442,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0)
| in(sK102(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f859]) ).
fof(f859,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK102(X0,X1),X3),X0)
| ~ in(sK102(X0,X1),X1) )
& ( in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0)
| in(sK102(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK104(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103,sK104])],[f855,f858,f857,f856]) ).
fof(f856,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK102(X0,X1),X3),X0)
| ~ in(sK102(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK102(X0,X1),X4),X0)
| in(sK102(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f857,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK102(X0,X1),X4),X0)
=> in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f858,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK104(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f855,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f854]) ).
fof(f854,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f503]) ).
fof(f503,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f12650,plain,
spl171_740,
inference(avatar_split_clause,[],[f1878,f12648]) ).
fof(f1878,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK100(X0,X1),sK99(X0,X1)),unordered_pair(sK100(X0,X1),sK100(X0,X1))),X0)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1438,f1762]) ).
fof(f1438,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK100(X0,X1),sK99(X0,X1)),X0)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f853]) ).
fof(f853,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK99(X0,X1)),X0)
| ~ in(sK99(X0,X1),X1) )
& ( in(ordered_pair(sK100(X0,X1),sK99(X0,X1)),X0)
| in(sK99(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK101(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101])],[f849,f852,f851,f850]) ).
fof(f850,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK99(X0,X1)),X0)
| ~ in(sK99(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK99(X0,X1)),X0)
| in(sK99(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f851,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK99(X0,X1)),X0)
=> in(ordered_pair(sK100(X0,X1),sK99(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f852,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK101(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f849,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f848]) ).
fof(f848,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f502]) ).
fof(f502,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f12605,plain,
spl171_739,
inference(avatar_split_clause,[],[f2005,f12603]) ).
fof(f12603,plain,
( spl171_739
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK137(X0,X1),sK136(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1)
| sP37(X0,X1)
| sK136(X0,X1) = sK137(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_739])]) ).
fof(f2005,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK137(X0,X1),sK136(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1)
| sP37(X0,X1)
| sK136(X0,X1) = sK137(X0,X1) ),
inference(forward_demodulation,[],[f1907,f1555]) ).
fof(f1907,plain,
! [X0,X1] :
( sP37(X0,X1)
| sK136(X0,X1) = sK137(X0,X1)
| in(unordered_pair(unordered_pair(sK136(X0,X1),sK137(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1585,f1762]) ).
fof(f1585,plain,
! [X0,X1] :
( sP37(X0,X1)
| sK136(X0,X1) = sK137(X0,X1)
| in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f12591,plain,
( spl171_738
| ~ spl171_34
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2476,f2354,f2186,f12588]) ).
fof(f12588,plain,
( spl171_738
<=> sP6(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_738])]) ).
fof(f2476,plain,
( sP6(sK169)
| ~ spl171_34
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2188]) ).
fof(f12586,plain,
spl171_737,
inference(avatar_split_clause,[],[f1131,f12584]) ).
fof(f12584,plain,
( spl171_737
<=> ! [X0,X1] :
( sP3(X0,X1)
| sK64(X0,X1) = apply(X1,sK65(X0,X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_737])]) ).
fof(f1131,plain,
! [X0,X1] :
( sP3(X0,X1)
| sK64(X0,X1) = apply(X1,sK65(X0,X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f12541,plain,
( spl171_736
| ~ spl171_203
| ~ spl171_734 ),
inference(avatar_split_clause,[],[f12485,f12482,f3373,f12539]) ).
fof(f12539,plain,
( spl171_736
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK88(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_736])]) ).
fof(f12482,plain,
( spl171_734
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,sK88(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_734])]) ).
fof(f12485,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK88(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_734 ),
inference(forward_demodulation,[],[f12483,f3374]) ).
fof(f12483,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK88(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) )
| ~ spl171_734 ),
inference(avatar_component_clause,[],[f12482]) ).
fof(f12489,plain,
spl171_735,
inference(avatar_split_clause,[],[f1881,f12487]) ).
fof(f12487,plain,
( spl171_735
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK102(X0,X1),X3),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| ~ in(sK102(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_735])]) ).
fof(f1881,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK102(X0,X1),X3),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0)
| ~ in(sK102(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1443,f1762]) ).
fof(f1443,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK102(X0,X1),X3),X0)
| ~ in(sK102(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f859]) ).
fof(f12484,plain,
spl171_734,
inference(avatar_split_clause,[],[f1864,f12482]) ).
fof(f1864,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK88(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP9(X0,X1,X2) ),
inference(definition_unfolding,[],[f1381,f1762,f1762]) ).
fof(f1381,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK88(X0,X1,X7,X8)),X1)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f818]) ).
fof(f12480,plain,
spl171_733,
inference(avatar_split_clause,[],[f1829,f12478]) ).
fof(f12478,plain,
( spl171_733
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_733])]) ).
fof(f1829,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f1278,f1762,f1762]) ).
fof(f1278,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f779]) ).
fof(f779,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(flattening,[],[f778]) ).
fof(f778,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(nnf_transformation,[],[f464]) ).
fof(f464,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
| ~ relation(X3) ),
inference(ennf_transformation,[],[f289]) ).
fof(f289,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f12462,plain,
( spl171_732
| ~ spl171_31
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2475,f2354,f2171,f12459]) ).
fof(f12459,plain,
( spl171_732
<=> sP6(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_732])]) ).
fof(f2475,plain,
( sP6(sK168)
| ~ spl171_31
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2173]) ).
fof(f12457,plain,
spl171_731,
inference(avatar_split_clause,[],[f1518,f12455]) ).
fof(f12455,plain,
( spl171_731
<=> ! [X4,X0,X2,X1] :
( sP33(X0,X1,X2)
| apply(X0,X4) != sK119(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK119(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_731])]) ).
fof(f1518,plain,
! [X2,X0,X1,X4] :
( sP33(X0,X1,X2)
| apply(X0,X4) != sK119(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK119(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f906,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ( ( ! [X4] :
( apply(X0,X4) != sK119(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK119(X0,X1,X2),X2) )
& ( ( sK119(X0,X1,X2) = apply(X0,sK120(X0,X1,X2))
& in(sK120(X0,X1,X2),X1)
& in(sK120(X0,X1,X2),relation_dom(X0)) )
| in(sK119(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK121(X0,X1,X6)) = X6
& in(sK121(X0,X1,X6),X1)
& in(sK121(X0,X1,X6),relation_dom(X0)) )
| ~ in(X6,X2) ) )
| ~ sP33(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK119,sK120,sK121])],[f902,f905,f904,f903]) ).
fof(f903,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( apply(X0,X4) != sK119(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK119(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK119(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK119(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f904,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK119(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK119(X0,X1,X2) = apply(X0,sK120(X0,X1,X2))
& in(sK120(X0,X1,X2),X1)
& in(sK120(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f905,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK121(X0,X1,X6)) = X6
& in(sK121(X0,X1,X6),X1)
& in(sK121(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f902,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
| ~ in(X6,X2) ) )
| ~ sP33(X0,X1,X2) ) ),
inference(rectify,[],[f901]) ).
fof(f901,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ~ sP33(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f653]) ).
fof(f653,plain,
! [X0,X1,X2] :
( sP33(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
fof(f12453,plain,
spl171_730,
inference(avatar_split_clause,[],[f1507,f12451]) ).
fof(f12451,plain,
( spl171_730
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ in(apply(X1,sK118(X0,X1,X2)),X0)
| ~ in(sK118(X0,X1,X2),relation_dom(X1))
| ~ in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_730])]) ).
fof(f1507,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| ~ in(apply(X1,sK118(X0,X1,X2)),X0)
| ~ in(sK118(X0,X1,X2),relation_dom(X1))
| ~ in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f899,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ( ( ~ in(apply(X1,sK118(X0,X1,X2)),X0)
| ~ in(sK118(X0,X1,X2),relation_dom(X1))
| ~ in(sK118(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK118(X0,X1,X2)),X0)
& in(sK118(X0,X1,X2),relation_dom(X1)) )
| in(sK118(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,X2) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118])],[f897,f898]) ).
fof(f898,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X1,sK118(X0,X1,X2)),X0)
| ~ in(sK118(X0,X1,X2),relation_dom(X1))
| ~ in(sK118(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK118(X0,X1,X2)),X0)
& in(sK118(X0,X1,X2),relation_dom(X1)) )
| in(sK118(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f897,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,X2) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f896]) ).
fof(f896,plain,
! [X1,X0,X2] :
( ( sP31(X1,X0,X2)
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ~ sP31(X1,X0,X2) ) ),
inference(flattening,[],[f895]) ).
fof(f895,plain,
! [X1,X0,X2] :
( ( sP31(X1,X0,X2)
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ~ sP31(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f650]) ).
fof(f650,plain,
! [X1,X0,X2] :
( sP31(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f12342,plain,
( spl171_729
| ~ spl171_203
| ~ spl171_724 ),
inference(avatar_split_clause,[],[f12169,f12166,f3373,f12340]) ).
fof(f12340,plain,
( spl171_729
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK112(X0,X1,X6)),unordered_pair(sK112(X0,X1,X6),sK112(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_729])]) ).
fof(f12166,plain,
( spl171_724
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(sK112(X0,X1,X6),X6),unordered_pair(sK112(X0,X1,X6),sK112(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_724])]) ).
fof(f12169,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK112(X0,X1,X6)),unordered_pair(sK112(X0,X1,X6),sK112(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_724 ),
inference(forward_demodulation,[],[f12167,f3374]) ).
fof(f12167,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK112(X0,X1,X6),X6),unordered_pair(sK112(X0,X1,X6),sK112(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) )
| ~ spl171_724 ),
inference(avatar_component_clause,[],[f12166]) ).
fof(f12297,plain,
( spl171_728
| ~ spl171_203
| ~ spl171_721 ),
inference(avatar_split_clause,[],[f12156,f12153,f3373,f12295]) ).
fof(f12295,plain,
( spl171_728
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_728])]) ).
fof(f12153,plain,
( spl171_721
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK75(X0,X1,X2),X0),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_721])]) ).
fof(f12156,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK75(X0,X1,X2)),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl171_203
| ~ spl171_721 ),
inference(forward_demodulation,[],[f12154,f3374]) ).
fof(f12154,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK75(X0,X1,X2),X0),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl171_721 ),
inference(avatar_component_clause,[],[f12153]) ).
fof(f12293,plain,
( spl171_727
| ~ spl171_29
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2474,f2354,f2161,f12290]) ).
fof(f12290,plain,
( spl171_727
<=> sP6(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_727])]) ).
fof(f2474,plain,
( sP6(sK167)
| ~ spl171_29
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2163]) ).
fof(f12177,plain,
spl171_726,
inference(avatar_split_clause,[],[f2006,f12175]) ).
fof(f12175,plain,
( spl171_726
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK137(X0,X1),sK136(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1)
| sP37(X0,X1)
| in(sK136(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_726])]) ).
fof(f2006,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK137(X0,X1),sK136(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1)
| sP37(X0,X1)
| in(sK136(X0,X1),X0) ),
inference(forward_demodulation,[],[f1908,f1555]) ).
fof(f1908,plain,
! [X0,X1] :
( sP37(X0,X1)
| in(sK136(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK136(X0,X1),sK137(X0,X1)),unordered_pair(sK136(X0,X1),sK136(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1584,f1762]) ).
fof(f1584,plain,
! [X0,X1] :
( sP37(X0,X1)
| in(sK136(X0,X1),X0)
| in(ordered_pair(sK136(X0,X1),sK137(X0,X1)),X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f12173,plain,
spl171_725,
inference(avatar_split_clause,[],[f1915,f12171]) ).
fof(f12171,plain,
( spl171_725
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X6,X1)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_725])]) ).
fof(f1915,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X6,X1)
| ~ sP39(X0,X1,X2) ),
inference(definition_unfolding,[],[f1592,f1762,f1762]) ).
fof(f1592,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f12168,plain,
spl171_724,
inference(avatar_split_clause,[],[f1898,f12166]) ).
fof(f1898,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK112(X0,X1,X6),X6),unordered_pair(sK112(X0,X1,X6),sK112(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ),
inference(definition_unfolding,[],[f1464,f1762]) ).
fof(f1464,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK112(X0,X1,X6),X6),X1)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f12164,plain,
spl171_723,
inference(avatar_split_clause,[],[f1895,f12162]) ).
fof(f12162,plain,
( spl171_723
<=> ! [X4,X0,X2,X1] :
( sP25(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK110(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK110(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_723])]) ).
fof(f1895,plain,
! [X2,X0,X1,X4] :
( sP25(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK110(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK110(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1469,f1762]) ).
fof(f1469,plain,
! [X2,X0,X1,X4] :
( sP25(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK110(X0,X1,X2)),X1)
| ~ in(sK110(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f12160,plain,
spl171_722,
inference(avatar_split_clause,[],[f1888,f12158]) ).
fof(f12158,plain,
( spl171_722
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_722])]) ).
fof(f1888,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP21(X0,X1,X2) ),
inference(definition_unfolding,[],[f1448,f1762,f1762]) ).
fof(f1448,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f12155,plain,
spl171_721,
inference(avatar_split_clause,[],[f1820,f12153]) ).
fof(f1820,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK75(X0,X1,X2),X0),unordered_pair(sK75(X0,X1,X2),sK75(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1243,f1762]) ).
fof(f1243,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK75(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f767]) ).
fof(f767,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ( in(sK75(X0,X1,X2),X1)
& in(ordered_pair(sK75(X0,X1,X2),X0),X2)
& in(sK75(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f765,f766]) ).
fof(f766,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK75(X0,X1,X2),X1)
& in(ordered_pair(sK75(X0,X1,X2),X0),X2)
& in(sK75(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f765,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f764]) ).
fof(f764,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f435]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f194]) ).
fof(f194,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f12151,plain,
spl171_720,
inference(avatar_split_clause,[],[f1778,f12149]) ).
fof(f12149,plain,
( spl171_720
<=> ! [X4,X0,X3] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_720])]) ).
fof(f1778,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1091,f1762,f1762]) ).
fof(f1091,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f701]) ).
fof(f701,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ( sK57(X0) != sK58(X0)
& in(ordered_pair(sK58(X0),sK57(X0)),X0)
& in(ordered_pair(sK57(X0),sK58(X0)),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58])],[f699,f700]) ).
fof(f700,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK57(X0) != sK58(X0)
& in(ordered_pair(sK58(X0),sK57(X0)),X0)
& in(ordered_pair(sK57(X0),sK58(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f699,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f698]) ).
fof(f698,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f339]) ).
fof(f339,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f152,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f12147,plain,
spl171_719,
inference(avatar_split_clause,[],[f1199,f12145]) ).
fof(f12145,plain,
( spl171_719
<=> ! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_719])]) ).
fof(f1199,plain,
! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f219,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f12143,plain,
( spl171_718
| ~ spl171_26
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2473,f2354,f2146,f12140]) ).
fof(f12140,plain,
( spl171_718
<=> sP6(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_718])]) ).
fof(f2473,plain,
( sP6(sK166)
| ~ spl171_26
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2148]) ).
fof(f12053,plain,
( spl171_717
| ~ spl171_203
| ~ spl171_713 ),
inference(avatar_split_clause,[],[f12025,f12022,f3373,f12051]) ).
fof(f12051,plain,
( spl171_717
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK82(X0,X1),sK81(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_717])]) ).
fof(f12022,plain,
( spl171_713
<=> ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_713])]) ).
fof(f12025,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK82(X0,X1),sK81(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_713 ),
inference(forward_demodulation,[],[f12023,f3374]) ).
fof(f12023,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_713 ),
inference(avatar_component_clause,[],[f12022]) ).
fof(f12049,plain,
( spl171_716
| ~ spl171_203
| ~ spl171_711 ),
inference(avatar_split_clause,[],[f12015,f12012,f3373,f12047]) ).
fof(f12047,plain,
( spl171_716
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK82(X0,X1),sK81(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_716])]) ).
fof(f12012,plain,
( spl171_711
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_711])]) ).
fof(f12015,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK82(X0,X1),sK81(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_711 ),
inference(forward_demodulation,[],[f12013,f3374]) ).
fof(f12013,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl171_711 ),
inference(avatar_component_clause,[],[f12012]) ).
fof(f12033,plain,
spl171_715,
inference(avatar_split_clause,[],[f1952,f12031]) ).
fof(f12031,plain,
( spl171_715
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_715])]) ).
fof(f1952,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1858]) ).
fof(f1858,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1375,f1762,f1762]) ).
fof(f1375,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f810]) ).
fof(f12029,plain,
spl171_714,
inference(avatar_split_clause,[],[f1951,f12027]) ).
fof(f12027,plain,
( spl171_714
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_714])]) ).
fof(f1951,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1857]) ).
fof(f1857,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1376,f1762,f1762]) ).
fof(f1376,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f810]) ).
fof(f12024,plain,
spl171_713,
inference(avatar_split_clause,[],[f1853,f12022]) ).
fof(f1853,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1373,f1762]) ).
fof(f1373,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f806]) ).
fof(f806,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X1)
& in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82])],[f804,f805]) ).
fof(f805,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X1)
& in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f804,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f803]) ).
fof(f803,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f491]) ).
fof(f491,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f12020,plain,
( spl171_712
| ~ spl171_24
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2472,f2354,f2136,f12017]) ).
fof(f12017,plain,
( spl171_712
<=> sP6(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_712])]) ).
fof(f2472,plain,
( sP6(sK165)
| ~ spl171_24
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2138]) ).
fof(f12014,plain,
spl171_711,
inference(avatar_split_clause,[],[f1852,f12012]) ).
fof(f1852,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK81(X0,X1),sK82(X0,X1)),unordered_pair(sK81(X0,X1),sK81(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1374,f1762]) ).
fof(f1374,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK81(X0,X1),sK82(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f806]) ).
fof(f12010,plain,
spl171_710,
inference(avatar_split_clause,[],[f1206,f12008]) ).
fof(f12008,plain,
( spl171_710
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_710])]) ).
fof(f1206,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f745]) ).
fof(f745,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f744]) ).
fof(f744,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f422]) ).
fof(f422,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f421]) ).
fof(f421,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f216]) ).
fof(f216,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f11995,plain,
spl171_709,
inference(avatar_split_clause,[],[f1130,f11993]) ).
fof(f11993,plain,
( spl171_709
<=> ! [X0,X1] :
( sP3(X0,X1)
| in(sK65(X0,X1),relation_dom(X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_709])]) ).
fof(f1130,plain,
! [X0,X1] :
( sP3(X0,X1)
| in(sK65(X0,X1),relation_dom(X1))
| ~ sP2(sK64(X0,X1),sK65(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f11839,plain,
spl171_708,
inference(avatar_split_clause,[],[f1830,f11837]) ).
fof(f11837,plain,
( spl171_708
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_708])]) ).
fof(f1830,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f1277,f1762,f1762]) ).
fof(f1277,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f779]) ).
fof(f11835,plain,
spl171_707,
inference(avatar_split_clause,[],[f1819,f11833]) ).
fof(f11833,plain,
( spl171_707
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_707])]) ).
fof(f1819,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1245,f1762]) ).
fof(f1245,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f767]) ).
fof(f11830,plain,
( spl171_706
| ~ spl171_23
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2471,f2354,f2131,f11827]) ).
fof(f11827,plain,
( spl171_706
<=> sP6(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_706])]) ).
fof(f2471,plain,
( sP6(sK164)
| ~ spl171_23
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2133]) ).
fof(f11825,plain,
spl171_705,
inference(avatar_split_clause,[],[f1817,f11823]) ).
fof(f11823,plain,
( spl171_705
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_705])]) ).
fof(f1817,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1241,f1762]) ).
fof(f1241,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f763]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ( in(sK74(X0,X1,X2),X1)
& in(ordered_pair(X0,sK74(X0,X1,X2)),X2)
& in(sK74(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f761,f762]) ).
fof(f762,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK74(X0,X1,X2),X1)
& in(ordered_pair(X0,sK74(X0,X1,X2)),X2)
& in(sK74(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f761,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f760]) ).
fof(f760,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f434]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f202]) ).
fof(f202,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f11821,plain,
spl171_704,
inference(avatar_split_clause,[],[f1198,f11819]) ).
fof(f11819,plain,
( spl171_704
<=> ! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_704])]) ).
fof(f1198,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f415]) ).
fof(f415,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f220]) ).
fof(f220,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f11613,plain,
spl171_703,
inference(avatar_split_clause,[],[f1715,f11611]) ).
fof(f11611,plain,
( spl171_703
<=> ! [X2,X0,X1] :
( sP48(X0,X1,X2)
| ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_703])]) ).
fof(f1715,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,plain,
! [X0,X1,X2] :
( ( sP48(X0,X1,X2)
| ( ( ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X2) )
& ( ( in(sK157(X0,X1,X2),X0)
& in(sK157(X0,X1,X2),X1) )
| in(sK157(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP48(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f1022,f1023]) ).
fof(f1023,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X2) )
& ( ( in(sK157(X0,X1,X2),X0)
& in(sK157(X0,X1,X2),X1) )
| in(sK157(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1022,plain,
! [X0,X1,X2] :
( ( sP48(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP48(X0,X1,X2) ) ),
inference(rectify,[],[f1021]) ).
fof(f1021,plain,
! [X1,X0,X2] :
( ( sP48(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP48(X1,X0,X2) ) ),
inference(flattening,[],[f1020]) ).
fof(f1020,plain,
! [X1,X0,X2] :
( ( sP48(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP48(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f678]) ).
fof(f678,plain,
! [X1,X0,X2] :
( sP48(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP48])]) ).
fof(f11609,plain,
spl171_702,
inference(avatar_split_clause,[],[f1707,f11607]) ).
fof(f11607,plain,
( spl171_702
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(sK156(X0,X1,X2),X0)
| ~ in(sK156(X0,X1,X2),X1)
| ~ in(sK156(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_702])]) ).
fof(f1707,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(sK156(X0,X1,X2),X0)
| ~ in(sK156(X0,X1,X2),X1)
| ~ in(sK156(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ( ( in(sK156(X0,X1,X2),X0)
| ~ in(sK156(X0,X1,X2),X1)
| ~ in(sK156(X0,X1,X2),X2) )
& ( ( ~ in(sK156(X0,X1,X2),X0)
& in(sK156(X0,X1,X2),X1) )
| in(sK156(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP47(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f1016,f1017]) ).
fof(f1017,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK156(X0,X1,X2),X0)
| ~ in(sK156(X0,X1,X2),X1)
| ~ in(sK156(X0,X1,X2),X2) )
& ( ( ~ in(sK156(X0,X1,X2),X0)
& in(sK156(X0,X1,X2),X1) )
| in(sK156(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1016,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP47(X0,X1,X2) ) ),
inference(rectify,[],[f1015]) ).
fof(f1015,plain,
! [X1,X0,X2] :
( ( sP47(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP47(X1,X0,X2) ) ),
inference(flattening,[],[f1014]) ).
fof(f1014,plain,
! [X1,X0,X2] :
( ( sP47(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP47(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f676]) ).
fof(f676,plain,
! [X1,X0,X2] :
( sP47(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
fof(f11605,plain,
spl171_701,
inference(avatar_split_clause,[],[f1697,f11603]) ).
fof(f11603,plain,
( spl171_701
<=> ! [X2,X0,X1] :
( sP46(X0,X1,X2)
| in(sK155(X0,X1,X2),X0)
| in(sK155(X0,X1,X2),X1)
| in(sK155(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_701])]) ).
fof(f1697,plain,
! [X2,X0,X1] :
( sP46(X0,X1,X2)
| in(sK155(X0,X1,X2),X0)
| in(sK155(X0,X1,X2),X1)
| in(sK155(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ( ( ~ in(sK155(X0,X1,X2),X0)
& ~ in(sK155(X0,X1,X2),X1) )
| ~ in(sK155(X0,X1,X2),X2) )
& ( in(sK155(X0,X1,X2),X0)
| in(sK155(X0,X1,X2),X1)
| in(sK155(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP46(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f1010,f1011]) ).
fof(f1011,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK155(X0,X1,X2),X0)
& ~ in(sK155(X0,X1,X2),X1) )
| ~ in(sK155(X0,X1,X2),X2) )
& ( in(sK155(X0,X1,X2),X0)
| in(sK155(X0,X1,X2),X1)
| in(sK155(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1010,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP46(X0,X1,X2) ) ),
inference(rectify,[],[f1009]) ).
fof(f1009,plain,
! [X1,X0,X2] :
( ( sP46(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP46(X1,X0,X2) ) ),
inference(flattening,[],[f1008]) ).
fof(f1008,plain,
! [X1,X0,X2] :
( ( sP46(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP46(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f674]) ).
fof(f674,plain,
! [X1,X0,X2] :
( sP46(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP46])]) ).
fof(f11601,plain,
spl171_700,
inference(avatar_split_clause,[],[f1679,f11599]) ).
fof(f11599,plain,
( spl171_700
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) = X0
| sK149(X0,X1,X2) = X1
| in(sK149(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_700])]) ).
fof(f1679,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) = X0
| sK149(X0,X1,X2) = X1
| in(sK149(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f999,plain,
! [X0,X1,X2] :
( ( sP44(X0,X1,X2)
| ( ( ( sK149(X0,X1,X2) != X0
& sK149(X0,X1,X2) != X1 )
| ~ in(sK149(X0,X1,X2),X2) )
& ( sK149(X0,X1,X2) = X0
| sK149(X0,X1,X2) = X1
| in(sK149(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP44(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f997,f998]) ).
fof(f998,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK149(X0,X1,X2) != X0
& sK149(X0,X1,X2) != X1 )
| ~ in(sK149(X0,X1,X2),X2) )
& ( sK149(X0,X1,X2) = X0
| sK149(X0,X1,X2) = X1
| in(sK149(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f997,plain,
! [X0,X1,X2] :
( ( sP44(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP44(X0,X1,X2) ) ),
inference(rectify,[],[f996]) ).
fof(f996,plain,
! [X1,X0,X2] :
( ( sP44(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP44(X1,X0,X2) ) ),
inference(flattening,[],[f995]) ).
fof(f995,plain,
! [X1,X0,X2] :
( ( sP44(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP44(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f670]) ).
fof(f670,plain,
! [X1,X0,X2] :
( sP44(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP44])]) ).
fof(f11597,plain,
( spl171_699
| ~ spl171_18
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2470,f2354,f2106,f11594]) ).
fof(f11594,plain,
( spl171_699
<=> sP6(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_699])]) ).
fof(f2470,plain,
( sP6(sK162)
| ~ spl171_18
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2108]) ).
fof(f11514,plain,
spl171_698,
inference(avatar_split_clause,[],[f1916,f11512]) ).
fof(f11512,plain,
( spl171_698
<=> ! [X6,X0,X5,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_698])]) ).
fof(f1916,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP39(X0,X1,X2) ),
inference(definition_unfolding,[],[f1591,f1762,f1762]) ).
fof(f1591,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f11510,plain,
spl171_697,
inference(avatar_split_clause,[],[f1889,f11508]) ).
fof(f11508,plain,
( spl171_697
<=> ! [X6,X0,X5,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_697])]) ).
fof(f1889,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP21(X0,X1,X2) ),
inference(definition_unfolding,[],[f1447,f1762,f1762]) ).
fof(f1447,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f11506,plain,
spl171_696,
inference(avatar_split_clause,[],[f1877,f11504]) ).
fof(f11504,plain,
( spl171_696
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK99(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK99(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_696])]) ).
fof(f1877,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK99(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1439,f1762]) ).
fof(f1439,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK99(X0,X1)),X0)
| ~ in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f853]) ).
fof(f11502,plain,
spl171_695,
inference(avatar_split_clause,[],[f1865,f11500]) ).
fof(f11500,plain,
( spl171_695
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_695])]) ).
fof(f1865,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1399,f1762]) ).
fof(f1399,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK89(X0,X1),sK89(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f826,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK89(X0,X1),sK89(X0,X1)),X0)
& in(sK89(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f824,f825]) ).
fof(f825,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK89(X0,X1),sK89(X0,X1)),X0)
& in(sK89(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f824,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f823]) ).
fof(f823,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f11459,plain,
spl171_694,
inference(avatar_split_clause,[],[f1517,f11457]) ).
fof(f11457,plain,
( spl171_694
<=> ! [X2,X0,X1] :
( sP33(X0,X1,X2)
| sK119(X0,X1,X2) = apply(X0,sK120(X0,X1,X2))
| in(sK119(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_694])]) ).
fof(f1517,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| sK119(X0,X1,X2) = apply(X0,sK120(X0,X1,X2))
| in(sK119(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f11454,plain,
( spl171_693
| ~ spl171_4
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2468,f2354,f2036,f11451]) ).
fof(f2468,plain,
( sP6(empty_set)
| ~ spl171_4
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2038]) ).
fof(f11410,plain,
( spl171_692
| ~ spl171_203
| ~ spl171_691 ),
inference(avatar_split_clause,[],[f11406,f11403,f3373,f11408]) ).
fof(f11408,plain,
( spl171_692
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK101(X0,X5)),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_692])]) ).
fof(f11403,plain,
( spl171_691
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK101(X0,X5),X5),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_691])]) ).
fof(f11406,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK101(X0,X5)),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_691 ),
inference(forward_demodulation,[],[f11404,f3374]) ).
fof(f11404,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK101(X0,X5),X5),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl171_691 ),
inference(avatar_component_clause,[],[f11403]) ).
fof(f11405,plain,
spl171_691,
inference(avatar_split_clause,[],[f1955,f11403]) ).
fof(f1955,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK101(X0,X5),X5),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1880]) ).
fof(f1880,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK101(X0,X5),X5),unordered_pair(sK101(X0,X5),sK101(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1436,f1762]) ).
fof(f1436,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK101(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f853]) ).
fof(f11383,plain,
( spl171_690
| ~ spl171_12
| ~ spl171_56
| ~ spl171_105
| ~ spl171_689 ),
inference(avatar_split_clause,[],[f11379,f11375,f2639,f2297,f2076,f11381]) ).
fof(f11381,plain,
( spl171_690
<=> ! [X0,X1] :
( sK160 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_690])]) ).
fof(f2297,plain,
( spl171_56
<=> ! [X0] : cast_to_subset(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_56])]) ).
fof(f11375,plain,
( spl171_689
<=> ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_689])]) ).
fof(f11379,plain,
( ! [X0,X1] :
( sK160 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_12
| ~ spl171_56
| ~ spl171_105
| ~ spl171_689 ),
inference(forward_demodulation,[],[f11378,f2706]) ).
fof(f11378,plain,
( ! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_56
| ~ spl171_689 ),
inference(forward_demodulation,[],[f11376,f2298]) ).
fof(f2298,plain,
( ! [X0] : cast_to_subset(X0) = X0
| ~ spl171_56 ),
inference(avatar_component_clause,[],[f2297]) ).
fof(f11376,plain,
( ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_689 ),
inference(avatar_component_clause,[],[f11375]) ).
fof(f11377,plain,
spl171_689,
inference(avatar_split_clause,[],[f1187,f11375]) ).
fof(f1187,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f403]) ).
fof(f403,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f402]) ).
fof(f402,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f261]) ).
fof(f261,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f11355,plain,
( spl171_688
| ~ spl171_12
| ~ spl171_56
| ~ spl171_105
| ~ spl171_687 ),
inference(avatar_split_clause,[],[f11351,f11347,f2639,f2297,f2076,f11353]) ).
fof(f11353,plain,
( spl171_688
<=> ! [X0,X1] :
( sK160 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_688])]) ).
fof(f11347,plain,
( spl171_687
<=> ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_687])]) ).
fof(f11351,plain,
( ! [X0,X1] :
( sK160 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_12
| ~ spl171_56
| ~ spl171_105
| ~ spl171_687 ),
inference(forward_demodulation,[],[f11350,f2706]) ).
fof(f11350,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_56
| ~ spl171_687 ),
inference(forward_demodulation,[],[f11348,f2298]) ).
fof(f11348,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_687 ),
inference(avatar_component_clause,[],[f11347]) ).
fof(f11349,plain,
spl171_687,
inference(avatar_split_clause,[],[f1186,f11347]) ).
fof(f1186,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f400]) ).
fof(f400,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f262]) ).
fof(f262,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f11342,plain,
( spl171_686
| ~ spl171_42
| ~ spl171_64 ),
inference(avatar_split_clause,[],[f2461,f2330,f2226,f11339]) ).
fof(f11339,plain,
( spl171_686
<=> ordinal(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_686])]) ).
fof(f2226,plain,
( spl171_42
<=> empty(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_42])]) ).
fof(f2330,plain,
( spl171_64
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_64])]) ).
fof(f2461,plain,
( ordinal(sK170)
| ~ spl171_42
| ~ spl171_64 ),
inference(resolution,[],[f2331,f2228]) ).
fof(f2228,plain,
( empty(sK170)
| ~ spl171_42 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f2331,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl171_64 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f11337,plain,
spl171_685,
inference(avatar_split_clause,[],[f1481,f11335]) ).
fof(f11335,plain,
( spl171_685
<=> ! [X4,X0,X3] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP27(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_685])]) ).
fof(f1481,plain,
! [X3,X0,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP27(X0) ),
inference(cnf_transformation,[],[f885]) ).
fof(f885,plain,
! [X0] :
( ( sP27(X0)
| ( sK113(X0) != sK114(X0)
& apply(X0,sK113(X0)) = apply(X0,sK114(X0))
& in(sK114(X0),relation_dom(X0))
& in(sK113(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP27(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK113,sK114])],[f883,f884]) ).
fof(f884,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK113(X0) != sK114(X0)
& apply(X0,sK113(X0)) = apply(X0,sK114(X0))
& in(sK114(X0),relation_dom(X0))
& in(sK113(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f883,plain,
! [X0] :
( ( sP27(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP27(X0) ) ),
inference(rectify,[],[f882]) ).
fof(f882,plain,
! [X0] :
( ( sP27(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) )
| ~ sP27(X0) ) ),
inference(nnf_transformation,[],[f644]) ).
fof(f644,plain,
! [X0] :
( sP27(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f11148,plain,
( spl171_684
| ~ spl171_203
| ~ spl171_675 ),
inference(avatar_split_clause,[],[f11033,f11030,f3373,f11146]) ).
fof(f11146,plain,
( spl171_684
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK97(X0,X1),sK96(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0)
| sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_684])]) ).
fof(f11030,plain,
( spl171_675
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK96(X0,X1),sK97(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_675])]) ).
fof(f11033,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK97(X0,X1),sK96(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0)
| sP19(X0,X1) )
| ~ spl171_203
| ~ spl171_675 ),
inference(forward_demodulation,[],[f11031,f3374]) ).
fof(f11031,plain,
( ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK96(X0,X1),sK97(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) )
| ~ spl171_675 ),
inference(avatar_component_clause,[],[f11030]) ).
fof(f11143,plain,
( spl171_683
| ~ spl171_22
| ~ spl171_64 ),
inference(avatar_split_clause,[],[f2459,f2330,f2126,f11140]) ).
fof(f11140,plain,
( spl171_683
<=> ordinal(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_683])]) ).
fof(f2126,plain,
( spl171_22
<=> empty(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_22])]) ).
fof(f2459,plain,
( ordinal(sK164)
| ~ spl171_22
| ~ spl171_64 ),
inference(resolution,[],[f2331,f2128]) ).
fof(f2128,plain,
( empty(sK164)
| ~ spl171_22 ),
inference(avatar_component_clause,[],[f2126]) ).
fof(f11138,plain,
( spl171_682
| ~ spl171_203
| ~ spl171_674 ),
inference(avatar_split_clause,[],[f11028,f11025,f3373,f11136]) ).
fof(f11136,plain,
( spl171_682
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1),sK97(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_682])]) ).
fof(f11025,plain,
( spl171_674
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK97(X0,X1),sK98(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_674])]) ).
fof(f11028,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1),sK97(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| sP19(X0,X1) )
| ~ spl171_203
| ~ spl171_674 ),
inference(forward_demodulation,[],[f11026,f3374]) ).
fof(f11026,plain,
( ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK97(X0,X1),sK98(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0) )
| ~ spl171_674 ),
inference(avatar_component_clause,[],[f11025]) ).
fof(f11134,plain,
( spl171_681
| ~ spl171_203
| ~ spl171_672 ),
inference(avatar_split_clause,[],[f11018,f11015,f3373,f11132]) ).
fof(f11132,plain,
( spl171_681
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK98(X0,X1),sK96(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0)
| sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_681])]) ).
fof(f11015,plain,
( spl171_672
<=> ! [X0,X1] :
( sP19(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK96(X0,X1),sK98(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_672])]) ).
fof(f11018,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK98(X0,X1),sK96(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0)
| sP19(X0,X1) )
| ~ spl171_203
| ~ spl171_672 ),
inference(forward_demodulation,[],[f11016,f3374]) ).
fof(f11016,plain,
( ! [X0,X1] :
( sP19(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK96(X0,X1),sK98(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) )
| ~ spl171_672 ),
inference(avatar_component_clause,[],[f11015]) ).
fof(f11130,plain,
( spl171_680
| ~ spl171_203
| ~ spl171_671 ),
inference(avatar_split_clause,[],[f11013,f11010,f3373,f11128]) ).
fof(f11128,plain,
( spl171_680
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK94(X0,X1)),unordered_pair(sK94(X0,X1),sK95(X0,X1))),X0)
| sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_680])]) ).
fof(f11010,plain,
( spl171_671
<=> ! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK95(X0,X1)),unordered_pair(sK94(X0,X1),sK94(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_671])]) ).
fof(f11013,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK94(X0,X1)),unordered_pair(sK94(X0,X1),sK95(X0,X1))),X0)
| sP17(X0,X1) )
| ~ spl171_203
| ~ spl171_671 ),
inference(forward_demodulation,[],[f11011,f3374]) ).
fof(f11011,plain,
( ! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK95(X0,X1)),unordered_pair(sK94(X0,X1),sK94(X0,X1))),X0) )
| ~ spl171_671 ),
inference(avatar_component_clause,[],[f11010]) ).
fof(f11126,plain,
( spl171_679
| ~ spl171_203
| ~ spl171_670 ),
inference(avatar_split_clause,[],[f11008,f11005,f3373,f11124]) ).
fof(f11124,plain,
( spl171_679
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK95(X0,X1)),unordered_pair(sK95(X0,X1),sK95(X0,X1))),X0)
| sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_679])]) ).
fof(f11005,plain,
( spl171_670
<=> ! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK95(X0,X1),sK94(X0,X1)),unordered_pair(sK95(X0,X1),sK95(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_670])]) ).
fof(f11008,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK95(X0,X1)),unordered_pair(sK95(X0,X1),sK95(X0,X1))),X0)
| sP17(X0,X1) )
| ~ spl171_203
| ~ spl171_670 ),
inference(forward_demodulation,[],[f11006,f3374]) ).
fof(f11006,plain,
( ! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK95(X0,X1),sK94(X0,X1)),unordered_pair(sK95(X0,X1),sK95(X0,X1))),X0) )
| ~ spl171_670 ),
inference(avatar_component_clause,[],[f11005]) ).
fof(f11122,plain,
( spl171_678
| ~ spl171_203
| ~ spl171_669 ),
inference(avatar_split_clause,[],[f11003,f11000,f3373,f11120]) ).
fof(f11120,plain,
( spl171_678
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK92(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK93(X0,X1))),X0)
| sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_678])]) ).
fof(f11000,plain,
( spl171_669
<=> ! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK93(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_669])]) ).
fof(f11003,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK92(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK93(X0,X1))),X0)
| sP15(X0,X1) )
| ~ spl171_203
| ~ spl171_669 ),
inference(forward_demodulation,[],[f11001,f3374]) ).
fof(f11001,plain,
( ! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK93(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0) )
| ~ spl171_669 ),
inference(avatar_component_clause,[],[f11000]) ).
fof(f11118,plain,
( spl171_677
| ~ spl171_203
| ~ spl171_668 ),
inference(avatar_split_clause,[],[f10998,f10995,f3373,f11116]) ).
fof(f11116,plain,
( spl171_677
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK92(X0,X1),sK93(X0,X1)),unordered_pair(sK93(X0,X1),sK93(X0,X1))),X0)
| sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_677])]) ).
fof(f10995,plain,
( spl171_668
<=> ! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1),sK92(X0,X1)),unordered_pair(sK93(X0,X1),sK93(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_668])]) ).
fof(f10998,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK92(X0,X1),sK93(X0,X1)),unordered_pair(sK93(X0,X1),sK93(X0,X1))),X0)
| sP15(X0,X1) )
| ~ spl171_203
| ~ spl171_668 ),
inference(forward_demodulation,[],[f10996,f3374]) ).
fof(f10996,plain,
( ! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1),sK92(X0,X1)),unordered_pair(sK93(X0,X1),sK93(X0,X1))),X0) )
| ~ spl171_668 ),
inference(avatar_component_clause,[],[f10995]) ).
fof(f11037,plain,
spl171_676,
inference(avatar_split_clause,[],[f1938,f11035]) ).
fof(f11035,plain,
( spl171_676
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK71(relation_dom(X1),X1) != apply(X1,sK71(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_676])]) ).
fof(f1938,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK71(relation_dom(X1),X1) != apply(X1,sK71(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1197]) ).
fof(f1197,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK71(X0,X1) != apply(X1,sK71(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f738]) ).
fof(f738,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK71(X0,X1) != apply(X1,sK71(X0,X1))
& in(sK71(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f736,f737]) ).
fof(f737,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK71(X0,X1) != apply(X1,sK71(X0,X1))
& in(sK71(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f736,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f735]) ).
fof(f735,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f734]) ).
fof(f734,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f414]) ).
fof(f414,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f413]) ).
fof(f413,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f236]) ).
fof(f236,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f11032,plain,
spl171_675,
inference(avatar_split_clause,[],[f1875,f11030]) ).
fof(f1875,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK96(X0,X1),sK97(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1432,f1762]) ).
fof(f1432,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(ordered_pair(sK96(X0,X1),sK97(X0,X1)),X0) ),
inference(cnf_transformation,[],[f847]) ).
fof(f11027,plain,
spl171_674,
inference(avatar_split_clause,[],[f1874,f11025]) ).
fof(f1874,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK97(X0,X1),sK98(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1433,f1762]) ).
fof(f1433,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0) ),
inference(cnf_transformation,[],[f847]) ).
fof(f11023,plain,
( spl171_673
| ~ spl171_12
| ~ spl171_64 ),
inference(avatar_split_clause,[],[f2458,f2330,f2076,f11020]) ).
fof(f11020,plain,
( spl171_673
<=> ordinal(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_673])]) ).
fof(f2458,plain,
( ordinal(sK160)
| ~ spl171_12
| ~ spl171_64 ),
inference(resolution,[],[f2331,f2078]) ).
fof(f11017,plain,
spl171_672,
inference(avatar_split_clause,[],[f1873,f11015]) ).
fof(f1873,plain,
! [X0,X1] :
( sP19(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK96(X0,X1),sK98(X0,X1)),unordered_pair(sK96(X0,X1),sK96(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1434,f1762]) ).
fof(f1434,plain,
! [X0,X1] :
( sP19(X0,X1)
| ~ in(ordered_pair(sK96(X0,X1),sK98(X0,X1)),X0) ),
inference(cnf_transformation,[],[f847]) ).
fof(f11012,plain,
spl171_671,
inference(avatar_split_clause,[],[f1871,f11010]) ).
fof(f1871,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK94(X0,X1),sK95(X0,X1)),unordered_pair(sK94(X0,X1),sK94(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1423,f1762]) ).
fof(f1423,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ in(ordered_pair(sK94(X0,X1),sK95(X0,X1)),X0) ),
inference(cnf_transformation,[],[f842]) ).
fof(f11007,plain,
spl171_670,
inference(avatar_split_clause,[],[f1870,f11005]) ).
fof(f1870,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK95(X0,X1),sK94(X0,X1)),unordered_pair(sK95(X0,X1),sK95(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1424,f1762]) ).
fof(f1424,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ in(ordered_pair(sK95(X0,X1),sK94(X0,X1)),X0) ),
inference(cnf_transformation,[],[f842]) ).
fof(f11002,plain,
spl171_669,
inference(avatar_split_clause,[],[f1868,f11000]) ).
fof(f1868,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK93(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1413,f1762]) ).
fof(f1413,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(ordered_pair(sK92(X0,X1),sK93(X0,X1)),X0) ),
inference(cnf_transformation,[],[f837]) ).
fof(f10997,plain,
spl171_668,
inference(avatar_split_clause,[],[f1867,f10995]) ).
fof(f1867,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1),sK92(X0,X1)),unordered_pair(sK93(X0,X1),sK93(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1414,f1762]) ).
fof(f1414,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(ordered_pair(sK93(X0,X1),sK92(X0,X1)),X0) ),
inference(cnf_transformation,[],[f837]) ).
fof(f10993,plain,
spl171_667,
inference(avatar_split_clause,[],[f1205,f10991]) ).
fof(f10991,plain,
( spl171_667
<=> ! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_667])]) ).
fof(f1205,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f745]) ).
fof(f10989,plain,
spl171_666,
inference(avatar_split_clause,[],[f1494,f10987]) ).
fof(f10987,plain,
( spl171_666
<=> ! [X0,X1,X3] :
( sP29(X0,X1)
| apply(X0,X3) != sK115(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK115(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_666])]) ).
fof(f1494,plain,
! [X3,X0,X1] :
( sP29(X0,X1)
| apply(X0,X3) != sK115(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK115(X0,X1),X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f892,plain,
! [X0,X1] :
( ( sP29(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK115(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK115(X0,X1),X1) )
& ( ( sK115(X0,X1) = apply(X0,sK116(X0,X1))
& in(sK116(X0,X1),relation_dom(X0)) )
| in(sK115(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK117(X0,X5)) = X5
& in(sK117(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP29(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116,sK117])],[f888,f891,f890,f889]) ).
fof(f889,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK115(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK115(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK115(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK115(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f890,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK115(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK115(X0,X1) = apply(X0,sK116(X0,X1))
& in(sK116(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f891,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK117(X0,X5)) = X5
& in(sK117(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f888,plain,
! [X0,X1] :
( ( sP29(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP29(X0,X1) ) ),
inference(rectify,[],[f887]) ).
fof(f887,plain,
! [X0,X1] :
( ( sP29(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| ~ sP29(X0,X1) ) ),
inference(nnf_transformation,[],[f647]) ).
fof(f647,plain,
! [X0,X1] :
( sP29(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f10943,plain,
( spl171_665
| ~ spl171_42
| ~ spl171_63 ),
inference(avatar_split_clause,[],[f2455,f2326,f2226,f10940]) ).
fof(f10940,plain,
( spl171_665
<=> epsilon_connected(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_665])]) ).
fof(f2326,plain,
( spl171_63
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_63])]) ).
fof(f2455,plain,
( epsilon_connected(sK170)
| ~ spl171_42
| ~ spl171_63 ),
inference(resolution,[],[f2327,f2228]) ).
fof(f2327,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl171_63 ),
inference(avatar_component_clause,[],[f2326]) ).
fof(f10897,plain,
( spl171_664
| ~ spl171_203
| ~ spl171_660 ),
inference(avatar_split_clause,[],[f10761,f10758,f3373,f10895]) ).
fof(f10895,plain,
( spl171_664
<=> ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X2,X0))),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_664])]) ).
fof(f10758,plain,
( spl171_660
<=> ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_660])]) ).
fof(f10761,plain,
( ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X2,X0))),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl171_203
| ~ spl171_660 ),
inference(forward_demodulation,[],[f10759,f3374]) ).
fof(f10759,plain,
( ! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl171_660 ),
inference(avatar_component_clause,[],[f10758]) ).
fof(f10871,plain,
( spl171_663
| ~ spl171_203
| ~ spl171_657 ),
inference(avatar_split_clause,[],[f10746,f10743,f3373,f10869]) ).
fof(f10869,plain,
( spl171_663
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK109(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_663])]) ).
fof(f10743,plain,
( spl171_657
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK109(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_657])]) ).
fof(f10746,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK109(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) )
| ~ spl171_203
| ~ spl171_657 ),
inference(forward_demodulation,[],[f10744,f3374]) ).
fof(f10744,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK109(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) )
| ~ spl171_657 ),
inference(avatar_component_clause,[],[f10743]) ).
fof(f10845,plain,
( spl171_662
| ~ spl171_203
| ~ spl171_655 ),
inference(avatar_split_clause,[],[f10737,f10734,f3373,f10843]) ).
fof(f10843,plain,
( spl171_662
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK74(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_662])]) ).
fof(f10734,plain,
( spl171_655
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK74(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_655])]) ).
fof(f10737,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK74(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl171_203
| ~ spl171_655 ),
inference(forward_demodulation,[],[f10735,f3374]) ).
fof(f10735,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK74(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl171_655 ),
inference(avatar_component_clause,[],[f10734]) ).
fof(f10765,plain,
spl171_661,
inference(avatar_split_clause,[],[f1990,f10763]) ).
fof(f10763,plain,
( spl171_661
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_661])]) ).
fof(f1990,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP45(X0,X1,X2) ),
inference(equality_resolution,[],[f1927]) ).
fof(f1927,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP45(X0,X1,X2) ),
inference(definition_unfolding,[],[f1687,f1762]) ).
fof(f1687,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f10760,plain,
spl171_660,
inference(avatar_split_clause,[],[f1948,f10758]) ).
fof(f1948,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(equality_resolution,[],[f1825]) ).
fof(f1825,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1264,f1762]) ).
fof(f1264,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f773]) ).
fof(f773,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f772]) ).
fof(f772,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(nnf_transformation,[],[f452]) ).
fof(f452,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f451]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f297]) ).
fof(f297,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f10755,plain,
( spl171_659
| ~ spl171_22
| ~ spl171_63 ),
inference(avatar_split_clause,[],[f2453,f2326,f2126,f10752]) ).
fof(f10752,plain,
( spl171_659
<=> epsilon_connected(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_659])]) ).
fof(f2453,plain,
( epsilon_connected(sK164)
| ~ spl171_22
| ~ spl171_63 ),
inference(resolution,[],[f2327,f2128]) ).
fof(f10750,plain,
spl171_658,
inference(avatar_split_clause,[],[f1897,f10748]) ).
fof(f10748,plain,
( spl171_658
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_658])]) ).
fof(f1897,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP25(X0,X1,X2) ),
inference(definition_unfolding,[],[f1466,f1762]) ).
fof(f1466,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f10745,plain,
spl171_657,
inference(avatar_split_clause,[],[f1894,f10743]) ).
fof(f1894,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK109(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ),
inference(definition_unfolding,[],[f1455,f1762]) ).
fof(f1455,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK109(X0,X1,X6)),X1)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f10741,plain,
spl171_656,
inference(avatar_split_clause,[],[f1893,f10739]) ).
fof(f10739,plain,
( spl171_656
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_656])]) ).
fof(f1893,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP23(X0,X1,X2) ),
inference(definition_unfolding,[],[f1457,f1762]) ).
fof(f1457,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f10736,plain,
spl171_655,
inference(avatar_split_clause,[],[f1818,f10734]) ).
fof(f1818,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK74(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1239,f1762]) ).
fof(f1239,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK74(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f763]) ).
fof(f10732,plain,
spl171_654,
inference(avatar_split_clause,[],[f1261,f10730]) ).
fof(f10730,plain,
( spl171_654
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_654])]) ).
fof(f1261,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f450]) ).
fof(f450,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f449]) ).
fof(f449,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f286]) ).
fof(f286,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f10566,plain,
( spl171_653
| ~ spl171_12
| ~ spl171_63 ),
inference(avatar_split_clause,[],[f2452,f2326,f2076,f10563]) ).
fof(f10563,plain,
( spl171_653
<=> epsilon_connected(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_653])]) ).
fof(f2452,plain,
( epsilon_connected(sK160)
| ~ spl171_12
| ~ spl171_63 ),
inference(resolution,[],[f2327,f2078]) ).
fof(f10561,plain,
spl171_652,
inference(avatar_split_clause,[],[f1936,f10559]) ).
fof(f10559,plain,
( spl171_652
<=> ! [X2,X0,X3] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_652])]) ).
fof(f1936,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f1134]) ).
fof(f1134,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f721]) ).
fof(f721,plain,
! [X0,X1,X2,X3] :
( ( sP2(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& apply(X3,X0) = X1
& in(X0,relation_rng(X2)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,X1,X2,X3) ) ),
inference(rectify,[],[f720]) ).
fof(f720,plain,
! [X2,X3,X0,X1] :
( ( sP2(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP2(X2,X3,X0,X1) ) ),
inference(flattening,[],[f719]) ).
fof(f719,plain,
! [X2,X3,X0,X1] :
( ( sP2(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP2(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f607]) ).
fof(f607,plain,
! [X2,X3,X0,X1] :
( sP2(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f10557,plain,
spl171_651,
inference(avatar_split_clause,[],[f1617,f10555]) ).
fof(f10555,plain,
( spl171_651
<=> ! [X2,X0,X1] :
( sP41(X0,X1,X2)
| ~ in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| ~ in(sK140(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_651])]) ).
fof(f1617,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| ~ in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| ~ in(sK140(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f965]) ).
fof(f965,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ( ( ~ in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| ~ in(sK140(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| in(sK140(X0,X1,X2),X2) )
& element(sK140(X0,X1,X2),powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP41(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK140])],[f963,f964]) ).
fof(f964,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) )
=> ( ( ~ in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| ~ in(sK140(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| in(sK140(X0,X1,X2),X2) )
& element(sK140(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f963,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP41(X0,X1,X2) ) ),
inference(rectify,[],[f962]) ).
fof(f962,plain,
! [X1,X0,X2] :
( ( sP41(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP41(X1,X0,X2) ) ),
inference(flattening,[],[f961]) ).
fof(f961,plain,
! [X1,X0,X2] :
( ( sP41(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP41(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f665]) ).
fof(f665,plain,
! [X1,X0,X2] :
( sP41(X1,X0,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f10553,plain,
spl171_650,
inference(avatar_split_clause,[],[f1616,f10551]) ).
fof(f10551,plain,
( spl171_650
<=> ! [X2,X0,X1] :
( sP41(X0,X1,X2)
| in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| in(sK140(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_650])]) ).
fof(f1616,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| in(subset_complement(X1,sK140(X0,X1,X2)),X0)
| in(sK140(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f965]) ).
fof(f10549,plain,
spl171_649,
inference(avatar_split_clause,[],[f1506,f10547]) ).
fof(f10547,plain,
( spl171_649
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(apply(X1,sK118(X0,X1,X2)),X0)
| in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_649])]) ).
fof(f1506,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(apply(X1,sK118(X0,X1,X2)),X0)
| in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f10545,plain,
spl171_648,
inference(avatar_split_clause,[],[f1395,f10543]) ).
fof(f10543,plain,
( spl171_648
<=> ! [X0,X1] :
( sP11(X0,X1)
| ~ is_well_founded_in(X1,X0)
| ~ is_connected_in(X1,X0)
| ~ is_antisymmetric_in(X1,X0)
| ~ is_transitive_in(X1,X0)
| ~ is_reflexive_in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_648])]) ).
fof(f1395,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ is_well_founded_in(X1,X0)
| ~ is_connected_in(X1,X0)
| ~ is_antisymmetric_in(X1,X0)
| ~ is_transitive_in(X1,X0)
| ~ is_reflexive_in(X1,X0) ),
inference(cnf_transformation,[],[f822]) ).
fof(f822,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ~ is_well_founded_in(X1,X0)
| ~ is_connected_in(X1,X0)
| ~ is_antisymmetric_in(X1,X0)
| ~ is_transitive_in(X1,X0)
| ~ is_reflexive_in(X1,X0) )
& ( ( is_well_founded_in(X1,X0)
& is_connected_in(X1,X0)
& is_antisymmetric_in(X1,X0)
& is_transitive_in(X1,X0)
& is_reflexive_in(X1,X0) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f821]) ).
fof(f821,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1) )
& ( ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) )
| ~ sP11(X1,X0) ) ),
inference(flattening,[],[f820]) ).
fof(f820,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1) )
& ( ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f620]) ).
fof(f620,plain,
! [X1,X0] :
( sP11(X1,X0)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f10375,plain,
( spl171_647
| ~ spl171_203
| ~ spl171_643 ),
inference(avatar_split_clause,[],[f10173,f10170,f3373,f10373]) ).
fof(f10373,plain,
( spl171_647
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK127(X4),sK126(X4)),unordered_pair(sK126(X4),sK126(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_647])]) ).
fof(f10170,plain,
( spl171_643
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK126(X4),sK127(X4)),unordered_pair(sK126(X4),sK126(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_643])]) ).
fof(f10173,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK127(X4),sK126(X4)),unordered_pair(sK126(X4),sK126(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_643 ),
inference(forward_demodulation,[],[f10171,f3374]) ).
fof(f10171,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK126(X4),sK127(X4)),unordered_pair(sK126(X4),sK126(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl171_643 ),
inference(avatar_component_clause,[],[f10170]) ).
fof(f10357,plain,
( spl171_646
| ~ spl171_42
| ~ spl171_62 ),
inference(avatar_split_clause,[],[f2449,f2322,f2226,f10354]) ).
fof(f10354,plain,
( spl171_646
<=> epsilon_transitive(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_646])]) ).
fof(f2322,plain,
( spl171_62
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_62])]) ).
fof(f2449,plain,
( epsilon_transitive(sK170)
| ~ spl171_42
| ~ spl171_62 ),
inference(resolution,[],[f2323,f2228]) ).
fof(f2323,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl171_62 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f10317,plain,
( spl171_645
| ~ spl171_12
| ~ spl171_105
| ~ spl171_203
| ~ spl171_638 ),
inference(avatar_split_clause,[],[f10150,f10146,f3373,f2639,f2076,f10315]) ).
fof(f10315,plain,
( spl171_645
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK55(X0),sK54(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| sK160 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_645])]) ).
fof(f10146,plain,
( spl171_638
<=> ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK54(X0),sK55(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_638])]) ).
fof(f10150,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK55(X0),sK54(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| sK160 = X0
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_203
| ~ spl171_638 ),
inference(forward_demodulation,[],[f10149,f3374]) ).
fof(f10149,plain,
( ! [X0] :
( sK160 = X0
| in(unordered_pair(unordered_pair(sK54(X0),sK55(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_638 ),
inference(forward_demodulation,[],[f10147,f2706]) ).
fof(f10147,plain,
( ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK54(X0),sK55(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| ~ relation(X0) )
| ~ spl171_638 ),
inference(avatar_component_clause,[],[f10146]) ).
fof(f10177,plain,
( spl171_644
| ~ spl171_12
| ~ spl171_105
| ~ spl171_635 ),
inference(avatar_split_clause,[],[f10136,f10133,f2639,f2076,f10175]) ).
fof(f10175,plain,
( spl171_644
<=> ! [X2,X0,X1] :
( sK160 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_644])]) ).
fof(f10133,plain,
( spl171_635
<=> ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_635])]) ).
fof(f10136,plain,
( ! [X2,X0,X1] :
( sK160 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_635 ),
inference(forward_demodulation,[],[f10134,f2706]) ).
fof(f10134,plain,
( ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 )
| ~ spl171_635 ),
inference(avatar_component_clause,[],[f10133]) ).
fof(f10172,plain,
spl171_643,
inference(avatar_split_clause,[],[f1902,f10170]) ).
fof(f1902,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK126(X4),sK127(X4)),unordered_pair(sK126(X4),sK126(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1537,f1762]) ).
fof(f1537,plain,
! [X0,X4] :
( ordered_pair(sK126(X4),sK127(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f922,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK125(X0)
& in(sK125(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK126(X4),sK127(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127])],[f919,f921,f920]) ).
fof(f920,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK125(X0)
& in(sK125(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f921,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK126(X4),sK127(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f919,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f918]) ).
fof(f918,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f533]) ).
fof(f533,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f10168,plain,
spl171_642,
inference(avatar_split_clause,[],[f1833,f10166]) ).
fof(f10166,plain,
( spl171_642
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_642])]) ).
fof(f1833,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1279,f1762,f1762]) ).
fof(f1279,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f465]) ).
fof(f465,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f235]) ).
fof(f235,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) = ordered_pair(X0,X1)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f10164,plain,
spl171_641,
inference(avatar_split_clause,[],[f1832,f10162]) ).
fof(f10162,plain,
( spl171_641
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_641])]) ).
fof(f1832,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1280,f1762,f1762]) ).
fof(f1280,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f465]) ).
fof(f10160,plain,
spl171_640,
inference(avatar_split_clause,[],[f1826,f10158]) ).
fof(f10158,plain,
( spl171_640
<=> ! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_640])]) ).
fof(f1826,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1263,f1762]) ).
fof(f1263,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f773]) ).
fof(f10155,plain,
( spl171_639
| ~ spl171_22
| ~ spl171_62 ),
inference(avatar_split_clause,[],[f2447,f2322,f2126,f10152]) ).
fof(f10152,plain,
( spl171_639
<=> epsilon_transitive(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_639])]) ).
fof(f2447,plain,
( epsilon_transitive(sK164)
| ~ spl171_22
| ~ spl171_62 ),
inference(resolution,[],[f2323,f2128]) ).
fof(f10148,plain,
spl171_638,
inference(avatar_split_clause,[],[f1773,f10146]) ).
fof(f1773,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK54(X0),sK55(X0)),unordered_pair(sK54(X0),sK54(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1085,f1762]) ).
fof(f1085,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK54(X0),sK55(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f692]) ).
fof(f692,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK54(X0),sK55(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f335,f691]) ).
fof(f691,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK54(X0),sK55(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f334]) ).
fof(f334,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f271]) ).
fof(f271,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f10144,plain,
spl171_637,
inference(avatar_split_clause,[],[f1193,f10142]) ).
fof(f10142,plain,
( spl171_637
<=> ! [X0,X1] :
( apply(relation_composition(function_inverse(X1),X1),X0) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_637])]) ).
fof(f1193,plain,
! [X0,X1] :
( apply(relation_composition(function_inverse(X1),X1),X0) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f411]) ).
fof(f411,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f272]) ).
fof(f272,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f10140,plain,
spl171_636,
inference(avatar_split_clause,[],[f1192,f10138]) ).
fof(f10138,plain,
( spl171_636
<=> ! [X0,X1] :
( apply(X1,apply(function_inverse(X1),X0)) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_636])]) ).
fof(f1192,plain,
! [X0,X1] :
( apply(X1,apply(function_inverse(X1),X0)) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f412]) ).
fof(f10135,plain,
spl171_635,
inference(avatar_split_clause,[],[f1119,f10133]) ).
fof(f1119,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f267]) ).
fof(f267,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f9901,plain,
( spl171_634
| ~ spl171_12
| ~ spl171_62 ),
inference(avatar_split_clause,[],[f2446,f2322,f2076,f9898]) ).
fof(f9898,plain,
( spl171_634
<=> epsilon_transitive(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_634])]) ).
fof(f2446,plain,
( epsilon_transitive(sK160)
| ~ spl171_12
| ~ spl171_62 ),
inference(resolution,[],[f2323,f2078]) ).
fof(f9896,plain,
spl171_633,
inference(avatar_split_clause,[],[f1937,f9894]) ).
fof(f9894,plain,
( spl171_633
<=> ! [X2,X0,X3] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_633])]) ).
fof(f1937,plain,
! [X2,X3,X0] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f1133]) ).
fof(f1133,plain,
! [X2,X3,X0,X1] :
( in(X1,relation_dom(X2))
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f721]) ).
fof(f9892,plain,
spl171_632,
inference(avatar_split_clause,[],[f1719,f9890]) ).
fof(f9890,plain,
( spl171_632
<=> ! [X3,X0,X5,X2,X1] :
( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3)
| ~ sP49(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_632])]) ).
fof(f1719,plain,
! [X2,X3,X0,X1,X5] :
( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3)
| ~ sP49(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f9888,plain,
spl171_631,
inference(avatar_split_clause,[],[f1525,f9886]) ).
fof(f9886,plain,
( spl171_631
<=> ! [X4,X0,X3] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_631])]) ).
fof(f1525,plain,
! [X3,X0,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f911]) ).
fof(f911,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK123(X0),sK122(X0))
& sK122(X0) != sK123(X0)
& ~ in(sK122(X0),sK123(X0))
& in(sK123(X0),X0)
& in(sK122(X0),X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f909,f910]) ).
fof(f910,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK123(X0),sK122(X0))
& sK122(X0) != sK123(X0)
& ~ in(sK122(X0),sK123(X0))
& in(sK123(X0),X0)
& in(sK122(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f909,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f908]) ).
fof(f908,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f531]) ).
fof(f531,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f9884,plain,
spl171_630,
inference(avatar_split_clause,[],[f1515,f9882]) ).
fof(f9882,plain,
( spl171_630
<=> ! [X2,X0,X1] :
( sP33(X0,X1,X2)
| in(sK120(X0,X1,X2),relation_dom(X0))
| in(sK119(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_630])]) ).
fof(f1515,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| in(sK120(X0,X1,X2),relation_dom(X0))
| in(sK119(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f9880,plain,
spl171_629,
inference(avatar_split_clause,[],[f1505,f9878]) ).
fof(f9878,plain,
( spl171_629
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(sK118(X0,X1,X2),relation_dom(X1))
| in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_629])]) ).
fof(f1505,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(sK118(X0,X1,X2),relation_dom(X1))
| in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f9876,plain,
spl171_628,
inference(avatar_split_clause,[],[f1493,f9874]) ).
fof(f9874,plain,
( spl171_628
<=> ! [X0,X1] :
( sP29(X0,X1)
| sK115(X0,X1) = apply(X0,sK116(X0,X1))
| in(sK115(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_628])]) ).
fof(f1493,plain,
! [X0,X1] :
( sP29(X0,X1)
| sK115(X0,X1) = apply(X0,sK116(X0,X1))
| in(sK115(X0,X1),X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f9764,plain,
( spl171_627
| ~ spl171_12
| ~ spl171_61 ),
inference(avatar_split_clause,[],[f2440,f2318,f2076,f9761]) ).
fof(f9761,plain,
( spl171_627
<=> relation(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_627])]) ).
fof(f2318,plain,
( spl171_61
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_61])]) ).
fof(f2440,plain,
( relation(sK160)
| ~ spl171_12
| ~ spl171_61 ),
inference(resolution,[],[f2319,f2078]) ).
fof(f2319,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl171_61 ),
inference(avatar_component_clause,[],[f2318]) ).
fof(f9653,plain,
( spl171_626
| ~ spl171_203
| ~ spl171_618 ),
inference(avatar_split_clause,[],[f9515,f9512,f3373,f9651]) ).
fof(f9651,plain,
( spl171_626
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK104(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_626])]) ).
fof(f9512,plain,
( spl171_618
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK104(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_618])]) ).
fof(f9515,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK104(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_618 ),
inference(forward_demodulation,[],[f9513,f3374]) ).
fof(f9513,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK104(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl171_618 ),
inference(avatar_component_clause,[],[f9512]) ).
fof(f9606,plain,
( spl171_625
| ~ spl171_203
| ~ spl171_614 ),
inference(avatar_split_clause,[],[f9498,f9495,f3373,f9604]) ).
fof(f9604,plain,
( spl171_625
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK62(X0),sK61(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_625])]) ).
fof(f9495,plain,
( spl171_614
<=> ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK61(X0),sK62(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_614])]) ).
fof(f9498,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK62(X0),sK61(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_614 ),
inference(forward_demodulation,[],[f9496,f3374]) ).
fof(f9496,plain,
( ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK61(X0),sK62(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) )
| ~ spl171_614 ),
inference(avatar_component_clause,[],[f9495]) ).
fof(f9602,plain,
( spl171_624
| ~ spl171_203
| ~ spl171_612 ),
inference(avatar_split_clause,[],[f9488,f9485,f3373,f9600]) ).
fof(f9600,plain,
( spl171_624
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK63(X0),sK62(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_624])]) ).
fof(f9485,plain,
( spl171_612
<=> ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_612])]) ).
fof(f9488,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK63(X0),sK62(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_612 ),
inference(forward_demodulation,[],[f9486,f3374]) ).
fof(f9486,plain,
( ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) )
| ~ spl171_612 ),
inference(avatar_component_clause,[],[f9485]) ).
fof(f9598,plain,
( spl171_623
| ~ spl171_203
| ~ spl171_611 ),
inference(avatar_split_clause,[],[f9483,f9480,f3373,f9596]) ).
fof(f9596,plain,
( spl171_623
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK63(X0),sK61(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_623])]) ).
fof(f9480,plain,
( spl171_611
<=> ! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK61(X0),sK63(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_611])]) ).
fof(f9483,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK63(X0),sK61(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_611 ),
inference(forward_demodulation,[],[f9481,f3374]) ).
fof(f9481,plain,
( ! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK61(X0),sK63(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) )
| ~ spl171_611 ),
inference(avatar_component_clause,[],[f9480]) ).
fof(f9593,plain,
( spl171_622
| ~ spl171_22
| ~ spl171_60 ),
inference(avatar_split_clause,[],[f2435,f2314,f2126,f9590]) ).
fof(f9590,plain,
( spl171_622
<=> function(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_622])]) ).
fof(f2314,plain,
( spl171_60
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_60])]) ).
fof(f2435,plain,
( function(sK164)
| ~ spl171_22
| ~ spl171_60 ),
inference(resolution,[],[f2315,f2128]) ).
fof(f2315,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl171_60 ),
inference(avatar_component_clause,[],[f2314]) ).
fof(f9588,plain,
( spl171_621
| ~ spl171_203
| ~ spl171_610 ),
inference(avatar_split_clause,[],[f9478,f9475,f3373,f9586]) ).
fof(f9586,plain,
( spl171_621
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK57(X0),sK57(X0)),unordered_pair(sK57(X0),sK58(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_621])]) ).
fof(f9475,plain,
( spl171_610
<=> ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK57(X0),sK58(X0)),unordered_pair(sK57(X0),sK57(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_610])]) ).
fof(f9478,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK57(X0),sK57(X0)),unordered_pair(sK57(X0),sK58(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_610 ),
inference(forward_demodulation,[],[f9476,f3374]) ).
fof(f9476,plain,
( ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK57(X0),sK58(X0)),unordered_pair(sK57(X0),sK57(X0))),X0)
| ~ relation(X0) )
| ~ spl171_610 ),
inference(avatar_component_clause,[],[f9475]) ).
fof(f9584,plain,
( spl171_620
| ~ spl171_203
| ~ spl171_609 ),
inference(avatar_split_clause,[],[f9473,f9470,f3373,f9582]) ).
fof(f9582,plain,
( spl171_620
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK57(X0),sK58(X0)),unordered_pair(sK58(X0),sK58(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_620])]) ).
fof(f9470,plain,
( spl171_609
<=> ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK58(X0),sK57(X0)),unordered_pair(sK58(X0),sK58(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_609])]) ).
fof(f9473,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK57(X0),sK58(X0)),unordered_pair(sK58(X0),sK58(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) )
| ~ spl171_203
| ~ spl171_609 ),
inference(forward_demodulation,[],[f9471,f3374]) ).
fof(f9471,plain,
( ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK58(X0),sK57(X0)),unordered_pair(sK58(X0),sK58(X0))),X0)
| ~ relation(X0) )
| ~ spl171_609 ),
inference(avatar_component_clause,[],[f9470]) ).
fof(f9519,plain,
( spl171_619
| ~ spl171_12
| ~ spl171_105 ),
inference(avatar_split_clause,[],[f3405,f2639,f2076,f9517]) ).
fof(f9517,plain,
( spl171_619
<=> ! [X0,X1,X3] :
( sK160 = X0
| ordinal_subset(sK70(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_619])]) ).
fof(f3405,plain,
( ! [X3,X0,X1] :
( sK160 = X0
| ordinal_subset(sK70(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl171_12
| ~ spl171_105 ),
inference(forward_demodulation,[],[f1158,f2706]) ).
fof(f1158,plain,
! [X3,X0,X1] :
( ordinal_subset(sK70(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f732]) ).
fof(f732,plain,
! [X0,X1] :
( ( ! [X3] :
( ordinal_subset(sK70(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK70(X0),X0)
& ordinal(sK70(X0)) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f371,f731]) ).
fof(f731,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
=> ( ! [X3] :
( ordinal_subset(sK70(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK70(X0),X0)
& ordinal(sK70(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f370]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f232]) ).
fof(f232,axiom,
! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0) ) )
& empty_set != X0
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(f9514,plain,
spl171_618,
inference(avatar_split_clause,[],[f1957,f9512]) ).
fof(f1957,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK104(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1884]) ).
fof(f1884,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK104(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1440,f1762]) ).
fof(f1440,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK104(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f859]) ).
fof(f9510,plain,
spl171_617,
inference(avatar_split_clause,[],[f1866,f9508]) ).
fof(f9508,plain,
( spl171_617
<=> ! [X0,X1,X3] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_617])]) ).
fof(f1866,plain,
! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1397,f1762]) ).
fof(f1397,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f9506,plain,
spl171_616,
inference(avatar_split_clause,[],[f1834,f9504]) ).
fof(f9504,plain,
( spl171_616
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_616])]) ).
fof(f1834,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f1284,f1762]) ).
fof(f1284,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f781]) ).
fof(f781,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f780]) ).
fof(f780,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f181]) ).
fof(f181,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f9502,plain,
spl171_615,
inference(avatar_split_clause,[],[f1831,f9500]) ).
fof(f9500,plain,
( spl171_615
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_615])]) ).
fof(f1831,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f1276,f1762]) ).
fof(f1276,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f779]) ).
fof(f9497,plain,
spl171_614,
inference(avatar_split_clause,[],[f1784,f9495]) ).
fof(f1784,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK61(X0),sK62(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1105,f1762]) ).
fof(f1105,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK61(X0),sK62(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f9493,plain,
( spl171_613
| ~ spl171_12
| ~ spl171_60 ),
inference(avatar_split_clause,[],[f2434,f2314,f2076,f9490]) ).
fof(f9490,plain,
( spl171_613
<=> function(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_613])]) ).
fof(f2434,plain,
( function(sK160)
| ~ spl171_12
| ~ spl171_60 ),
inference(resolution,[],[f2315,f2078]) ).
fof(f9487,plain,
spl171_612,
inference(avatar_split_clause,[],[f1783,f9485]) ).
fof(f1783,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1106,f1762]) ).
fof(f1106,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK62(X0),sK63(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f9482,plain,
spl171_611,
inference(avatar_split_clause,[],[f1782,f9480]) ).
fof(f1782,plain,
! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK61(X0),sK63(X0)),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1107,f1762]) ).
fof(f1107,plain,
! [X0] :
( transitive(X0)
| ~ in(ordered_pair(sK61(X0),sK63(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f9477,plain,
spl171_610,
inference(avatar_split_clause,[],[f1777,f9475]) ).
fof(f1777,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK57(X0),sK58(X0)),unordered_pair(sK57(X0),sK57(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1092,f1762]) ).
fof(f1092,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK57(X0),sK58(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f701]) ).
fof(f9472,plain,
spl171_609,
inference(avatar_split_clause,[],[f1776,f9470]) ).
fof(f1776,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK58(X0),sK57(X0)),unordered_pair(sK58(X0),sK58(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1093,f1762]) ).
fof(f1093,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK58(X0),sK57(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f701]) ).
fof(f9468,plain,
spl171_608,
inference(avatar_split_clause,[],[f1775,f9466]) ).
fof(f9466,plain,
( spl171_608
<=> ! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_608])]) ).
fof(f1775,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1088,f1762]) ).
fof(f1088,plain,
! [X2,X0] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f697]) ).
fof(f697,plain,
! [X0] :
( ( ( reflexive(X0)
| ( ~ in(ordered_pair(sK56(X0),sK56(X0)),X0)
& in(sK56(X0),relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f695,f696]) ).
fof(f696,plain,
! [X0] :
( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
=> ( ~ in(ordered_pair(sK56(X0),sK56(X0)),X0)
& in(sK56(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f695,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f694]) ).
fof(f694,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( reflexive(X0)
<=> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f9464,plain,
spl171_607,
inference(avatar_split_clause,[],[f1774,f9462]) ).
fof(f9462,plain,
( spl171_607
<=> ! [X0] :
( reflexive(X0)
| ~ in(unordered_pair(unordered_pair(sK56(X0),sK56(X0)),unordered_pair(sK56(X0),sK56(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_607])]) ).
fof(f1774,plain,
! [X0] :
( reflexive(X0)
| ~ in(unordered_pair(unordered_pair(sK56(X0),sK56(X0)),unordered_pair(sK56(X0),sK56(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1090,f1762]) ).
fof(f1090,plain,
! [X0] :
( reflexive(X0)
| ~ in(ordered_pair(sK56(X0),sK56(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f697]) ).
fof(f8766,plain,
( spl171_606
| ~ spl171_12
| ~ spl171_105
| ~ spl171_585 ),
inference(avatar_split_clause,[],[f8678,f8675,f2639,f2076,f8764]) ).
fof(f8764,plain,
( spl171_606
<=> ! [X4,X0,X1] :
( sK160 = X4
| disjoint(fiber(X0,sK91(X0,X4)),X4)
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_606])]) ).
fof(f8675,plain,
( spl171_585
<=> ! [X4,X0,X1] :
( disjoint(fiber(X0,sK91(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_585])]) ).
fof(f8678,plain,
( ! [X0,X1,X4] :
( sK160 = X4
| disjoint(fiber(X0,sK91(X0,X4)),X4)
| ~ subset(X4,X1)
| ~ sP13(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_585 ),
inference(forward_demodulation,[],[f8676,f2706]) ).
fof(f8676,plain,
( ! [X0,X1,X4] :
( disjoint(fiber(X0,sK91(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) )
| ~ spl171_585 ),
inference(avatar_component_clause,[],[f8675]) ).
fof(f8762,plain,
( spl171_605
| ~ spl171_12
| ~ spl171_105
| ~ spl171_584 ),
inference(avatar_split_clause,[],[f8673,f8670,f2639,f2076,f8760]) ).
fof(f8760,plain,
( spl171_605
<=> ! [X0,X3] :
( sK160 = X3
| disjoint(fiber(X0,sK78(X0,X3)),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_605])]) ).
fof(f8670,plain,
( spl171_584
<=> ! [X0,X3] :
( disjoint(fiber(X0,sK78(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_584])]) ).
fof(f8673,plain,
( ! [X3,X0] :
( sK160 = X3
| disjoint(fiber(X0,sK78(X0,X3)),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_584 ),
inference(forward_demodulation,[],[f8671,f2706]) ).
fof(f8671,plain,
( ! [X3,X0] :
( disjoint(fiber(X0,sK78(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) )
| ~ spl171_584 ),
inference(avatar_component_clause,[],[f8670]) ).
fof(f8758,plain,
spl171_604,
inference(avatar_split_clause,[],[f1968,f8756]) ).
fof(f8756,plain,
( spl171_604
<=> ! [X0,X7,X2,X1] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_604])]) ).
fof(f1968,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP33(X0,X1,X2) ),
inference(equality_resolution,[],[f1514]) ).
fof(f1514,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f8754,plain,
spl171_603,
inference(avatar_split_clause,[],[f1714,f8752]) ).
fof(f8752,plain,
( spl171_603
<=> ! [X2,X0,X1] :
( sP48(X0,X1,X2)
| in(sK157(X0,X1,X2),X0)
| in(sK157(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_603])]) ).
fof(f1714,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| in(sK157(X0,X1,X2),X0)
| in(sK157(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f8747,plain,
spl171_602,
inference(avatar_split_clause,[],[f1713,f8745]) ).
fof(f8745,plain,
( spl171_602
<=> ! [X2,X0,X1] :
( sP48(X0,X1,X2)
| in(sK157(X0,X1,X2),X1)
| in(sK157(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_602])]) ).
fof(f1713,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| in(sK157(X0,X1,X2),X1)
| in(sK157(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f8743,plain,
spl171_601,
inference(avatar_split_clause,[],[f1706,f8741]) ).
fof(f8741,plain,
( spl171_601
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| ~ in(sK156(X0,X1,X2),X0)
| in(sK156(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_601])]) ).
fof(f1706,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| ~ in(sK156(X0,X1,X2),X0)
| in(sK156(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f8739,plain,
spl171_600,
inference(avatar_split_clause,[],[f1705,f8737]) ).
fof(f8737,plain,
( spl171_600
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(sK156(X0,X1,X2),X1)
| in(sK156(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_600])]) ).
fof(f1705,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(sK156(X0,X1,X2),X1)
| in(sK156(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f8735,plain,
spl171_599,
inference(avatar_split_clause,[],[f1699,f8733]) ).
fof(f8733,plain,
( spl171_599
<=> ! [X2,X0,X1] :
( sP46(X0,X1,X2)
| ~ in(sK155(X0,X1,X2),X0)
| ~ in(sK155(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_599])]) ).
fof(f1699,plain,
! [X2,X0,X1] :
( sP46(X0,X1,X2)
| ~ in(sK155(X0,X1,X2),X0)
| ~ in(sK155(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f8731,plain,
spl171_598,
inference(avatar_split_clause,[],[f1698,f8729]) ).
fof(f8729,plain,
( spl171_598
<=> ! [X2,X0,X1] :
( sP46(X0,X1,X2)
| ~ in(sK155(X0,X1,X2),X1)
| ~ in(sK155(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_598])]) ).
fof(f1698,plain,
! [X2,X0,X1] :
( sP46(X0,X1,X2)
| ~ in(sK155(X0,X1,X2),X1)
| ~ in(sK155(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f8727,plain,
spl171_597,
inference(avatar_split_clause,[],[f1689,f8725]) ).
fof(f8725,plain,
( spl171_597
<=> ! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK152(X0,X1,X2),X0)
| in(sK150(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_597])]) ).
fof(f1689,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK152(X0,X1,X2),X0)
| in(sK150(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f8723,plain,
spl171_596,
inference(avatar_split_clause,[],[f1688,f8721]) ).
fof(f8721,plain,
( spl171_596
<=> ! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK151(X0,X1,X2),X1)
| in(sK150(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_596])]) ).
fof(f1688,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK151(X0,X1,X2),X1)
| in(sK150(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f8719,plain,
spl171_595,
inference(avatar_split_clause,[],[f1675,f8717]) ).
fof(f8717,plain,
( spl171_595
<=> ! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_595])]) ).
fof(f1675,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f601]) ).
fof(f601,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f600]) ).
fof(f600,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f8715,plain,
spl171_594,
inference(avatar_split_clause,[],[f1656,f8713]) ).
fof(f8713,plain,
( spl171_594
<=> ! [X0,X1,X3] :
( sP43(X0,X1)
| ~ in(X3,X0)
| ~ in(sK143(X0,X1),X3)
| ~ in(sK143(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_594])]) ).
fof(f1656,plain,
! [X3,X0,X1] :
( sP43(X0,X1)
| ~ in(X3,X0)
| ~ in(sK143(X0,X1),X3)
| ~ in(sK143(X0,X1),X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f982,plain,
! [X0,X1] :
( ( sP43(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK143(X0,X1),X3) )
| ~ in(sK143(X0,X1),X1) )
& ( ( in(sK144(X0,X1),X0)
& in(sK143(X0,X1),sK144(X0,X1)) )
| in(sK143(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK145(X0,X5),X0)
& in(X5,sK145(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP43(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143,sK144,sK145])],[f978,f981,f980,f979]) ).
fof(f979,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK143(X0,X1),X3) )
| ~ in(sK143(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK143(X0,X1),X4) )
| in(sK143(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f980,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK143(X0,X1),X4) )
=> ( in(sK144(X0,X1),X0)
& in(sK143(X0,X1),sK144(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f981,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK145(X0,X5),X0)
& in(X5,sK145(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f978,plain,
! [X0,X1] :
( ( sP43(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| ~ sP43(X0,X1) ) ),
inference(rectify,[],[f977]) ).
fof(f977,plain,
! [X0,X1] :
( ( sP43(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| ~ sP43(X0,X1) ) ),
inference(nnf_transformation,[],[f668]) ).
fof(f668,plain,
! [X0,X1] :
( sP43(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
fof(f8711,plain,
spl171_593,
inference(avatar_split_clause,[],[f1614,f8709]) ).
fof(f8709,plain,
( spl171_593
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_593])]) ).
fof(f1614,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f965]) ).
fof(f8707,plain,
( ~ spl171_592
| ~ spl171_81
| ~ spl171_559 ),
inference(avatar_split_clause,[],[f8357,f8053,f2399,f8704]) ).
fof(f8704,plain,
( spl171_592
<=> in(sK130(relation_rng(sK51)),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_592])]) ).
fof(f2399,plain,
( spl171_81
<=> ! [X0] : in(X0,sK130(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_81])]) ).
fof(f8053,plain,
( spl171_559
<=> ! [X0] :
( ~ in(X0,sK160)
| ~ in(relation_rng(sK51),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_559])]) ).
fof(f8357,plain,
( ~ in(sK130(relation_rng(sK51)),sK160)
| ~ spl171_81
| ~ spl171_559 ),
inference(resolution,[],[f8054,f2400]) ).
fof(f2400,plain,
( ! [X0] : in(X0,sK130(X0))
| ~ spl171_81 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f8054,plain,
( ! [X0] :
( ~ in(relation_rng(sK51),X0)
| ~ in(X0,sK160) )
| ~ spl171_559 ),
inference(avatar_component_clause,[],[f8053]) ).
fof(f8702,plain,
spl171_591,
inference(avatar_split_clause,[],[f1613,f8700]) ).
fof(f8700,plain,
( spl171_591
<=> ! [X2,X4,X0,X1] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_591])]) ).
fof(f1613,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f965]) ).
fof(f8698,plain,
spl171_590,
inference(avatar_split_clause,[],[f1568,f8696]) ).
fof(f8696,plain,
( spl171_590
<=> ! [X4,X0,X1] :
( sP35(X0,X1)
| in(sK133(X0,X1),X4)
| ~ in(X4,X0)
| in(sK133(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_590])]) ).
fof(f1568,plain,
! [X0,X1,X4] :
( sP35(X0,X1)
| in(sK133(X0,X1),X4)
| ~ in(X4,X0)
| in(sK133(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f943,plain,
! [X0,X1] :
( ( sP35(X0,X1)
| ( ( ( ~ in(sK133(X0,X1),sK134(X0,X1))
& in(sK134(X0,X1),X0) )
| ~ in(sK133(X0,X1),X1) )
& ( ! [X4] :
( in(sK133(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK133(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK135(X0,X5))
& in(sK135(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP35(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133,sK134,sK135])],[f939,f942,f941,f940]) ).
fof(f940,plain,
! [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) )
=> ( ( ? [X3] :
( ~ in(sK133(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK133(X0,X1),X1) )
& ( ! [X4] :
( in(sK133(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK133(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f941,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK133(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK133(X0,X1),sK134(X0,X1))
& in(sK134(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f942,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK135(X0,X5))
& in(sK135(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f939,plain,
! [X0,X1] :
( ( sP35(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP35(X0,X1) ) ),
inference(rectify,[],[f938]) ).
fof(f938,plain,
! [X0,X1] :
( ( sP35(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| ~ sP35(X0,X1) ) ),
inference(nnf_transformation,[],[f656]) ).
fof(f656,plain,
! [X0,X1] :
( sP35(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP35])]) ).
fof(f8694,plain,
spl171_589,
inference(avatar_split_clause,[],[f1516,f8692]) ).
fof(f8692,plain,
( spl171_589
<=> ! [X2,X0,X1] :
( sP33(X0,X1,X2)
| in(sK120(X0,X1,X2),X1)
| in(sK119(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_589])]) ).
fof(f1516,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| in(sK120(X0,X1,X2),X1)
| in(sK119(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f8690,plain,
spl171_588,
inference(avatar_split_clause,[],[f1504,f8688]) ).
fof(f8688,plain,
( spl171_588
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_588])]) ).
fof(f1504,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f8686,plain,
spl171_587,
inference(avatar_split_clause,[],[f1468,f8684]) ).
fof(f8684,plain,
( spl171_587
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK111(X0,X1,X2),X0)
| in(sK110(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_587])]) ).
fof(f1468,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK111(X0,X1,X2),X0)
| in(sK110(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f8682,plain,
spl171_586,
inference(avatar_split_clause,[],[f1459,f8680]) ).
fof(f8680,plain,
( spl171_586
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(sK108(X0,X1,X2),X0)
| in(sK107(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_586])]) ).
fof(f1459,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| in(sK108(X0,X1,X2),X0)
| in(sK107(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f8677,plain,
spl171_585,
inference(avatar_split_clause,[],[f1403,f8675]) ).
fof(f1403,plain,
! [X0,X1,X4] :
( disjoint(fiber(X0,sK91(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f832]) ).
fof(f832,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK90(X0,X1))
| ~ in(X3,sK90(X0,X1)) )
& empty_set != sK90(X0,X1)
& subset(sK90(X0,X1),X1) ) )
& ( ! [X4] :
( ( disjoint(fiber(X0,sK91(X0,X4)),X4)
& in(sK91(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) )
| ~ sP13(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90,sK91])],[f829,f831,f830]) ).
fof(f830,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
=> ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK90(X0,X1))
| ~ in(X3,sK90(X0,X1)) )
& empty_set != sK90(X0,X1)
& subset(sK90(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f831,plain,
! [X0,X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
=> ( disjoint(fiber(X0,sK91(X0,X4)),X4)
& in(sK91(X0,X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f829,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) )
& ( ! [X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
| empty_set = X4
| ~ subset(X4,X1) )
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f828]) ).
fof(f828,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) )
& ( ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) )
| ~ sP13(X0,X1) ) ),
inference(nnf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0,X1] :
( sP13(X0,X1)
<=> ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f8672,plain,
spl171_584,
inference(avatar_split_clause,[],[f1362,f8670]) ).
fof(f1362,plain,
! [X3,X0] :
( disjoint(fiber(X0,sK78(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f798]) ).
fof(f798,plain,
! [X0] :
( ( sP7(X0)
| ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK77(X0))
| ~ in(X2,sK77(X0)) )
& empty_set != sK77(X0)
& subset(sK77(X0),relation_field(X0)) ) )
& ( ! [X3] :
( ( disjoint(fiber(X0,sK78(X0,X3)),X3)
& in(sK78(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f795,f797,f796]) ).
fof(f796,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
=> ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK77(X0))
| ~ in(X2,sK77(X0)) )
& empty_set != sK77(X0)
& subset(sK77(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f797,plain,
! [X0,X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
=> ( disjoint(fiber(X0,sK78(X0,X3)),X3)
& in(sK78(X0,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f795,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) )
& ( ! [X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f794]) ).
fof(f794,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) )
& ( ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f614]) ).
fof(f614,plain,
! [X0] :
( sP7(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f8627,plain,
( ~ spl171_583
| ~ spl171_55
| ~ spl171_559 ),
inference(avatar_split_clause,[],[f8356,f8053,f2282,f8624]) ).
fof(f8624,plain,
( spl171_583
<=> in(sK67(relation_rng(sK51)),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_583])]) ).
fof(f8356,plain,
( ~ in(sK67(relation_rng(sK51)),sK160)
| ~ spl171_55
| ~ spl171_559 ),
inference(resolution,[],[f8054,f2283]) ).
fof(f8453,plain,
spl171_582,
inference(avatar_split_clause,[],[f1939,f8451]) ).
fof(f8451,plain,
( spl171_582
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK71(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_582])]) ).
fof(f1939,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK71(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1196]) ).
fof(f1196,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK71(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f738]) ).
fof(f8449,plain,
spl171_581,
inference(avatar_split_clause,[],[f1917,f8447]) ).
fof(f8447,plain,
( spl171_581
<=> ! [X5,X0,X6,X2,X1] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_581])]) ).
fof(f1917,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP39(X0,X1,X2) ),
inference(definition_unfolding,[],[f1590,f1762]) ).
fof(f1590,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f958]) ).
fof(f8445,plain,
spl171_580,
inference(avatar_split_clause,[],[f1890,f8443]) ).
fof(f8443,plain,
( spl171_580
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_580])]) ).
fof(f1890,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP21(X0,X1,X2) ),
inference(definition_unfolding,[],[f1446,f1762]) ).
fof(f1446,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f866]) ).
fof(f8438,plain,
spl171_579,
inference(avatar_split_clause,[],[f1770,f8436]) ).
fof(f8436,plain,
( spl171_579
<=> ! [X2,X0] :
( in(set_union2(X2,unordered_pair(X2,X2)),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_579])]) ).
fof(f1770,plain,
! [X2,X0] :
( in(set_union2(X2,unordered_pair(X2,X2)),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1072,f1763]) ).
fof(f1763,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1313,f1065]) ).
fof(f1313,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f1072,plain,
! [X2,X0] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f689]) ).
fof(f689,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK53(X0)),X0)
& in(sK53(X0),X0)
& ordinal(sK53(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f687,f688]) ).
fof(f688,plain,
! [X0] :
( ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) )
=> ( ~ in(succ(sK53(X0)),X0)
& in(sK53(X0),X0)
& ordinal(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f687,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(rectify,[],[f686]) ).
fof(f686,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f251]) ).
fof(f251,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f8434,plain,
spl171_578,
inference(avatar_split_clause,[],[f1260,f8432]) ).
fof(f8432,plain,
( spl171_578
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_578])]) ).
fof(f1260,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f448]) ).
fof(f448,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f447]) ).
fof(f447,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f288]) ).
fof(f288,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f8430,plain,
spl171_577,
inference(avatar_split_clause,[],[f1185,f8428]) ).
fof(f8428,plain,
( spl171_577
<=> ! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_577])]) ).
fof(f1185,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f733]) ).
fof(f733,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f399]) ).
fof(f399,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f253]) ).
fof(f253,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f8426,plain,
spl171_576,
inference(avatar_split_clause,[],[f1184,f8424]) ).
fof(f8424,plain,
( spl171_576
<=> ! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_576])]) ).
fof(f1184,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f733]) ).
fof(f8422,plain,
spl171_575,
inference(avatar_split_clause,[],[f1118,f8420]) ).
fof(f8420,plain,
( spl171_575
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_575])]) ).
fof(f1118,plain,
! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f260]) ).
fof(f260,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f8418,plain,
spl171_574,
inference(avatar_split_clause,[],[f1117,f8416]) ).
fof(f8416,plain,
( spl171_574
<=> ! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_574])]) ).
fof(f1117,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f257]) ).
fof(f257,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f8402,plain,
( ~ spl171_573
| ~ spl171_517
| ~ spl171_559 ),
inference(avatar_split_clause,[],[f8359,f8053,f7241,f8399]) ).
fof(f8399,plain,
( spl171_573
<=> in(relation_rng(sK51),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_573])]) ).
fof(f7241,plain,
( spl171_517
<=> ! [X0] :
( ~ in(X0,sK160)
| in(X0,relation_rng(sK51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_517])]) ).
fof(f8359,plain,
( ~ in(relation_rng(sK51),sK160)
| ~ spl171_517
| ~ spl171_559 ),
inference(duplicate_literal_removal,[],[f8354]) ).
fof(f8354,plain,
( ~ in(relation_rng(sK51),sK160)
| ~ in(relation_rng(sK51),sK160)
| ~ spl171_517
| ~ spl171_559 ),
inference(resolution,[],[f8054,f7242]) ).
fof(f7242,plain,
( ! [X0] :
( in(X0,relation_rng(sK51))
| ~ in(X0,sK160) )
| ~ spl171_517 ),
inference(avatar_component_clause,[],[f7241]) ).
fof(f8383,plain,
spl171_572,
inference(avatar_split_clause,[],[f2019,f8381]) ).
fof(f8381,plain,
( spl171_572
<=> ! [X0,X3,X2,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X2
| ~ in(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_572])]) ).
fof(f2019,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X2
| ~ in(X2,X3) ),
inference(inner_rewriting,[],[f1724]) ).
fof(f1724,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X2
| ~ in(sK158(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f8379,plain,
spl171_571,
inference(avatar_split_clause,[],[f2018,f8377]) ).
fof(f8377,plain,
( spl171_571
<=> ! [X0,X3,X2,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X1
| ~ in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_571])]) ).
fof(f2018,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X1
| ~ in(X1,X3) ),
inference(inner_rewriting,[],[f1725]) ).
fof(f1725,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X1
| ~ in(sK158(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f8375,plain,
spl171_570,
inference(avatar_split_clause,[],[f2017,f8373]) ).
fof(f8373,plain,
( spl171_570
<=> ! [X0,X3,X2,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X0
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_570])]) ).
fof(f2017,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X0
| ~ in(X0,X3) ),
inference(inner_rewriting,[],[f1726]) ).
fof(f1726,plain,
! [X2,X3,X0,X1] :
( sP49(X0,X1,X2,X3)
| sK158(X0,X1,X2,X3) != X0
| ~ in(sK158(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f8371,plain,
spl171_569,
inference(avatar_split_clause,[],[f1674,f8369]) ).
fof(f8369,plain,
( spl171_569
<=> ! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_569])]) ).
fof(f1674,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f599]) ).
fof(f599,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f598]) ).
fof(f598,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f8367,plain,
spl171_568,
inference(avatar_split_clause,[],[f1654,f8365]) ).
fof(f8365,plain,
( spl171_568
<=> ! [X0,X1] :
( sP43(X0,X1)
| in(sK143(X0,X1),sK144(X0,X1))
| in(sK143(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_568])]) ).
fof(f1654,plain,
! [X0,X1] :
( sP43(X0,X1)
| in(sK143(X0,X1),sK144(X0,X1))
| in(sK143(X0,X1),X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f8363,plain,
spl171_567,
inference(avatar_split_clause,[],[f1570,f8361]) ).
fof(f8361,plain,
( spl171_567
<=> ! [X0,X1] :
( sP35(X0,X1)
| ~ in(sK133(X0,X1),sK134(X0,X1))
| ~ in(sK133(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_567])]) ).
fof(f1570,plain,
! [X0,X1] :
( sP35(X0,X1)
| ~ in(sK133(X0,X1),sK134(X0,X1))
| ~ in(sK133(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f8346,plain,
spl171_566,
inference(avatar_split_clause,[],[f1513,f8344]) ).
fof(f8344,plain,
( spl171_566
<=> ! [X0,X6,X2,X1] :
( apply(X0,sK121(X0,X1,X6)) = X6
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_566])]) ).
fof(f1513,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK121(X0,X1,X6)) = X6
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f8342,plain,
spl171_565,
inference(avatar_split_clause,[],[f1406,f8340]) ).
fof(f8340,plain,
( spl171_565
<=> ! [X0,X1,X3] :
( sP13(X0,X1)
| ~ disjoint(fiber(X0,X3),sK90(X0,X1))
| ~ in(X3,sK90(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_565])]) ).
fof(f1406,plain,
! [X3,X0,X1] :
( sP13(X0,X1)
| ~ disjoint(fiber(X0,X3),sK90(X0,X1))
| ~ in(X3,sK90(X0,X1)) ),
inference(cnf_transformation,[],[f832]) ).
fof(f8213,plain,
( spl171_564
| ~ spl171_165
| ~ spl171_517 ),
inference(avatar_split_clause,[],[f7969,f7241,f2997,f8211]) ).
fof(f8211,plain,
( spl171_564
<=> ! [X0] :
( ~ in(X0,sK160)
| element(X0,relation_rng(sK51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_564])]) ).
fof(f2997,plain,
( spl171_165
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_165])]) ).
fof(f7969,plain,
( ! [X0] :
( ~ in(X0,sK160)
| element(X0,relation_rng(sK51)) )
| ~ spl171_165
| ~ spl171_517 ),
inference(resolution,[],[f7242,f2998]) ).
fof(f2998,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl171_165 ),
inference(avatar_component_clause,[],[f2997]) ).
fof(f8171,plain,
( spl171_563
| ~ spl171_203
| ~ spl171_550 ),
inference(avatar_split_clause,[],[f7986,f7983,f3373,f8169]) ).
fof(f8169,plain,
( spl171_563
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK59(X0),sK59(X0)),unordered_pair(sK59(X0),sK60(X0))),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_563])]) ).
fof(f7983,plain,
( spl171_550
<=> ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK59(X0),sK60(X0)),unordered_pair(sK59(X0),sK59(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_550])]) ).
fof(f7986,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK59(X0),sK59(X0)),unordered_pair(sK59(X0),sK60(X0))),X0)
| sP0(X0) )
| ~ spl171_203
| ~ spl171_550 ),
inference(forward_demodulation,[],[f7984,f3374]) ).
fof(f7984,plain,
( ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK59(X0),sK60(X0)),unordered_pair(sK59(X0),sK59(X0))),X0) )
| ~ spl171_550 ),
inference(avatar_component_clause,[],[f7983]) ).
fof(f8167,plain,
( spl171_562
| ~ spl171_203
| ~ spl171_549 ),
inference(avatar_split_clause,[],[f7966,f7963,f3373,f8165]) ).
fof(f8165,plain,
( spl171_562
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK59(X0),sK60(X0)),unordered_pair(sK60(X0),sK60(X0))),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_562])]) ).
fof(f7963,plain,
( spl171_549
<=> ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK60(X0),sK59(X0)),unordered_pair(sK60(X0),sK60(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_549])]) ).
fof(f7966,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK59(X0),sK60(X0)),unordered_pair(sK60(X0),sK60(X0))),X0)
| sP0(X0) )
| ~ spl171_203
| ~ spl171_549 ),
inference(forward_demodulation,[],[f7964,f3374]) ).
fof(f7964,plain,
( ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK60(X0),sK59(X0)),unordered_pair(sK60(X0),sK60(X0))),X0) )
| ~ spl171_549 ),
inference(avatar_component_clause,[],[f7963]) ).
fof(f8063,plain,
spl171_561,
inference(avatar_split_clause,[],[f1976,f8061]) ).
fof(f8061,plain,
( spl171_561
<=> ! [X5,X1,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP37(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_561])]) ).
fof(f1976,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP37(X0,X1) ),
inference(equality_resolution,[],[f1909]) ).
fof(f1909,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP37(X0,X1) ),
inference(definition_unfolding,[],[f1583,f1762]) ).
fof(f1583,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f8059,plain,
spl171_560,
inference(avatar_split_clause,[],[f1922,f8057]) ).
fof(f8057,plain,
( spl171_560
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK146(X0,X1) = X0
| in(sK146(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_560])]) ).
fof(f1922,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK146(X0,X1) = X0
| in(sK146(X0,X1),X1) ),
inference(definition_unfolding,[],[f1661,f1065]) ).
fof(f1661,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK146(X0,X1) = X0
| in(sK146(X0,X1),X1) ),
inference(cnf_transformation,[],[f987]) ).
fof(f987,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK146(X0,X1) != X0
| ~ in(sK146(X0,X1),X1) )
& ( sK146(X0,X1) = X0
| in(sK146(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK146])],[f985,f986]) ).
fof(f986,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK146(X0,X1) != X0
| ~ in(sK146(X0,X1),X1) )
& ( sK146(X0,X1) = X0
| in(sK146(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f985,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f984]) ).
fof(f984,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8055,plain,
( spl171_559
| ~ spl171_164
| ~ spl171_517 ),
inference(avatar_split_clause,[],[f7968,f7241,f2993,f8053]) ).
fof(f2993,plain,
( spl171_164
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_164])]) ).
fof(f7968,plain,
( ! [X0] :
( ~ in(X0,sK160)
| ~ in(relation_rng(sK51),X0) )
| ~ spl171_164
| ~ spl171_517 ),
inference(resolution,[],[f7242,f2994]) ).
fof(f2994,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl171_164 ),
inference(avatar_component_clause,[],[f2993]) ).
fof(f8051,plain,
spl171_558,
inference(avatar_split_clause,[],[f1911,f8049]) ).
fof(f8049,plain,
( spl171_558
<=> ! [X4,X0,X5,X1] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP37(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_558])]) ).
fof(f1911,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP37(X0,X1) ),
inference(definition_unfolding,[],[f1581,f1762]) ).
fof(f1581,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f8047,plain,
spl171_557,
inference(avatar_split_clause,[],[f1910,f8045]) ).
fof(f8045,plain,
( spl171_557
<=> ! [X4,X5,X1,X0] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP37(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_557])]) ).
fof(f1910,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP37(X0,X1) ),
inference(definition_unfolding,[],[f1582,f1762]) ).
fof(f1582,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f951]) ).
fof(f8043,plain,
spl171_556,
inference(avatar_split_clause,[],[f1816,f8041]) ).
fof(f8041,plain,
( spl171_556
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_556])]) ).
fof(f1816,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1233,f1762]) ).
fof(f1233,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f432]) ).
fof(f432,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f431]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f215]) ).
fof(f215,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f8039,plain,
spl171_555,
inference(avatar_split_clause,[],[f1815,f8037]) ).
fof(f8037,plain,
( spl171_555
<=> ! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_555])]) ).
fof(f1815,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1234,f1762]) ).
fof(f1234,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f432]) ).
fof(f8035,plain,
spl171_554,
inference(avatar_split_clause,[],[f1814,f8033]) ).
fof(f8033,plain,
( spl171_554
<=> ! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_554])]) ).
fof(f1814,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1231,f1762]) ).
fof(f1231,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f429]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f230]) ).
fof(f230,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f8031,plain,
spl171_553,
inference(avatar_split_clause,[],[f1813,f8029]) ).
fof(f8029,plain,
( spl171_553
<=> ! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_553])]) ).
fof(f1813,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1232,f1762]) ).
fof(f1232,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f430]) ).
fof(f7995,plain,
( spl171_552
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_551 ),
inference(avatar_split_clause,[],[f7991,f7988,f7378,f2580,f2244,f7993]) ).
fof(f7988,plain,
( spl171_551
<=> ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_551])]) ).
fof(f7991,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1)))))
| ~ relation(X1) )
| ~ spl171_46
| ~ spl171_91
| ~ spl171_526
| ~ spl171_551 ),
inference(forward_demodulation,[],[f7989,f7509]) ).
fof(f7989,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) )
| ~ spl171_551 ),
inference(avatar_component_clause,[],[f7988]) ).
fof(f7990,plain,
spl171_551,
inference(avatar_split_clause,[],[f1791,f7988]) ).
fof(f1791,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1171,f1148]) ).
fof(f1171,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f384]) ).
fof(f384,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f197]) ).
fof(f197,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f7985,plain,
spl171_550,
inference(avatar_split_clause,[],[f1780,f7983]) ).
fof(f1780,plain,
! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK59(X0),sK60(X0)),unordered_pair(sK59(X0),sK59(X0))),X0) ),
inference(definition_unfolding,[],[f1101,f1762]) ).
fof(f1101,plain,
! [X0] :
( sP0(X0)
| ~ in(ordered_pair(sK59(X0),sK60(X0)),X0) ),
inference(cnf_transformation,[],[f706]) ).
fof(f7965,plain,
spl171_549,
inference(avatar_split_clause,[],[f1779,f7963]) ).
fof(f1779,plain,
! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK60(X0),sK59(X0)),unordered_pair(sK60(X0),sK60(X0))),X0) ),
inference(definition_unfolding,[],[f1102,f1762]) ).
fof(f1102,plain,
! [X0] :
( sP0(X0)
| ~ in(ordered_pair(sK60(X0),sK59(X0)),X0) ),
inference(cnf_transformation,[],[f706]) ).
fof(f7961,plain,
spl171_548,
inference(avatar_split_clause,[],[f1251,f7959]) ).
fof(f7959,plain,
( spl171_548
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_548])]) ).
fof(f1251,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f771]) ).
fof(f771,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f770]) ).
fof(f770,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f437]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f294]) ).
fof(f294,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f7957,plain,
spl171_547,
inference(avatar_split_clause,[],[f1248,f7955]) ).
fof(f7955,plain,
( spl171_547
<=> ! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_547])]) ).
fof(f1248,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f769]) ).
fof(f769,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f768]) ).
fof(f768,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f436]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f184]) ).
fof(f184,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f7953,plain,
spl171_546,
inference(avatar_split_clause,[],[f1237,f7951]) ).
fof(f7951,plain,
( spl171_546
<=> ! [X2,X0,X1] :
( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_546])]) ).
fof(f1237,plain,
! [X2,X0,X1] :
( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f759]) ).
fof(f759,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f758]) ).
fof(f758,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f433]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f7949,plain,
spl171_545,
inference(avatar_split_clause,[],[f1191,f7947]) ).
fof(f7947,plain,
( spl171_545
<=> ! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_545])]) ).
fof(f1191,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f409]) ).
fof(f409,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f7760,plain,
( spl171_544
| ~ spl171_12
| ~ spl171_105
| ~ spl171_535 ),
inference(avatar_split_clause,[],[f7723,f7720,f2639,f2076,f7758]) ).
fof(f7758,plain,
( spl171_544
<=> ! [X4,X0,X1] :
( sK160 = X4
| in(sK91(X0,X4),X4)
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_544])]) ).
fof(f7720,plain,
( spl171_535
<=> ! [X4,X0,X1] :
( in(sK91(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_535])]) ).
fof(f7723,plain,
( ! [X0,X1,X4] :
( sK160 = X4
| in(sK91(X0,X4),X4)
| ~ subset(X4,X1)
| ~ sP13(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_535 ),
inference(forward_demodulation,[],[f7721,f2706]) ).
fof(f7721,plain,
( ! [X0,X1,X4] :
( in(sK91(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) )
| ~ spl171_535 ),
inference(avatar_component_clause,[],[f7720]) ).
fof(f7756,plain,
( spl171_543
| ~ spl171_12
| ~ spl171_105
| ~ spl171_534 ),
inference(avatar_split_clause,[],[f7718,f7715,f2639,f2076,f7754]) ).
fof(f7754,plain,
( spl171_543
<=> ! [X0,X3] :
( sK160 = X3
| in(sK78(X0,X3),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_543])]) ).
fof(f7715,plain,
( spl171_534
<=> ! [X0,X3] :
( in(sK78(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_534])]) ).
fof(f7718,plain,
( ! [X3,X0] :
( sK160 = X3
| in(sK78(X0,X3),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_534 ),
inference(forward_demodulation,[],[f7716,f2706]) ).
fof(f7716,plain,
( ! [X3,X0] :
( in(sK78(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) )
| ~ spl171_534 ),
inference(avatar_component_clause,[],[f7715]) ).
fof(f7752,plain,
spl171_542,
inference(avatar_split_clause,[],[f1933,f7750]) ).
fof(f7750,plain,
( spl171_542
<=> ! [X5,X1,X0] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_542])]) ).
fof(f1933,plain,
! [X0,X1,X5] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f1129]) ).
fof(f1129,plain,
! [X0,X1,X4,X5] :
( apply(X0,X4) = X5
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f7748,plain,
spl171_541,
inference(avatar_split_clause,[],[f1666,f7746]) ).
fof(f7746,plain,
( spl171_541
<=> ! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK147(X0,X1),X0)
| ~ in(sK147(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_541])]) ).
fof(f1666,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK147(X0,X1),X0)
| ~ in(sK147(X0,X1),X1) ),
inference(cnf_transformation,[],[f991]) ).
fof(f991,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK147(X0,X1),X0)
| ~ in(sK147(X0,X1),X1) )
& ( subset(sK147(X0,X1),X0)
| in(sK147(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147])],[f989,f990]) ).
fof(f990,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK147(X0,X1),X0)
| ~ in(sK147(X0,X1),X1) )
& ( subset(sK147(X0,X1),X0)
| in(sK147(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f989,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f988]) ).
fof(f988,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f7744,plain,
spl171_540,
inference(avatar_split_clause,[],[f1665,f7742]) ).
fof(f7742,plain,
( spl171_540
<=> ! [X0,X1] :
( powerset(X0) = X1
| subset(sK147(X0,X1),X0)
| in(sK147(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_540])]) ).
fof(f1665,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK147(X0,X1),X0)
| in(sK147(X0,X1),X1) ),
inference(cnf_transformation,[],[f991]) ).
fof(f7740,plain,
spl171_539,
inference(avatar_split_clause,[],[f1618,f7738]) ).
fof(f7738,plain,
( spl171_539
<=> ! [X2,X0,X1] :
( sP42(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_539])]) ).
fof(f1618,plain,
! [X2,X0,X1] :
( sP42(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f667]) ).
fof(f667,plain,
! [X0,X1] :
( ! [X2] :
( sP42(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f560,f666,f665]) ).
fof(f666,plain,
! [X2,X0,X1] :
( ( complements_of_subsets(X0,X1) = X2
<=> sP41(X1,X0,X2) )
| ~ sP42(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
fof(f560,plain,
! [X0,X1] :
( ! [X2] :
( ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f7736,plain,
spl171_538,
inference(avatar_split_clause,[],[f1511,f7734]) ).
fof(f7734,plain,
( spl171_538
<=> ! [X0,X6,X2,X1] :
( in(sK121(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_538])]) ).
fof(f1511,plain,
! [X2,X0,X1,X6] :
( in(sK121(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f7732,plain,
( spl171_214
| ~ spl171_537
| ~ spl171_185
| ~ spl171_516 ),
inference(avatar_split_clause,[],[f7322,f7116,f3299,f7729,f3454]) ).
fof(f3454,plain,
( spl171_214
<=> sP0(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_214])]) ).
fof(f7729,plain,
( spl171_537
<=> in(sK60(sK51),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_537])]) ).
fof(f3299,plain,
( spl171_185
<=> ! [X0] :
( sP0(X0)
| in(sK60(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_185])]) ).
fof(f7116,plain,
( spl171_516
<=> ! [X0] :
( ~ in(X0,sK160)
| ~ in(X0,relation_field(sK51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_516])]) ).
fof(f7322,plain,
( ~ in(sK60(sK51),sK160)
| sP0(sK51)
| ~ spl171_185
| ~ spl171_516 ),
inference(resolution,[],[f7117,f3300]) ).
fof(f3300,plain,
( ! [X0] :
( in(sK60(X0),relation_field(X0))
| sP0(X0) )
| ~ spl171_185 ),
inference(avatar_component_clause,[],[f3299]) ).
fof(f7117,plain,
( ! [X0] :
( ~ in(X0,relation_field(sK51))
| ~ in(X0,sK160) )
| ~ spl171_516 ),
inference(avatar_component_clause,[],[f7116]) ).
fof(f7727,plain,
spl171_536,
inference(avatar_split_clause,[],[f1492,f7725]) ).
fof(f7725,plain,
( spl171_536
<=> ! [X0,X1] :
( sP29(X0,X1)
| in(sK116(X0,X1),relation_dom(X0))
| in(sK115(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_536])]) ).
fof(f1492,plain,
! [X0,X1] :
( sP29(X0,X1)
| in(sK116(X0,X1),relation_dom(X0))
| in(sK115(X0,X1),X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f7722,plain,
spl171_535,
inference(avatar_split_clause,[],[f1402,f7720]) ).
fof(f1402,plain,
! [X0,X1,X4] :
( in(sK91(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f832]) ).
fof(f7717,plain,
spl171_534,
inference(avatar_split_clause,[],[f1361,f7715]) ).
fof(f1361,plain,
! [X3,X0] :
( in(sK78(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f798]) ).
fof(f7409,plain,
( spl171_533
| ~ spl171_12
| ~ spl171_105
| ~ spl171_519 ),
inference(avatar_split_clause,[],[f7352,f7348,f2639,f2076,f7407]) ).
fof(f7407,plain,
( spl171_533
<=> ! [X0,X1] :
( sK160 = X0
| relation_inverse_image(X1,X0) != sK160
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_533])]) ).
fof(f7348,plain,
( spl171_519
<=> ! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_519])]) ).
fof(f7352,plain,
( ! [X0,X1] :
( sK160 = X0
| relation_inverse_image(X1,X0) != sK160
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_519 ),
inference(forward_demodulation,[],[f7351,f2706]) ).
fof(f7351,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,X0) != sK160
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_519 ),
inference(forward_demodulation,[],[f7349,f2706]) ).
fof(f7349,plain,
( ! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl171_519 ),
inference(avatar_component_clause,[],[f7348]) ).
fof(f7405,plain,
spl171_532,
inference(avatar_split_clause,[],[f1931,f7403]) ).
fof(f7403,plain,
( spl171_532
<=> ! [X1] :
( ~ being_limit_ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1)
| ~ ordinal(set_union2(X1,unordered_pair(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_532])]) ).
fof(f1931,plain,
! [X1] :
( ~ being_limit_ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1)
| ~ ordinal(set_union2(X1,unordered_pair(X1,X1))) ),
inference(equality_resolution,[],[f1767]) ).
fof(f1767,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| set_union2(X1,unordered_pair(X1,X1)) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1071,f1763]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| succ(X1) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f685]) ).
fof(f685,plain,
! [X0] :
( ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( succ(X1) != X0
| ~ ordinal(X1) ) )
& ( ( succ(sK52(X0)) = X0
& ordinal(sK52(X0)) )
| being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f323,f684]) ).
fof(f684,plain,
! [X0] :
( ? [X2] :
( succ(X2) = X0
& ordinal(X2) )
=> ( succ(sK52(X0)) = X0
& ordinal(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( succ(X1) != X0
| ~ ordinal(X1) ) )
& ( ? [X2] :
( succ(X2) = X0
& ordinal(X2) )
| being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f308]) ).
fof(f308,plain,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X2] :
( ordinal(X2)
=> succ(X2) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f252]) ).
fof(f252,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> succ(X1) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f7401,plain,
spl171_531,
inference(avatar_split_clause,[],[f1836,f7399]) ).
fof(f7399,plain,
( spl171_531
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_531])]) ).
fof(f1836,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f1282,f1762]) ).
fof(f1282,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f781]) ).
fof(f7397,plain,
spl171_530,
inference(avatar_split_clause,[],[f1835,f7395]) ).
fof(f7395,plain,
( spl171_530
<=> ! [X0,X3,X2,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_530])]) ).
fof(f1835,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f1283,f1762]) ).
fof(f1283,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f781]) ).
fof(f7393,plain,
( spl171_214
| ~ spl171_529
| ~ spl171_184
| ~ spl171_516 ),
inference(avatar_split_clause,[],[f7321,f7116,f3295,f7390,f3454]) ).
fof(f7390,plain,
( spl171_529
<=> in(sK59(sK51),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_529])]) ).
fof(f3295,plain,
( spl171_184
<=> ! [X0] :
( sP0(X0)
| in(sK59(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_184])]) ).
fof(f7321,plain,
( ~ in(sK59(sK51),sK160)
| sP0(sK51)
| ~ spl171_184
| ~ spl171_516 ),
inference(resolution,[],[f7117,f3296]) ).
fof(f3296,plain,
( ! [X0] :
( in(sK59(X0),relation_field(X0))
| sP0(X0) )
| ~ spl171_184 ),
inference(avatar_component_clause,[],[f3295]) ).
fof(f7388,plain,
spl171_528,
inference(avatar_split_clause,[],[f1821,f7386]) ).
fof(f7386,plain,
( spl171_528
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_528])]) ).
fof(f1821,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1252,f1148,f1148]) ).
fof(f1252,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f438]) ).
fof(f438,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f224]) ).
fof(f224,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f7384,plain,
spl171_527,
inference(avatar_split_clause,[],[f1790,f7382]) ).
fof(f1790,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1170,f1148]) ).
fof(f1170,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f301]) ).
fof(f301,axiom,
! [X0,X1] :
( relation(X1)
=> set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f7380,plain,
spl171_526,
inference(avatar_split_clause,[],[f1789,f7378]) ).
fof(f1789,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1169,f1148]) ).
fof(f1169,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f189]) ).
fof(f189,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f7376,plain,
spl171_525,
inference(avatar_split_clause,[],[f1772,f7374]) ).
fof(f7374,plain,
( spl171_525
<=> ! [X0,X1] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_525])]) ).
fof(f1772,plain,
! [X0,X1] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1076,f1763]) ).
fof(f1076,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f690]) ).
fof(f690,plain,
! [X0] :
( ! [X1] :
( ( ( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1) )
& ( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) ) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f233]) ).
fof(f233,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f7372,plain,
spl171_524,
inference(avatar_split_clause,[],[f1771,f7370]) ).
fof(f7370,plain,
( spl171_524
<=> ! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_524])]) ).
fof(f1771,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1077,f1763]) ).
fof(f1077,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f690]) ).
fof(f7368,plain,
spl171_523,
inference(avatar_split_clause,[],[f1769,f7366]) ).
fof(f7366,plain,
( spl171_523
<=> ! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK53(X0),unordered_pair(sK53(X0),sK53(X0))),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_523])]) ).
fof(f1769,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK53(X0),unordered_pair(sK53(X0),sK53(X0))),X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1075,f1763]) ).
fof(f1075,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(succ(sK53(X0)),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f689]) ).
fof(f7364,plain,
spl171_522,
inference(avatar_split_clause,[],[f1768,f7362]) ).
fof(f7362,plain,
( spl171_522
<=> ! [X0] :
( set_union2(sK52(X0),unordered_pair(sK52(X0),sK52(X0))) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_522])]) ).
fof(f1768,plain,
! [X0] :
( set_union2(sK52(X0),unordered_pair(sK52(X0),sK52(X0))) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1070,f1763]) ).
fof(f1070,plain,
! [X0] :
( succ(sK52(X0)) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f685]) ).
fof(f7360,plain,
spl171_521,
inference(avatar_split_clause,[],[f1242,f7358]) ).
fof(f7358,plain,
( spl171_521
<=> ! [X2,X0,X1] :
( in(sK75(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_521])]) ).
fof(f1242,plain,
! [X2,X0,X1] :
( in(sK75(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f767]) ).
fof(f7356,plain,
spl171_520,
inference(avatar_split_clause,[],[f1238,f7354]) ).
fof(f7354,plain,
( spl171_520
<=> ! [X2,X0,X1] :
( in(sK74(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_520])]) ).
fof(f1238,plain,
! [X2,X0,X1] :
( in(sK74(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f763]) ).
fof(f7350,plain,
spl171_519,
inference(avatar_split_clause,[],[f1173,f7348]) ).
fof(f1173,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f388]) ).
fof(f388,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(flattening,[],[f387]) ).
fof(f387,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f205,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f7291,plain,
( spl171_518
| ~ spl171_12
| ~ spl171_105
| ~ spl171_513 ),
inference(avatar_split_clause,[],[f7103,f7100,f2639,f2076,f7289]) ).
fof(f7289,plain,
( spl171_518
<=> ! [X0,X1] :
( apply(X0,X1) = sK160
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_518])]) ).
fof(f7100,plain,
( spl171_513
<=> ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_513])]) ).
fof(f7103,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK160
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_513 ),
inference(forward_demodulation,[],[f7101,f2706]) ).
fof(f7101,plain,
( ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl171_513 ),
inference(avatar_component_clause,[],[f7100]) ).
fof(f7243,plain,
( spl171_517
| ~ spl171_401
| ~ spl171_490 ),
inference(avatar_split_clause,[],[f6935,f6789,f5452,f7241]) ).
fof(f5452,plain,
( spl171_401
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_401])]) ).
fof(f6789,plain,
( spl171_490
<=> sP47(relation_field(sK51),relation_rng(sK51),sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_490])]) ).
fof(f6935,plain,
( ! [X0] :
( ~ in(X0,sK160)
| in(X0,relation_rng(sK51)) )
| ~ spl171_401
| ~ spl171_490 ),
inference(resolution,[],[f6791,f5453]) ).
fof(f5453,plain,
( ! [X2,X0,X1,X4] :
( ~ sP47(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl171_401 ),
inference(avatar_component_clause,[],[f5452]) ).
fof(f6791,plain,
( sP47(relation_field(sK51),relation_rng(sK51),sK160)
| ~ spl171_490 ),
inference(avatar_component_clause,[],[f6789]) ).
fof(f7118,plain,
( spl171_516
| ~ spl171_402
| ~ spl171_490 ),
inference(avatar_split_clause,[],[f6934,f6789,f5456,f7116]) ).
fof(f5456,plain,
( spl171_402
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_402])]) ).
fof(f6934,plain,
( ! [X0] :
( ~ in(X0,sK160)
| ~ in(X0,relation_field(sK51)) )
| ~ spl171_402
| ~ spl171_490 ),
inference(resolution,[],[f6791,f5457]) ).
fof(f5457,plain,
( ! [X2,X0,X1,X4] :
( ~ sP47(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl171_402 ),
inference(avatar_component_clause,[],[f5456]) ).
fof(f7111,plain,
spl171_515,
inference(avatar_split_clause,[],[f2014,f7109]) ).
fof(f7109,plain,
( spl171_515
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_515])]) ).
fof(f2014,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f1680]) ).
fof(f1680,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X1
| ~ in(sK149(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f7107,plain,
spl171_514,
inference(avatar_split_clause,[],[f2013,f7105]) ).
fof(f7105,plain,
( spl171_514
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_514])]) ).
fof(f2013,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f1681]) ).
fof(f1681,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| sK149(X0,X1,X2) != X0
| ~ in(sK149(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f7102,plain,
spl171_513,
inference(avatar_split_clause,[],[f1963,f7100]) ).
fof(f1963,plain,
! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1499]) ).
fof(f1499,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| empty_set != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f893]) ).
fof(f893,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f524]) ).
fof(f524,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f523]) ).
fof(f523,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f7098,plain,
spl171_512,
inference(avatar_split_clause,[],[f1934,f7096]) ).
fof(f7096,plain,
( spl171_512
<=> ! [X5,X1,X0] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_512])]) ).
fof(f1934,plain,
! [X0,X1,X5] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f1128]) ).
fof(f1128,plain,
! [X0,X1,X4,X5] :
( in(X4,relation_rng(X1))
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f7094,plain,
spl171_511,
inference(avatar_split_clause,[],[f1712,f7092]) ).
fof(f7092,plain,
( spl171_511
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_511])]) ).
fof(f1712,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f7090,plain,
spl171_510,
inference(avatar_split_clause,[],[f1704,f7088]) ).
fof(f7088,plain,
( spl171_510
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_510])]) ).
fof(f1704,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f7086,plain,
spl171_509,
inference(avatar_split_clause,[],[f1694,f7084]) ).
fof(f7084,plain,
( spl171_509
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_509])]) ).
fof(f1694,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f7078,plain,
spl171_508,
inference(avatar_split_clause,[],[f1685,f7076]) ).
fof(f7076,plain,
( spl171_508
<=> ! [X0,X8,X2,X1] :
( in(sK154(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_508])]) ).
fof(f1685,plain,
! [X2,X0,X1,X8] :
( in(sK154(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f7074,plain,
spl171_507,
inference(avatar_split_clause,[],[f1684,f7072]) ).
fof(f7072,plain,
( spl171_507
<=> ! [X0,X8,X2,X1] :
( in(sK153(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_507])]) ).
fof(f1684,plain,
! [X2,X0,X1,X8] :
( in(sK153(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f7070,plain,
spl171_506,
inference(avatar_split_clause,[],[f1676,f7068]) ).
fof(f7068,plain,
( spl171_506
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_506])]) ).
fof(f1676,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f7066,plain,
spl171_505,
inference(avatar_split_clause,[],[f1655,f7064]) ).
fof(f7064,plain,
( spl171_505
<=> ! [X0,X1] :
( sP43(X0,X1)
| in(sK144(X0,X1),X0)
| in(sK143(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_505])]) ).
fof(f1655,plain,
! [X0,X1] :
( sP43(X0,X1)
| in(sK144(X0,X1),X0)
| in(sK143(X0,X1),X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f7062,plain,
spl171_504,
inference(avatar_split_clause,[],[f1641,f7060]) ).
fof(f7060,plain,
( spl171_504
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK141(X0,X1),X1)
| ~ in(sK141(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_504])]) ).
fof(f1641,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK141(X0,X1),X1)
| ~ in(sK141(X0,X1),X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f969,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK141(X0,X1),X1)
| ~ in(sK141(X0,X1),X0) )
& ( in(sK141(X0,X1),X1)
| in(sK141(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141])],[f967,f968]) ).
fof(f968,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK141(X0,X1),X1)
| ~ in(sK141(X0,X1),X0) )
& ( in(sK141(X0,X1),X1)
| in(sK141(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f967,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f589]) ).
fof(f589,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f228]) ).
fof(f228,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f7058,plain,
spl171_503,
inference(avatar_split_clause,[],[f1640,f7056]) ).
fof(f7056,plain,
( spl171_503
<=> ! [X0,X1] :
( X0 = X1
| in(sK141(X0,X1),X1)
| in(sK141(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_503])]) ).
fof(f1640,plain,
! [X0,X1] :
( X0 = X1
| in(sK141(X0,X1),X1)
| in(sK141(X0,X1),X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f7054,plain,
spl171_502,
inference(avatar_split_clause,[],[f1612,f7052]) ).
fof(f7052,plain,
( spl171_502
<=> ! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP41(X2,X1,X0)
| ~ sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_502])]) ).
fof(f1612,plain,
! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP41(X2,X1,X0)
| ~ sP42(X0,X1,X2) ),
inference(cnf_transformation,[],[f960]) ).
fof(f960,plain,
! [X0,X1,X2] :
( ( ( complements_of_subsets(X1,X2) = X0
| ~ sP41(X2,X1,X0) )
& ( sP41(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0 ) )
| ~ sP42(X0,X1,X2) ),
inference(rectify,[],[f959]) ).
fof(f959,plain,
! [X2,X0,X1] :
( ( ( complements_of_subsets(X0,X1) = X2
| ~ sP41(X1,X0,X2) )
& ( sP41(X1,X0,X2)
| complements_of_subsets(X0,X1) != X2 ) )
| ~ sP42(X2,X0,X1) ),
inference(nnf_transformation,[],[f666]) ).
fof(f7050,plain,
spl171_501,
inference(avatar_split_clause,[],[f1589,f7048]) ).
fof(f7048,plain,
( spl171_501
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP39(X2,X1,X0)
| ~ sP40(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_501])]) ).
fof(f1589,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP39(X2,X1,X0)
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f953]) ).
fof(f953,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP39(X2,X1,X0) )
& ( sP39(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP40(X0,X1,X2) ),
inference(rectify,[],[f952]) ).
fof(f952,plain,
! [X2,X0,X1] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP39(X1,X0,X2) )
& ( sP39(X1,X0,X2)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP40(X2,X0,X1) ),
inference(nnf_transformation,[],[f663]) ).
fof(f663,plain,
! [X2,X0,X1] :
( ( relation_rng_restriction(X0,X1) = X2
<=> sP39(X1,X0,X2) )
| ~ sP40(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
fof(f7046,plain,
spl171_500,
inference(avatar_split_clause,[],[f1569,f7044]) ).
fof(f7044,plain,
( spl171_500
<=> ! [X0,X1] :
( sP35(X0,X1)
| in(sK134(X0,X1),X0)
| ~ in(sK133(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_500])]) ).
fof(f1569,plain,
! [X0,X1] :
( sP35(X0,X1)
| in(sK134(X0,X1),X0)
| ~ in(sK133(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f7042,plain,
spl171_499,
inference(avatar_split_clause,[],[f1512,f7040]) ).
fof(f7040,plain,
( spl171_499
<=> ! [X0,X6,X2,X1] :
( in(sK121(X0,X1,X6),X1)
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_499])]) ).
fof(f1512,plain,
! [X2,X0,X1,X6] :
( in(sK121(X0,X1,X6),X1)
| ~ in(X6,X2)
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f906]) ).
fof(f7038,plain,
( spl171_498
| ~ spl171_183
| ~ spl171_251
| ~ spl171_474 ),
inference(avatar_split_clause,[],[f6650,f6573,f3756,f3265,f7035]) ).
fof(f7035,plain,
( spl171_498
<=> sP48(relation_field(sK51),relation_rng(sK51),relation_rng(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_498])]) ).
fof(f3265,plain,
( spl171_183
<=> ! [X0] : set_difference(X0,sK160) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_183])]) ).
fof(f3756,plain,
( spl171_251
<=> ! [X0,X1] : sP48(X1,X0,set_difference(X0,set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_251])]) ).
fof(f6573,plain,
( spl171_474
<=> sK160 = set_difference(relation_rng(sK51),relation_field(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_474])]) ).
fof(f6650,plain,
( sP48(relation_field(sK51),relation_rng(sK51),relation_rng(sK51))
| ~ spl171_183
| ~ spl171_251
| ~ spl171_474 ),
inference(forward_demodulation,[],[f6636,f3266]) ).
fof(f3266,plain,
( ! [X0] : set_difference(X0,sK160) = X0
| ~ spl171_183 ),
inference(avatar_component_clause,[],[f3265]) ).
fof(f6636,plain,
( sP48(relation_field(sK51),relation_rng(sK51),set_difference(relation_rng(sK51),sK160))
| ~ spl171_251
| ~ spl171_474 ),
inference(superposition,[],[f3757,f6575]) ).
fof(f6575,plain,
( sK160 = set_difference(relation_rng(sK51),relation_field(sK51))
| ~ spl171_474 ),
inference(avatar_component_clause,[],[f6573]) ).
fof(f3757,plain,
( ! [X0,X1] : sP48(X1,X0,set_difference(X0,set_difference(X0,X1)))
| ~ spl171_251 ),
inference(avatar_component_clause,[],[f3756]) ).
fof(f7033,plain,
spl171_497,
inference(avatar_split_clause,[],[f1490,f7031]) ).
fof(f7031,plain,
( spl171_497
<=> ! [X5,X0,X1] :
( apply(X0,sK117(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_497])]) ).
fof(f1490,plain,
! [X0,X1,X5] :
( apply(X0,sK117(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f7029,plain,
spl171_496,
inference(avatar_split_clause,[],[f1465,f7027]) ).
fof(f7027,plain,
( spl171_496
<=> ! [X0,X6,X2,X1] :
( in(sK112(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_496])]) ).
fof(f1465,plain,
! [X2,X0,X1,X6] :
( in(sK112(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f880]) ).
fof(f7025,plain,
spl171_495,
inference(avatar_split_clause,[],[f1456,f7023]) ).
fof(f7023,plain,
( spl171_495
<=> ! [X0,X6,X2,X1] :
( in(sK109(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_495])]) ).
fof(f1456,plain,
! [X2,X0,X1,X6] :
( in(sK109(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f873]) ).
fof(f7021,plain,
spl171_494,
inference(avatar_split_clause,[],[f1445,f7019]) ).
fof(f7019,plain,
( spl171_494
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP21(X2,X1,X0)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_494])]) ).
fof(f1445,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP21(X2,X1,X0)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f861]) ).
fof(f861,plain,
! [X0,X1,X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| ~ sP21(X2,X1,X0) )
& ( sP21(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ sP22(X0,X1,X2) ),
inference(rectify,[],[f860]) ).
fof(f860,plain,
! [X2,X1,X0] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ~ sP21(X0,X1,X2) )
& ( sP21(X0,X1,X2)
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ sP22(X2,X1,X0) ),
inference(nnf_transformation,[],[f636]) ).
fof(f636,plain,
! [X2,X1,X0] :
( ( relation_dom_restriction(X0,X1) = X2
<=> sP21(X0,X1,X2) )
| ~ sP22(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f7017,plain,
spl171_493,
inference(avatar_split_clause,[],[f1380,f7015]) ).
fof(f7015,plain,
( spl171_493
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_493])]) ).
fof(f1380,plain,
! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f812]) ).
fof(f812,plain,
! [X0,X1,X2] :
( ( ( relation_composition(X1,X2) = X0
| ~ sP9(X2,X1,X0) )
& ( sP9(X2,X1,X0)
| relation_composition(X1,X2) != X0 ) )
| ~ sP10(X0,X1,X2) ),
inference(rectify,[],[f811]) ).
fof(f811,plain,
! [X2,X0,X1] :
( ( ( relation_composition(X0,X1) = X2
| ~ sP9(X1,X0,X2) )
& ( sP9(X1,X0,X2)
| relation_composition(X0,X1) != X2 ) )
| ~ sP10(X2,X0,X1) ),
inference(nnf_transformation,[],[f618]) ).
fof(f618,plain,
! [X2,X0,X1] :
( ( relation_composition(X0,X1) = X2
<=> sP9(X1,X0,X2) )
| ~ sP10(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f6914,plain,
( spl171_492
| ~ spl171_12
| ~ spl171_105
| ~ spl171_485 ),
inference(avatar_split_clause,[],[f6676,f6673,f2639,f2076,f6912]) ).
fof(f6912,plain,
( spl171_492
<=> ! [X0,X1] :
( sK160 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_492])]) ).
fof(f6673,plain,
( spl171_485
<=> ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_485])]) ).
fof(f6676,plain,
( ! [X0,X1] :
( sK160 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_485 ),
inference(forward_demodulation,[],[f6674,f2706]) ).
fof(f6674,plain,
( ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl171_485 ),
inference(avatar_component_clause,[],[f6673]) ).
fof(f6812,plain,
( spl171_491
| ~ spl171_12
| ~ spl171_105
| ~ spl171_479 ),
inference(avatar_split_clause,[],[f6624,f6620,f2639,f2076,f6810]) ).
fof(f6810,plain,
( spl171_491
<=> ! [X0,X1] :
( sK160 = X1
| complements_of_subsets(X0,X1) != sK160
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_491])]) ).
fof(f6620,plain,
( spl171_479
<=> ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_479])]) ).
fof(f6624,plain,
( ! [X0,X1] :
( sK160 = X1
| complements_of_subsets(X0,X1) != sK160
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_479 ),
inference(forward_demodulation,[],[f6623,f2706]) ).
fof(f6623,plain,
( ! [X0,X1] :
( complements_of_subsets(X0,X1) != sK160
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_479 ),
inference(forward_demodulation,[],[f6621,f2706]) ).
fof(f6621,plain,
( ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl171_479 ),
inference(avatar_component_clause,[],[f6620]) ).
fof(f6792,plain,
( spl171_490
| ~ spl171_170
| ~ spl171_474 ),
inference(avatar_split_clause,[],[f6634,f6573,f3017,f6789]) ).
fof(f3017,plain,
( spl171_170
<=> ! [X0,X1] : sP47(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_170])]) ).
fof(f6634,plain,
( sP47(relation_field(sK51),relation_rng(sK51),sK160)
| ~ spl171_170
| ~ spl171_474 ),
inference(superposition,[],[f3018,f6575]) ).
fof(f3018,plain,
( ! [X0,X1] : sP47(X1,X0,set_difference(X0,X1))
| ~ spl171_170 ),
inference(avatar_component_clause,[],[f3017]) ).
fof(f6692,plain,
spl171_489,
inference(avatar_split_clause,[],[f2012,f6690]) ).
fof(f6690,plain,
( spl171_489
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK146(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_489])]) ).
fof(f2012,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK146(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK146(X0,X1) != X0
| ~ in(sK146(X0,X1),X1) ),
inference(definition_unfolding,[],[f1662,f1065]) ).
fof(f1662,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK146(X0,X1) != X0
| ~ in(sK146(X0,X1),X1) ),
inference(cnf_transformation,[],[f987]) ).
fof(f6688,plain,
spl171_488,
inference(avatar_split_clause,[],[f1847,f6686]) ).
fof(f1847,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1)))
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1367,f1148]) ).
fof(f1367,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f489]) ).
fof(f489,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f6684,plain,
spl171_487,
inference(avatar_split_clause,[],[f1828,f6682]) ).
fof(f6682,plain,
( spl171_487
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_487])]) ).
fof(f1828,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1270,f1148]) ).
fof(f1270,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f460]) ).
fof(f460,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f459]) ).
fof(f459,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f210]) ).
fof(f210,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f6680,plain,
spl171_486,
inference(avatar_split_clause,[],[f1822,f6678]) ).
fof(f6678,plain,
( spl171_486
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_486])]) ).
fof(f1822,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1256,f1065]) ).
fof(f1256,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f442]) ).
fof(f442,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f441]) ).
fof(f441,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f6675,plain,
spl171_485,
inference(avatar_split_clause,[],[f1802,f6673]) ).
fof(f1802,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f1211,f1065,f1065]) ).
fof(f1211,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f750]) ).
fof(f750,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f749]) ).
fof(f749,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f244,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f6671,plain,
spl171_484,
inference(avatar_split_clause,[],[f1288,f6669]) ).
fof(f6669,plain,
( spl171_484
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_484])]) ).
fof(f1288,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f468]) ).
fof(f468,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f6667,plain,
spl171_483,
inference(avatar_split_clause,[],[f1281,f6665]) ).
fof(f6665,plain,
( spl171_483
<=> ! [X0,X3,X2,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_483])]) ).
fof(f1281,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f467]) ).
fof(f467,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f466]) ).
fof(f466,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f190]) ).
fof(f190,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f6663,plain,
spl171_482,
inference(avatar_split_clause,[],[f1244,f6661]) ).
fof(f6661,plain,
( spl171_482
<=> ! [X2,X0,X1] :
( in(sK75(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_482])]) ).
fof(f1244,plain,
! [X2,X0,X1] :
( in(sK75(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f767]) ).
fof(f6632,plain,
spl171_481,
inference(avatar_split_clause,[],[f1240,f6630]) ).
fof(f6630,plain,
( spl171_481
<=> ! [X2,X0,X1] :
( in(sK74(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_481])]) ).
fof(f1240,plain,
! [X2,X0,X1] :
( in(sK74(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f763]) ).
fof(f6628,plain,
spl171_480,
inference(avatar_split_clause,[],[f1229,f6626]) ).
fof(f1229,plain,
! [X2,X0,X1] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f193]) ).
fof(f193,axiom,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f6622,plain,
spl171_479,
inference(avatar_split_clause,[],[f1188,f6620]) ).
fof(f1188,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f404]) ).
fof(f404,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f258]) ).
fof(f258,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( empty_set = complements_of_subsets(X0,X1)
& empty_set != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f6618,plain,
spl171_478,
inference(avatar_split_clause,[],[f1172,f6616]) ).
fof(f6616,plain,
( spl171_478
<=> ! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_478])]) ).
fof(f1172,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f386]) ).
fof(f386,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(flattening,[],[f385]) ).
fof(f385,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f198]) ).
fof(f198,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f6614,plain,
spl171_477,
inference(avatar_split_clause,[],[f1138,f6612]) ).
fof(f6612,plain,
( spl171_477
<=> ! [X0,X1] :
( sP4(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_477])]) ).
fof(f1138,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f610]) ).
fof(f610,plain,
! [X0] :
( ! [X1] :
( sP4(X0,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f362,f609,f608,f607]) ).
fof(f609,plain,
! [X0,X1] :
( ( function_inverse(X0) = X1
<=> sP3(X1,X0) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f268]) ).
fof(f268,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f6610,plain,
spl171_476,
inference(avatar_split_clause,[],[f1114,f6608]) ).
fof(f1114,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f201]) ).
fof(f201,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f6606,plain,
spl171_475,
inference(avatar_split_clause,[],[f1078,f6604]) ).
fof(f6604,plain,
( spl171_475
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_475])]) ).
fof(f1078,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f222]) ).
fof(f222,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f6576,plain,
( spl171_474
| ~ spl171_253
| ~ spl171_424 ),
inference(avatar_split_clause,[],[f6027,f5981,f3880,f6573]) ).
fof(f3880,plain,
( spl171_253
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK160
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_253])]) ).
fof(f5981,plain,
( spl171_424
<=> subset(relation_rng(sK51),relation_field(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_424])]) ).
fof(f6027,plain,
( sK160 = set_difference(relation_rng(sK51),relation_field(sK51))
| ~ spl171_253
| ~ spl171_424 ),
inference(resolution,[],[f5983,f3881]) ).
fof(f3881,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK160 )
| ~ spl171_253 ),
inference(avatar_component_clause,[],[f3880]) ).
fof(f5983,plain,
( subset(relation_rng(sK51),relation_field(sK51))
| ~ spl171_424 ),
inference(avatar_component_clause,[],[f5981]) ).
fof(f6527,plain,
spl171_473,
inference(avatar_split_clause,[],[f1978,f6525]) ).
fof(f6525,plain,
( spl171_473
<=> ! [X2,X1] :
( sP41(X2,X1,complements_of_subsets(X1,X2))
| ~ sP42(complements_of_subsets(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_473])]) ).
fof(f1978,plain,
! [X2,X1] :
( sP41(X2,X1,complements_of_subsets(X1,X2))
| ~ sP42(complements_of_subsets(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1611]) ).
fof(f1611,plain,
! [X2,X0,X1] :
( sP41(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0
| ~ sP42(X0,X1,X2) ),
inference(cnf_transformation,[],[f960]) ).
fof(f6523,plain,
spl171_472,
inference(avatar_split_clause,[],[f1977,f6521]) ).
fof(f6521,plain,
( spl171_472
<=> ! [X2,X1] :
( sP39(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP40(relation_rng_restriction(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_472])]) ).
fof(f1977,plain,
! [X2,X1] :
( sP39(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP40(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1588]) ).
fof(f1588,plain,
! [X2,X0,X1] :
( sP39(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f953]) ).
fof(f6519,plain,
spl171_471,
inference(avatar_split_clause,[],[f1962,f6517]) ).
fof(f6517,plain,
( spl171_471
<=> ! [X6,X0,X1] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_471])]) ).
fof(f1962,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP29(X0,X1) ),
inference(equality_resolution,[],[f1491]) ).
fof(f1491,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f6515,plain,
spl171_470,
inference(avatar_split_clause,[],[f1958,f6513]) ).
fof(f6513,plain,
( spl171_470
<=> ! [X2,X1] :
( sP21(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP22(relation_dom_restriction(X2,X1),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_470])]) ).
fof(f1958,plain,
! [X2,X1] :
( sP21(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP22(relation_dom_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f1444]) ).
fof(f1444,plain,
! [X2,X0,X1] :
( sP21(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f861]) ).
fof(f6511,plain,
spl171_469,
inference(avatar_split_clause,[],[f1953,f6509]) ).
fof(f6509,plain,
( spl171_469
<=> ! [X2,X1] :
( sP9(X2,X1,relation_composition(X1,X2))
| ~ sP10(relation_composition(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_469])]) ).
fof(f1953,plain,
! [X2,X1] :
( sP9(X2,X1,relation_composition(X1,X2))
| ~ sP10(relation_composition(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1379]) ).
fof(f1379,plain,
! [X2,X0,X1] :
( sP9(X2,X1,X0)
| relation_composition(X1,X2) != X0
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f812]) ).
fof(f6507,plain,
spl171_468,
inference(avatar_split_clause,[],[f1653,f6505]) ).
fof(f6505,plain,
( spl171_468
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_468])]) ).
fof(f1653,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f6503,plain,
spl171_467,
inference(avatar_split_clause,[],[f1631,f6501]) ).
fof(f6501,plain,
( spl171_467
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_467])]) ).
fof(f1631,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f576]) ).
fof(f576,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f575]) ).
fof(f575,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f6499,plain,
spl171_466,
inference(avatar_split_clause,[],[f1610,f6497]) ).
fof(f6497,plain,
( spl171_466
<=> ! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_466])]) ).
fof(f1610,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f559]) ).
fof(f559,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f6495,plain,
( spl171_465
| ~ spl171_169
| ~ spl171_416 ),
inference(avatar_split_clause,[],[f5797,f5647,f3013,f6492]) ).
fof(f6492,plain,
( spl171_465
<=> sP46(relation_dom(sK51),relation_rng(sK51),relation_field(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_465])]) ).
fof(f3013,plain,
( spl171_169
<=> ! [X0,X1] : sP46(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_169])]) ).
fof(f5647,plain,
( spl171_416
<=> relation_field(sK51) = set_union2(relation_rng(sK51),relation_dom(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_416])]) ).
fof(f5797,plain,
( sP46(relation_dom(sK51),relation_rng(sK51),relation_field(sK51))
| ~ spl171_169
| ~ spl171_416 ),
inference(superposition,[],[f3014,f5649]) ).
fof(f5649,plain,
( relation_field(sK51) = set_union2(relation_rng(sK51),relation_dom(sK51))
| ~ spl171_416 ),
inference(avatar_component_clause,[],[f5647]) ).
fof(f3014,plain,
( ! [X0,X1] : sP46(X1,X0,set_union2(X0,X1))
| ~ spl171_169 ),
inference(avatar_component_clause,[],[f3013]) ).
fof(f6490,plain,
spl171_464,
inference(avatar_split_clause,[],[f1609,f6488]) ).
fof(f6488,plain,
( spl171_464
<=> ! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_464])]) ).
fof(f1609,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f558]) ).
fof(f558,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f139]) ).
fof(f139,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f6486,plain,
spl171_463,
inference(avatar_split_clause,[],[f1565,f6484]) ).
fof(f6484,plain,
( spl171_463
<=> ! [X0,X5,X1,X7] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_463])]) ).
fof(f1565,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f6482,plain,
spl171_462,
inference(avatar_split_clause,[],[f1546,f6480]) ).
fof(f6480,plain,
( spl171_462
<=> ! [X2,X0,X4] :
( in(X4,sK131(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK130(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_462])]) ).
fof(f1546,plain,
! [X2,X0,X4] :
( in(X4,sK131(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK130(X0)) ),
inference(cnf_transformation,[],[f932]) ).
fof(f932,plain,
! [X0] :
( ! [X2] :
( ( ! [X4] :
( in(X4,sK131(X0,X2))
| ~ subset(X4,X2) )
& in(sK131(X0,X2),sK130(X0)) )
| ~ in(X2,sK130(X0)) )
& ! [X5,X6] :
( in(X6,sK130(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK130(X0)) )
& in(X0,sK130(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130,sK131])],[f929,f931,f930]) ).
fof(f930,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK130(X0)) )
| ~ in(X2,sK130(X0)) )
& ! [X6,X5] :
( in(X6,sK130(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK130(X0)) )
& in(X0,sK130(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f931,plain,
! [X0,X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK130(X0)) )
=> ( ! [X4] :
( in(X4,sK131(X0,X2))
| ~ subset(X4,X2) )
& in(sK131(X0,X2),sK130(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f929,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f535]) ).
fof(f535,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(flattening,[],[f534]) ).
fof(f534,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
? [X1] :
( ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f312]) ).
fof(f312,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f6478,plain,
spl171_461,
inference(avatar_split_clause,[],[f1503,f6476]) ).
fof(f6476,plain,
( spl171_461
<=> ! [X2,X4,X0,X1] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_461])]) ).
fof(f1503,plain,
! [X2,X0,X1,X4] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f6474,plain,
spl171_460,
inference(avatar_split_clause,[],[f1489,f6472]) ).
fof(f6472,plain,
( spl171_460
<=> ! [X5,X0,X1] :
( in(sK117(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_460])]) ).
fof(f1489,plain,
! [X0,X1,X5] :
( in(sK117(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f892]) ).
fof(f6470,plain,
spl171_459,
inference(avatar_split_clause,[],[f1365,f6468]) ).
fof(f6468,plain,
( spl171_459
<=> ! [X2,X0] :
( sP7(X0)
| ~ disjoint(fiber(X0,X2),sK77(X0))
| ~ in(X2,sK77(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_459])]) ).
fof(f1365,plain,
! [X2,X0] :
( sP7(X0)
| ~ disjoint(fiber(X0,X2),sK77(X0))
| ~ in(X2,sK77(X0)) ),
inference(cnf_transformation,[],[f798]) ).
fof(f6466,plain,
spl171_458,
inference(avatar_split_clause,[],[f1349,f6464]) ).
fof(f6464,plain,
( spl171_458
<=> ! [X0] :
( sP5(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_458])]) ).
fof(f1349,plain,
! [X0] :
( sP5(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f788,plain,
! [X0] :
( ( sP5(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ sP5(X0) ) ),
inference(flattening,[],[f787]) ).
fof(f787,plain,
! [X0] :
( ( sP5(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f611]) ).
fof(f611,plain,
! [X0] :
( sP5(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f6246,plain,
( spl171_457
| ~ spl171_12
| ~ spl171_105 ),
inference(avatar_split_clause,[],[f3404,f2639,f2076,f6244]) ).
fof(f6244,plain,
( spl171_457
<=> ! [X0,X1] :
( sK160 = X0
| in(sK70(X0),X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_457])]) ).
fof(f3404,plain,
( ! [X0,X1] :
( sK160 = X0
| in(sK70(X0),X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl171_12
| ~ spl171_105 ),
inference(forward_demodulation,[],[f1157,f2706]) ).
fof(f1157,plain,
! [X0,X1] :
( in(sK70(X0),X0)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f732]) ).
fof(f6241,plain,
spl171_456,
inference(avatar_split_clause,[],[f1901,f6239]) ).
fof(f6239,plain,
( spl171_456
<=> ! [X2,X0,X3] :
( relation(X0)
| sK125(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_456])]) ).
fof(f1901,plain,
! [X2,X3,X0] :
( relation(X0)
| sK125(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1539,f1762]) ).
fof(f1539,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK125(X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f6237,plain,
spl171_455,
inference(avatar_split_clause,[],[f1788,f6235]) ).
fof(f6235,plain,
( spl171_455
<=> ! [X0,X1] :
( in(sK68(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_455])]) ).
fof(f1788,plain,
! [X0,X1] :
( in(sK68(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1150,f1148]) ).
fof(f1150,plain,
! [X0,X1] :
( in(sK68(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f728]) ).
fof(f728,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK68(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f366,f727]) ).
fof(f727,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK68(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f366,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f6233,plain,
spl171_454,
inference(avatar_split_clause,[],[f1257,f6231]) ).
fof(f6231,plain,
( spl171_454
<=> ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_454])]) ).
fof(f1257,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f444]) ).
fof(f444,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f443]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f269]) ).
fof(f269,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f6229,plain,
spl171_453,
inference(avatar_split_clause,[],[f1250,f6227]) ).
fof(f6227,plain,
( spl171_453
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_453])]) ).
fof(f1250,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f771]) ).
fof(f6225,plain,
spl171_452,
inference(avatar_split_clause,[],[f1247,f6223]) ).
fof(f6223,plain,
( spl171_452
<=> ! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_452])]) ).
fof(f1247,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f769]) ).
fof(f6221,plain,
spl171_451,
inference(avatar_split_clause,[],[f1236,f6219]) ).
fof(f6219,plain,
( spl171_451
<=> ! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_451])]) ).
fof(f1236,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f759]) ).
fof(f6217,plain,
spl171_450,
inference(avatar_split_clause,[],[f1230,f6215]) ).
fof(f6215,plain,
( spl171_450
<=> ! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_450])]) ).
fof(f1230,plain,
! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f428]) ).
fof(f428,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f427]) ).
fof(f427,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f206]) ).
fof(f206,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f6213,plain,
spl171_449,
inference(avatar_split_clause,[],[f1123,f6211]) ).
fof(f6211,plain,
( spl171_449
<=> ! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_449])]) ).
fof(f1123,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f270]) ).
fof(f270,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f6209,plain,
spl171_448,
inference(avatar_split_clause,[],[f1122,f6207]) ).
fof(f6207,plain,
( spl171_448
<=> ! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_448])]) ).
fof(f1122,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f6205,plain,
spl171_447,
inference(avatar_split_clause,[],[f1116,f6203]) ).
fof(f6203,plain,
( spl171_447
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_447])]) ).
fof(f1116,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f223]) ).
fof(f223,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f6201,plain,
( spl171_445
| ~ spl171_446
| ~ spl171_157
| ~ spl171_416 ),
inference(avatar_split_clause,[],[f5795,f5647,f2965,f6198,f6194]) ).
fof(f6194,plain,
( spl171_445
<=> empty(relation_rng(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_445])]) ).
fof(f6198,plain,
( spl171_446
<=> empty(relation_field(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_446])]) ).
fof(f2965,plain,
( spl171_157
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_157])]) ).
fof(f5795,plain,
( ~ empty(relation_field(sK51))
| empty(relation_rng(sK51))
| ~ spl171_157
| ~ spl171_416 ),
inference(superposition,[],[f2966,f5649]) ).
fof(f2966,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl171_157 ),
inference(avatar_component_clause,[],[f2965]) ).
fof(f6192,plain,
spl171_444,
inference(avatar_split_clause,[],[f1115,f6190]) ).
fof(f1115,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f6076,plain,
( ~ spl171_443
| ~ spl171_122
| ~ spl171_424 ),
inference(avatar_split_clause,[],[f6025,f5981,f2802,f6073]) ).
fof(f6073,plain,
( spl171_443
<=> proper_subset(relation_field(sK51),relation_rng(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_443])]) ).
fof(f6025,plain,
( ~ proper_subset(relation_field(sK51),relation_rng(sK51))
| ~ spl171_122
| ~ spl171_424 ),
inference(resolution,[],[f5983,f2803]) ).
fof(f6067,plain,
spl171_442,
inference(avatar_split_clause,[],[f1935,f6065]) ).
fof(f6065,plain,
( spl171_442
<=> ! [X2,X1,X3] :
( sP2(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_442])]) ).
fof(f1935,plain,
! [X2,X3,X1] :
( sP2(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ),
inference(equality_resolution,[],[f1137]) ).
fof(f1137,plain,
! [X2,X3,X0,X1] :
( sP2(X0,X1,X2,X3)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f721]) ).
fof(f6063,plain,
spl171_441,
inference(avatar_split_clause,[],[f1728,f6061]) ).
fof(f6061,plain,
( spl171_441
<=> ! [X0,X3,X2,X1] :
( unordered_triple(X0,X1,X2) = X3
| ~ sP49(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_441])]) ).
fof(f1728,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| ~ sP49(X2,X1,X0,X3) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ~ sP49(X2,X1,X0,X3) )
& ( sP49(X2,X1,X0,X3)
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(nnf_transformation,[],[f681]) ).
fof(f681,plain,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> sP49(X2,X1,X0,X3) ),
inference(definition_folding,[],[f603,f680]) ).
fof(f603,plain,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> ! [X4] :
( in(X4,X3)
<=> ~ ( X2 != X4
& X1 != X4
& X0 != X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
fof(f6059,plain,
spl171_440,
inference(avatar_split_clause,[],[f1652,f6057]) ).
fof(f6057,plain,
( spl171_440
<=> ! [X5,X0,X1] :
( in(sK145(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_440])]) ).
fof(f1652,plain,
! [X0,X1,X5] :
( in(sK145(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f6055,plain,
spl171_439,
inference(avatar_split_clause,[],[f1651,f6053]) ).
fof(f6053,plain,
( spl171_439
<=> ! [X5,X0,X1] :
( in(X5,sK145(X0,X5))
| ~ in(X5,X1)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_439])]) ).
fof(f1651,plain,
! [X0,X1,X5] :
( in(X5,sK145(X0,X5))
| ~ in(X5,X1)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f982]) ).
fof(f6051,plain,
spl171_438,
inference(avatar_split_clause,[],[f1615,f6049]) ).
fof(f6049,plain,
( spl171_438
<=> ! [X2,X0,X1] :
( sP41(X0,X1,X2)
| element(sK140(X0,X1,X2),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_438])]) ).
fof(f1615,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| element(sK140(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f965]) ).
fof(f6047,plain,
spl171_437,
inference(avatar_split_clause,[],[f1608,f6045]) ).
fof(f6045,plain,
( spl171_437
<=> ! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_437])]) ).
fof(f1608,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f557]) ).
fof(f557,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f6043,plain,
spl171_436,
inference(avatar_split_clause,[],[f1607,f6041]) ).
fof(f6041,plain,
( spl171_436
<=> ! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_436])]) ).
fof(f1607,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f556]) ).
fof(f556,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f6039,plain,
spl171_435,
inference(avatar_split_clause,[],[f1606,f6037]) ).
fof(f6037,plain,
( spl171_435
<=> ! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_435])]) ).
fof(f1606,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f555]) ).
fof(f555,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f174]) ).
fof(f174,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f6024,plain,
spl171_434,
inference(avatar_split_clause,[],[f1605,f6022]) ).
fof(f6022,plain,
( spl171_434
<=> ! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_434])]) ).
fof(f1605,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f554]) ).
fof(f554,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f175]) ).
fof(f175,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f6020,plain,
spl171_433,
inference(avatar_split_clause,[],[f1604,f6018]) ).
fof(f6018,plain,
( spl171_433
<=> ! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_433])]) ).
fof(f1604,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f553]) ).
fof(f553,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f6016,plain,
spl171_432,
inference(avatar_split_clause,[],[f1603,f6014]) ).
fof(f6014,plain,
( spl171_432
<=> ! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_432])]) ).
fof(f1603,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f552]) ).
fof(f552,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f6012,plain,
spl171_431,
inference(avatar_split_clause,[],[f1567,f6010]) ).
fof(f6010,plain,
( spl171_431
<=> ! [X5,X1,X0] :
( in(X5,X1)
| ~ in(X5,sK135(X0,X5))
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_431])]) ).
fof(f1567,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK135(X0,X5))
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f6008,plain,
spl171_430,
inference(avatar_split_clause,[],[f1566,f6006]) ).
fof(f6006,plain,
( spl171_430
<=> ! [X5,X1,X0] :
( in(X5,X1)
| in(sK135(X0,X5),X0)
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_430])]) ).
fof(f1566,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK135(X0,X5),X0)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f6004,plain,
spl171_429,
inference(avatar_split_clause,[],[f1544,f6002]) ).
fof(f6002,plain,
( spl171_429
<=> ! [X6,X0,X5] :
( in(X6,sK130(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK130(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_429])]) ).
fof(f1544,plain,
! [X0,X6,X5] :
( in(X6,sK130(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK130(X0)) ),
inference(cnf_transformation,[],[f932]) ).
fof(f6000,plain,
spl171_428,
inference(avatar_split_clause,[],[f1510,f5998]) ).
fof(f5998,plain,
( spl171_428
<=> ! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP33(X0,X1,X2)
| ~ sP34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_428])]) ).
fof(f1510,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP33(X0,X1,X2)
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f900]) ).
fof(f900,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP33(X0,X1,X2) )
& ( sP33(X0,X1,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP34(X0) ),
inference(nnf_transformation,[],[f654]) ).
fof(f654,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP33(X0,X1,X2) )
| ~ sP34(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f5996,plain,
spl171_427,
inference(avatar_split_clause,[],[f1502,f5994]) ).
fof(f5994,plain,
( spl171_427
<=> ! [X4,X0,X1,X2] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_427])]) ).
fof(f1502,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f899]) ).
fof(f5992,plain,
spl171_426,
inference(avatar_split_clause,[],[f1501,f5990]) ).
fof(f5990,plain,
( spl171_426
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP31(X1,X0,X2)
| ~ sP32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_426])]) ).
fof(f1501,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP31(X1,X0,X2)
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f894]) ).
fof(f894,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP31(X1,X0,X2) )
& ( sP31(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP32(X0) ),
inference(nnf_transformation,[],[f651]) ).
fof(f651,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP31(X1,X0,X2) )
| ~ sP32(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f5988,plain,
spl171_425,
inference(avatar_split_clause,[],[f1484,f5986]) ).
fof(f5986,plain,
( spl171_425
<=> ! [X0] :
( sP27(X0)
| apply(X0,sK113(X0)) = apply(X0,sK114(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_425])]) ).
fof(f1484,plain,
! [X0] :
( sP27(X0)
| apply(X0,sK113(X0)) = apply(X0,sK114(X0)) ),
inference(cnf_transformation,[],[f885]) ).
fof(f5984,plain,
( spl171_424
| ~ spl171_92
| ~ spl171_416 ),
inference(avatar_split_clause,[],[f5794,f5647,f2584,f5981]) ).
fof(f2584,plain,
( spl171_92
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_92])]) ).
fof(f5794,plain,
( subset(relation_rng(sK51),relation_field(sK51))
| ~ spl171_92
| ~ spl171_416 ),
inference(superposition,[],[f2585,f5649]) ).
fof(f2585,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl171_92 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f5979,plain,
spl171_423,
inference(avatar_split_clause,[],[f1478,f5977]) ).
fof(f5977,plain,
( spl171_423
<=> ! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_423])]) ).
fof(f1478,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f518]) ).
fof(f518,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f517]) ).
fof(f517,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> relation_inverse(X0) = function_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f5975,plain,
spl171_422,
inference(avatar_split_clause,[],[f1463,f5973]) ).
fof(f5973,plain,
( spl171_422
<=> ! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP25(X1,X0,X2)
| ~ sP26(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_422])]) ).
fof(f1463,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP25(X1,X0,X2)
| ~ sP26(X0) ),
inference(cnf_transformation,[],[f874]) ).
fof(f874,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP25(X1,X0,X2) )
& ( sP25(X1,X0,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP26(X0) ),
inference(nnf_transformation,[],[f642]) ).
fof(f642,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP25(X1,X0,X2) )
| ~ sP26(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f5971,plain,
spl171_421,
inference(avatar_split_clause,[],[f1454,f5969]) ).
fof(f5969,plain,
( spl171_421
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP23(X1,X0,X2)
| ~ sP24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_421])]) ).
fof(f1454,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP23(X1,X0,X2)
| ~ sP24(X0) ),
inference(cnf_transformation,[],[f867]) ).
fof(f867,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP23(X1,X0,X2) )
& ( sP23(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP24(X0) ),
inference(nnf_transformation,[],[f639]) ).
fof(f639,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP23(X1,X0,X2) )
| ~ sP24(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f5666,plain,
( spl171_420
| ~ spl171_12
| ~ spl171_105 ),
inference(avatar_split_clause,[],[f3403,f2639,f2076,f5664]) ).
fof(f5664,plain,
( spl171_420
<=> ! [X0,X1] :
( sK160 = X0
| ordinal(sK70(X0))
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_420])]) ).
fof(f3403,plain,
( ! [X0,X1] :
( sK160 = X0
| ordinal(sK70(X0))
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl171_12
| ~ spl171_105 ),
inference(forward_demodulation,[],[f1156,f2706]) ).
fof(f1156,plain,
! [X0,X1] :
( ordinal(sK70(X0))
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f732]) ).
fof(f5662,plain,
spl171_419,
inference(avatar_split_clause,[],[f1929,f5660]) ).
fof(f5660,plain,
( spl171_419
<=> ! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP48(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_419])]) ).
fof(f1929,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP48(X1,X0,X2) ),
inference(definition_unfolding,[],[f1717,f1148]) ).
fof(f1717,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP48(X1,X0,X2) ),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP48(X1,X0,X2) )
& ( sP48(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f679]) ).
fof(f679,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP48(X1,X0,X2) ),
inference(definition_folding,[],[f43,f678]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5658,plain,
spl171_418,
inference(avatar_split_clause,[],[f1905,f5656]) ).
fof(f5656,plain,
( spl171_418
<=> ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_418])]) ).
fof(f1905,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f1557,f1148,f1148]) ).
fof(f1557,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f5654,plain,
spl171_417,
inference(avatar_split_clause,[],[f1274,f5652]) ).
fof(f5652,plain,
( spl171_417
<=> ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_417])]) ).
fof(f1274,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f777]) ).
fof(f777,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f776]) ).
fof(f776,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f5650,plain,
( spl171_416
| ~ spl171_1
| ~ spl171_405 ),
inference(avatar_split_clause,[],[f5593,f5470,f2021,f5647]) ).
fof(f5470,plain,
( spl171_405
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_405])]) ).
fof(f5593,plain,
( relation_field(sK51) = set_union2(relation_rng(sK51),relation_dom(sK51))
| ~ spl171_1
| ~ spl171_405 ),
inference(resolution,[],[f5471,f2023]) ).
fof(f5471,plain,
( ! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0)) )
| ~ spl171_405 ),
inference(avatar_component_clause,[],[f5470]) ).
fof(f5645,plain,
spl171_415,
inference(avatar_split_clause,[],[f1271,f5643]) ).
fof(f5643,plain,
( spl171_415
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_415])]) ).
fof(f1271,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f462]) ).
fof(f462,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f461]) ).
fof(f461,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f299]) ).
fof(f299,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f5641,plain,
spl171_414,
inference(avatar_split_clause,[],[f1249,f5639]) ).
fof(f5639,plain,
( spl171_414
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_414])]) ).
fof(f1249,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f771]) ).
fof(f5637,plain,
spl171_413,
inference(avatar_split_clause,[],[f1246,f5635]) ).
fof(f5635,plain,
( spl171_413
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_413])]) ).
fof(f1246,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f769]) ).
fof(f5633,plain,
spl171_412,
inference(avatar_split_clause,[],[f1190,f5631]) ).
fof(f5631,plain,
( spl171_412
<=> ! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_412])]) ).
fof(f1190,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f407]) ).
fof(f407,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f196]) ).
fof(f196,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f5629,plain,
spl171_411,
inference(avatar_split_clause,[],[f1168,f5627]) ).
fof(f1168,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f207]) ).
fof(f207,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f5625,plain,
spl171_410,
inference(avatar_split_clause,[],[f1167,f5623]) ).
fof(f1167,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f209]) ).
fof(f209,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
fof(f5621,plain,
spl171_409,
inference(avatar_split_clause,[],[f1142,f5619]) ).
fof(f5619,plain,
( spl171_409
<=> ! [X4,X0,X3] :
( in(X4,sK67(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK67(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_409])]) ).
fof(f1142,plain,
! [X3,X0,X4] :
( in(X4,sK67(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK67(X0)) ),
inference(cnf_transformation,[],[f726]) ).
fof(f726,plain,
! [X0] :
( ! [X2] :
( in(powerset(X2),sK67(X0))
| ~ in(X2,sK67(X0)) )
& ! [X3,X4] :
( in(X4,sK67(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK67(X0)) )
& in(X0,sK67(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f724,f725]) ).
fof(f725,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(powerset(X2),sK67(X0))
| ~ in(X2,sK67(X0)) )
& ! [X4,X3] :
( in(X4,sK67(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK67(X0)) )
& in(X0,sK67(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f724,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f365]) ).
fof(f365,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(flattening,[],[f364]) ).
fof(f364,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f309]) ).
fof(f309,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f5617,plain,
spl171_408,
inference(avatar_split_clause,[],[f1113,f5615]) ).
fof(f5615,plain,
( spl171_408
<=> ! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_408])]) ).
fof(f1113,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f254]) ).
fof(f254,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f5613,plain,
spl171_407,
inference(avatar_split_clause,[],[f1112,f5611]) ).
fof(f5611,plain,
( spl171_407
<=> ! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_407])]) ).
fof(f1112,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f255]) ).
fof(f255,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f5512,plain,
( spl171_406
| ~ spl171_12
| ~ spl171_37
| ~ spl171_105
| ~ spl171_334 ),
inference(avatar_split_clause,[],[f4583,f4579,f2639,f2201,f2076,f5509]) ).
fof(f5509,plain,
( spl171_406
<=> sP1(sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_406])]) ).
fof(f2201,plain,
( spl171_37
<=> empty(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_37])]) ).
fof(f4579,plain,
( spl171_334
<=> sP1(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_334])]) ).
fof(f4583,plain,
( sP1(sK160)
| ~ spl171_12
| ~ spl171_37
| ~ spl171_105
| ~ spl171_334 ),
inference(forward_demodulation,[],[f4581,f2711]) ).
fof(f2711,plain,
( sK160 = sK169
| ~ spl171_12
| ~ spl171_37
| ~ spl171_105 ),
inference(forward_demodulation,[],[f2708,f2706]) ).
fof(f2708,plain,
( empty_set = sK169
| ~ spl171_37
| ~ spl171_105 ),
inference(resolution,[],[f2640,f2203]) ).
fof(f2203,plain,
( empty(sK169)
| ~ spl171_37 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f4581,plain,
( sP1(sK169)
| ~ spl171_334 ),
inference(avatar_component_clause,[],[f4579]) ).
fof(f5472,plain,
( spl171_405
| ~ spl171_204
| ~ spl171_385 ),
inference(avatar_split_clause,[],[f5386,f5383,f3377,f5470]) ).
fof(f3377,plain,
( spl171_204
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_204])]) ).
fof(f5383,plain,
( spl171_385
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_385])]) ).
fof(f5386,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) )
| ~ spl171_204
| ~ spl171_385 ),
inference(forward_demodulation,[],[f5384,f3378]) ).
fof(f3378,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl171_204 ),
inference(avatar_component_clause,[],[f3377]) ).
fof(f5384,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) )
| ~ spl171_385 ),
inference(avatar_component_clause,[],[f5383]) ).
fof(f5466,plain,
spl171_404,
inference(avatar_split_clause,[],[f1711,f5464]) ).
fof(f5464,plain,
( spl171_404
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_404])]) ).
fof(f1711,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f5462,plain,
spl171_403,
inference(avatar_split_clause,[],[f1710,f5460]) ).
fof(f5460,plain,
( spl171_403
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_403])]) ).
fof(f1710,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f5458,plain,
spl171_402,
inference(avatar_split_clause,[],[f1703,f5456]) ).
fof(f1703,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f5454,plain,
spl171_401,
inference(avatar_split_clause,[],[f1702,f5452]) ).
fof(f1702,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f5450,plain,
spl171_400,
inference(avatar_split_clause,[],[f1696,f5448]) ).
fof(f5448,plain,
( spl171_400
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_400])]) ).
fof(f1696,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f5446,plain,
spl171_399,
inference(avatar_split_clause,[],[f1695,f5444]) ).
fof(f5444,plain,
( spl171_399
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_399])]) ).
fof(f1695,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f5442,plain,
spl171_398,
inference(avatar_split_clause,[],[f1673,f5440]) ).
fof(f5440,plain,
( spl171_398
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_398])]) ).
fof(f1673,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f597]) ).
fof(f597,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f596]) ).
fof(f596,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f265]) ).
fof(f265,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f5438,plain,
spl171_397,
inference(avatar_split_clause,[],[f1672,f5436]) ).
fof(f5436,plain,
( spl171_397
<=> ! [X0,X1,X3] :
( ~ in(X3,sK148(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_397])]) ).
fof(f1672,plain,
! [X3,X0,X1] :
( ~ in(X3,sK148(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f994]) ).
fof(f994,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK148(X1))
| ~ in(X3,X1) )
& in(sK148(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f595,f993]) ).
fof(f993,plain,
! [X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
=> ( ! [X3] :
( ~ in(X3,sK148(X1))
| ~ in(X3,X1) )
& in(sK148(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f595,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f291]) ).
fof(f291,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f5432,plain,
spl171_396,
inference(avatar_split_clause,[],[f1623,f5430]) ).
fof(f5430,plain,
( spl171_396
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_396])]) ).
fof(f1623,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f966]) ).
fof(f966,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f568]) ).
fof(f568,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f567]) ).
fof(f567,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f5428,plain,
spl171_395,
inference(avatar_split_clause,[],[f1622,f5426]) ).
fof(f5426,plain,
( spl171_395
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_395])]) ).
fof(f1622,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f966]) ).
fof(f5424,plain,
spl171_394,
inference(avatar_split_clause,[],[f1621,f5422]) ).
fof(f5422,plain,
( spl171_394
<=> ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_394])]) ).
fof(f1621,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f566]) ).
fof(f566,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f565]) ).
fof(f565,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f5420,plain,
spl171_393,
inference(avatar_split_clause,[],[f1602,f5418]) ).
fof(f5418,plain,
( spl171_393
<=> ! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_393])]) ).
fof(f1602,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f551]) ).
fof(f551,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f5416,plain,
spl171_392,
inference(avatar_split_clause,[],[f1580,f5414]) ).
fof(f5414,plain,
( spl171_392
<=> ! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP37(X1,X0)
| ~ sP38(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_392])]) ).
fof(f1580,plain,
! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP37(X1,X0)
| ~ sP38(X0,X1) ),
inference(cnf_transformation,[],[f946]) ).
fof(f946,plain,
! [X0,X1] :
( ( ( identity_relation(X1) = X0
| ~ sP37(X1,X0) )
& ( sP37(X1,X0)
| identity_relation(X1) != X0 ) )
| ~ sP38(X0,X1) ),
inference(rectify,[],[f945]) ).
fof(f945,plain,
! [X1,X0] :
( ( ( identity_relation(X0) = X1
| ~ sP37(X0,X1) )
& ( sP37(X0,X1)
| identity_relation(X0) != X1 ) )
| ~ sP38(X1,X0) ),
inference(nnf_transformation,[],[f660]) ).
fof(f660,plain,
! [X1,X0] :
( ( identity_relation(X0) = X1
<=> sP37(X0,X1) )
| ~ sP38(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f5412,plain,
spl171_391,
inference(avatar_split_clause,[],[f1564,f5410]) ).
fof(f5410,plain,
( spl171_391
<=> ! [X0,X1] :
( set_meet(X1) = X0
| ~ sP35(X1,X0)
| ~ sP36(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_391])]) ).
fof(f1564,plain,
! [X0,X1] :
( set_meet(X1) = X0
| ~ sP35(X1,X0)
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f937]) ).
fof(f937,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP35(X1,X0) )
& ( sP35(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP36(X0,X1) ),
inference(rectify,[],[f936]) ).
fof(f936,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP35(X0,X1) )
& ( sP35(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP36(X1,X0) ),
inference(nnf_transformation,[],[f657]) ).
fof(f657,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP35(X0,X1) )
| ~ sP36(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f5408,plain,
spl171_390,
inference(avatar_split_clause,[],[f1545,f5406]) ).
fof(f5406,plain,
( spl171_390
<=> ! [X2,X0] :
( in(sK131(X0,X2),sK130(X0))
| ~ in(X2,sK130(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_390])]) ).
fof(f1545,plain,
! [X2,X0] :
( in(sK131(X0,X2),sK130(X0))
| ~ in(X2,sK130(X0)) ),
inference(cnf_transformation,[],[f932]) ).
fof(f5404,plain,
spl171_389,
inference(avatar_split_clause,[],[f1422,f5402]) ).
fof(f5402,plain,
( spl171_389
<=> ! [X0,X1] :
( sP17(X0,X1)
| sK94(X0,X1) != sK95(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_389])]) ).
fof(f1422,plain,
! [X0,X1] :
( sP17(X0,X1)
| sK94(X0,X1) != sK95(X0,X1) ),
inference(cnf_transformation,[],[f842]) ).
fof(f5400,plain,
spl171_388,
inference(avatar_split_clause,[],[f1415,f5398]) ).
fof(f5398,plain,
( spl171_388
<=> ! [X0,X1] :
( sP15(X0,X1)
| sK92(X0,X1) != sK93(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_388])]) ).
fof(f1415,plain,
! [X0,X1] :
( sP15(X0,X1)
| sK92(X0,X1) != sK93(X0,X1) ),
inference(cnf_transformation,[],[f837]) ).
fof(f5396,plain,
spl171_387,
inference(avatar_split_clause,[],[f1398,f5394]) ).
fof(f5394,plain,
( spl171_387
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK89(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_387])]) ).
fof(f1398,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK89(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f5390,plain,
spl171_386,
inference(avatar_split_clause,[],[f1387,f5388]) ).
fof(f5388,plain,
( spl171_386
<=> ! [X2,X0,X1] :
( sP10(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_386])]) ).
fof(f1387,plain,
! [X2,X0,X1] :
( sP10(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f619]) ).
fof(f619,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP10(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f493,f618,f617]) ).
fof(f493,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f5385,plain,
spl171_385,
inference(avatar_split_clause,[],[f1341,f5383]) ).
fof(f1341,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f482]) ).
fof(f482,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f5381,plain,
spl171_384,
inference(avatar_split_clause,[],[f1136,f5379]) ).
fof(f5379,plain,
( spl171_384
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2,X3)
| apply(X3,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_384])]) ).
fof(f1136,plain,
! [X2,X3,X0,X1] :
( sP2(X0,X1,X2,X3)
| apply(X3,X0) = X1 ),
inference(cnf_transformation,[],[f721]) ).
fof(f5377,plain,
spl171_383,
inference(avatar_split_clause,[],[f1125,f5375]) ).
fof(f5375,plain,
( spl171_383
<=> ! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_383])]) ).
fof(f1125,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f713]) ).
fof(f713,plain,
! [X0,X1] :
( ( ( function_inverse(X0) = X1
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| function_inverse(X0) != X1 ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f609]) ).
fof(f5339,plain,
( spl171_382
| ~ spl171_12
| ~ spl171_105
| ~ spl171_377 ),
inference(avatar_split_clause,[],[f5046,f5043,f2639,f2076,f5337]) ).
fof(f5337,plain,
( spl171_382
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK160
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_382])]) ).
fof(f5043,plain,
( spl171_377
<=> ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_377])]) ).
fof(f5046,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK160
| ~ disjoint(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_377 ),
inference(forward_demodulation,[],[f5044,f2706]) ).
fof(f5044,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl171_377 ),
inference(avatar_component_clause,[],[f5043]) ).
fof(f5335,plain,
( spl171_381
| ~ spl171_12
| ~ spl171_105
| ~ spl171_376 ),
inference(avatar_split_clause,[],[f5041,f5038,f2639,f2076,f5333]) ).
fof(f5333,plain,
( spl171_381
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK160
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_381])]) ).
fof(f5038,plain,
( spl171_376
<=> ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_376])]) ).
fof(f5041,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK160
| disjoint(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_376 ),
inference(forward_demodulation,[],[f5039,f2706]) ).
fof(f5039,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) )
| ~ spl171_376 ),
inference(avatar_component_clause,[],[f5038]) ).
fof(f5141,plain,
( spl171_380
| ~ spl171_1
| ~ spl171_361 ),
inference(avatar_split_clause,[],[f5070,f4970,f2021,f5139]) ).
fof(f5139,plain,
( spl171_380
<=> ! [X0] : relation_dom_restriction(sK51,X0) = relation_composition(identity_relation(X0),sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_380])]) ).
fof(f4970,plain,
( spl171_361
<=> ! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_361])]) ).
fof(f5070,plain,
( ! [X0] : relation_dom_restriction(sK51,X0) = relation_composition(identity_relation(X0),sK51)
| ~ spl171_1
| ~ spl171_361 ),
inference(resolution,[],[f4971,f2023]) ).
fof(f4971,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) )
| ~ spl171_361 ),
inference(avatar_component_clause,[],[f4970]) ).
fof(f5054,plain,
( spl171_379
| ~ spl171_12
| ~ spl171_105
| ~ spl171_360 ),
inference(avatar_split_clause,[],[f4968,f4964,f2639,f2076,f5052]) ).
fof(f5052,plain,
( spl171_379
<=> ! [X0] :
( relation_rng(X0) != sK160
| relation_dom(X0) = sK160
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_379])]) ).
fof(f4964,plain,
( spl171_360
<=> ! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_360])]) ).
fof(f4968,plain,
( ! [X0] :
( relation_rng(X0) != sK160
| relation_dom(X0) = sK160
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_360 ),
inference(forward_demodulation,[],[f4967,f2706]) ).
fof(f4967,plain,
( ! [X0] :
( relation_dom(X0) = sK160
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_360 ),
inference(forward_demodulation,[],[f4965,f2706]) ).
fof(f4965,plain,
( ! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl171_360 ),
inference(avatar_component_clause,[],[f4964]) ).
fof(f5050,plain,
( spl171_378
| ~ spl171_12
| ~ spl171_105
| ~ spl171_359 ),
inference(avatar_split_clause,[],[f4962,f4958,f2639,f2076,f5048]) ).
fof(f5048,plain,
( spl171_378
<=> ! [X0] :
( relation_dom(X0) != sK160
| relation_rng(X0) = sK160
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_378])]) ).
fof(f4958,plain,
( spl171_359
<=> ! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_359])]) ).
fof(f4962,plain,
( ! [X0] :
( relation_dom(X0) != sK160
| relation_rng(X0) = sK160
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_359 ),
inference(forward_demodulation,[],[f4961,f2706]) ).
fof(f4961,plain,
( ! [X0] :
( relation_rng(X0) = sK160
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_359 ),
inference(forward_demodulation,[],[f4959,f2706]) ).
fof(f4959,plain,
( ! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl171_359 ),
inference(avatar_component_clause,[],[f4958]) ).
fof(f5045,plain,
spl171_377,
inference(avatar_split_clause,[],[f1920,f5043]) ).
fof(f1920,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1646,f1148]) ).
fof(f1646,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f972]) ).
fof(f972,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f5040,plain,
spl171_376,
inference(avatar_split_clause,[],[f1919,f5038]) ).
fof(f1919,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f1647,f1148]) ).
fof(f1647,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f972]) ).
fof(f5034,plain,
spl171_375,
inference(avatar_split_clause,[],[f1918,f5032]) ).
fof(f5032,plain,
( spl171_375
<=> ! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_375])]) ).
fof(f1918,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1638,f1148]) ).
fof(f1638,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f586]) ).
fof(f586,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f585]) ).
fof(f585,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f5030,plain,
spl171_374,
inference(avatar_split_clause,[],[f1824,f5028]) ).
fof(f5028,plain,
( spl171_374
<=> ! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_374])]) ).
fof(f1824,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f1259,f1065]) ).
fof(f1259,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f446]) ).
fof(f446,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f300]) ).
fof(f300,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f5026,plain,
spl171_373,
inference(avatar_split_clause,[],[f1823,f5024]) ).
fof(f5024,plain,
( spl171_373
<=> ! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_373])]) ).
fof(f1823,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f1258,f1065]) ).
fof(f1258,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f445]) ).
fof(f445,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f307]) ).
fof(f307,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f5022,plain,
spl171_372,
inference(avatar_split_clause,[],[f1811,f5020]) ).
fof(f5020,plain,
( spl171_372
<=> ! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_372])]) ).
fof(f1811,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f1225,f1065]) ).
fof(f1225,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f757]) ).
fof(f757,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f281]) ).
fof(f281,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f5018,plain,
spl171_371,
inference(avatar_split_clause,[],[f1810,f5016]) ).
fof(f5016,plain,
( spl171_371
<=> ! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_371])]) ).
fof(f1810,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f1226,f1065]) ).
fof(f1226,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f757]) ).
fof(f5014,plain,
spl171_370,
inference(avatar_split_clause,[],[f1796,f5012]) ).
fof(f5012,plain,
( spl171_370
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_370])]) ).
fof(f1796,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f1189,f1065,f1065]) ).
fof(f1189,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f406]) ).
fof(f406,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f285]) ).
fof(f285,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f5010,plain,
spl171_369,
inference(avatar_split_clause,[],[f1794,f5008]) ).
fof(f5008,plain,
( spl171_369
<=> ! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_369])]) ).
fof(f1794,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f1180,f1065]) ).
fof(f1180,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
fof(f395,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f143]) ).
fof(f143,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f5006,plain,
spl171_368,
inference(avatar_split_clause,[],[f1793,f5004]) ).
fof(f5004,plain,
( spl171_368
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_368])]) ).
fof(f1793,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1176,f1148]) ).
fof(f1176,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f225]) ).
fof(f225,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f5002,plain,
spl171_367,
inference(avatar_split_clause,[],[f1787,f5000]) ).
fof(f5000,plain,
( spl171_367
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_367])]) ).
fof(f1787,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f1151,f1148]) ).
fof(f1151,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f728]) ).
fof(f4998,plain,
spl171_366,
inference(avatar_split_clause,[],[f1255,f4996]) ).
fof(f4996,plain,
( spl171_366
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_366])]) ).
fof(f1255,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f4988,plain,
spl171_365,
inference(avatar_split_clause,[],[f1254,f4986]) ).
fof(f4986,plain,
( spl171_365
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_365])]) ).
fof(f1254,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
fof(f4984,plain,
spl171_364,
inference(avatar_split_clause,[],[f1253,f4982]) ).
fof(f4982,plain,
( spl171_364
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_364])]) ).
fof(f1253,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f439]) ).
fof(f439,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f234]) ).
fof(f234,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f4980,plain,
spl171_363,
inference(avatar_split_clause,[],[f1235,f4978]) ).
fof(f4978,plain,
( spl171_363
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_363])]) ).
fof(f1235,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f759]) ).
fof(f4976,plain,
spl171_362,
inference(avatar_split_clause,[],[f1183,f4974]) ).
fof(f4974,plain,
( spl171_362
<=> ! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_362])]) ).
fof(f1183,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f4972,plain,
spl171_361,
inference(avatar_split_clause,[],[f1166,f4970]) ).
fof(f1166,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f303]) ).
fof(f303,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f4966,plain,
spl171_360,
inference(avatar_split_clause,[],[f1109,f4964]) ).
fof(f1109,plain,
! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f711]) ).
fof(f711,plain,
! [X0] :
( ( ( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0) )
& ( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ( relation_dom(X0) = empty_set
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f280]) ).
fof(f280,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> empty_set = relation_rng(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f4960,plain,
spl171_359,
inference(avatar_split_clause,[],[f1108,f4958]) ).
fof(f1108,plain,
! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f711]) ).
fof(f4956,plain,
spl171_358,
inference(avatar_split_clause,[],[f1068,f4954]) ).
fof(f4954,plain,
( spl171_358
<=> ! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_358])]) ).
fof(f1068,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f321]) ).
fof(f321,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f4884,plain,
spl171_357,
inference(avatar_split_clause,[],[f1718,f4882]) ).
fof(f4882,plain,
( spl171_357
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_357])]) ).
fof(f1718,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f602]) ).
fof(f602,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f273]) ).
fof(f273,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f4874,plain,
spl171_356,
inference(avatar_split_clause,[],[f1709,f4872]) ).
fof(f4872,plain,
( spl171_356
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP47(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_356])]) ).
fof(f1709,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP47(X1,X0,X2) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP47(X1,X0,X2) )
& ( sP47(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f677]) ).
fof(f677,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP47(X1,X0,X2) ),
inference(definition_folding,[],[f51,f676]) ).
fof(f51,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f4870,plain,
spl171_355,
inference(avatar_split_clause,[],[f1701,f4868]) ).
fof(f4868,plain,
( spl171_355
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP46(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_355])]) ).
fof(f1701,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP46(X1,X0,X2) ),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP46(X1,X0,X2) )
& ( sP46(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f675]) ).
fof(f675,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP46(X1,X0,X2) ),
inference(definition_folding,[],[f37,f674]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4866,plain,
spl171_354,
inference(avatar_split_clause,[],[f1693,f4864]) ).
fof(f4864,plain,
( spl171_354
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP45(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_354])]) ).
fof(f1693,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP45(X1,X0,X2) ),
inference(cnf_transformation,[],[f1007]) ).
fof(f1007,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP45(X1,X0,X2) )
& ( sP45(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f673]) ).
fof(f673,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP45(X1,X0,X2) ),
inference(definition_folding,[],[f38,f672]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4862,plain,
spl171_353,
inference(avatar_split_clause,[],[f1683,f4860]) ).
fof(f4860,plain,
( spl171_353
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP44(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_353])]) ).
fof(f1683,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP44(X1,X0,X2) ),
inference(cnf_transformation,[],[f1000]) ).
fof(f1000,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP44(X1,X0,X2) )
& ( sP44(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f671]) ).
fof(f671,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP44(X1,X0,X2) ),
inference(definition_folding,[],[f35,f670]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f4858,plain,
spl171_352,
inference(avatar_split_clause,[],[f1648,f4856]) ).
fof(f4856,plain,
( spl171_352
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_352])]) ).
fof(f1648,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f976]) ).
fof(f976,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK142(X0,X1),X1)
& in(sK142(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142])],[f974,f975]) ).
fof(f975,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK142(X0,X1),X1)
& in(sK142(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f974,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f973]) ).
fof(f973,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f592]) ).
fof(f592,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4854,plain,
spl171_351,
inference(avatar_split_clause,[],[f1645,f4852]) ).
fof(f4852,plain,
( spl171_351
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_351])]) ).
fof(f1645,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f591]) ).
fof(f591,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f590]) ).
fof(f590,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f317]) ).
fof(f317,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f4850,plain,
spl171_350,
inference(avatar_split_clause,[],[f1644,f4848]) ).
fof(f4848,plain,
( spl171_350
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_350])]) ).
fof(f1644,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f971]) ).
fof(f971,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f970]) ).
fof(f970,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4846,plain,
spl171_349,
inference(avatar_split_clause,[],[f1488,f4844]) ).
fof(f4844,plain,
( spl171_349
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP29(X0,X1)
| ~ sP30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_349])]) ).
fof(f1488,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP29(X0,X1)
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f886]) ).
fof(f886,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP29(X0,X1) )
& ( sP29(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP30(X0) ),
inference(nnf_transformation,[],[f648]) ).
fof(f648,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP29(X0,X1) )
| ~ sP30(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f4842,plain,
spl171_348,
inference(avatar_split_clause,[],[f1475,f4840]) ).
fof(f4840,plain,
( spl171_348
<=> ! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_348])]) ).
fof(f1475,plain,
! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f514]) ).
fof(f514,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f513]) ).
fof(f513,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f4838,plain,
spl171_347,
inference(avatar_split_clause,[],[f1135,f4836]) ).
fof(f4836,plain,
( spl171_347
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_347])]) ).
fof(f1135,plain,
! [X2,X3,X0,X1] :
( sP2(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f721]) ).
fof(f4833,plain,
( spl171_346
| ~ spl171_41
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2295,f2278,f2221,f4830]) ).
fof(f4830,plain,
( spl171_346
<=> sP1(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_346])]) ).
fof(f2295,plain,
( sP1(sK170)
| ~ spl171_41
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2223]) ).
fof(f4674,plain,
( spl171_345
| ~ spl171_12
| ~ spl171_105
| ~ spl171_325 ),
inference(avatar_split_clause,[],[f4545,f4541,f2639,f2076,f4672]) ).
fof(f4672,plain,
( spl171_345
<=> ! [X0] :
( relation_rng(X0) != sK160
| sK160 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_345])]) ).
fof(f4541,plain,
( spl171_325
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_325])]) ).
fof(f4545,plain,
( ! [X0] :
( relation_rng(X0) != sK160
| sK160 = X0
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_325 ),
inference(forward_demodulation,[],[f4544,f2706]) ).
fof(f4544,plain,
( ! [X0] :
( sK160 = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_325 ),
inference(forward_demodulation,[],[f4542,f2706]) ).
fof(f4542,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl171_325 ),
inference(avatar_component_clause,[],[f4541]) ).
fof(f4670,plain,
( spl171_344
| ~ spl171_12
| ~ spl171_105
| ~ spl171_324 ),
inference(avatar_split_clause,[],[f4539,f4535,f2639,f2076,f4668]) ).
fof(f4668,plain,
( spl171_344
<=> ! [X0] :
( relation_dom(X0) != sK160
| sK160 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_344])]) ).
fof(f4535,plain,
( spl171_324
<=> ! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_324])]) ).
fof(f4539,plain,
( ! [X0] :
( relation_dom(X0) != sK160
| sK160 = X0
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_324 ),
inference(forward_demodulation,[],[f4538,f2706]) ).
fof(f4538,plain,
( ! [X0] :
( sK160 = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_324 ),
inference(forward_demodulation,[],[f4536,f2706]) ).
fof(f4536,plain,
( ! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl171_324 ),
inference(avatar_component_clause,[],[f4535]) ).
fof(f4666,plain,
( spl171_343
| ~ spl171_1
| ~ spl171_321 ),
inference(avatar_split_clause,[],[f4631,f4522,f2021,f4663]) ).
fof(f4663,plain,
( spl171_343
<=> relation_rng(sK51) = relation_image(sK51,relation_dom(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_343])]) ).
fof(f4522,plain,
( spl171_321
<=> ! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_321])]) ).
fof(f4631,plain,
( relation_rng(sK51) = relation_image(sK51,relation_dom(sK51))
| ~ spl171_1
| ~ spl171_321 ),
inference(resolution,[],[f4523,f2023]) ).
fof(f4523,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) )
| ~ spl171_321 ),
inference(avatar_component_clause,[],[f4522]) ).
fof(f4615,plain,
spl171_342,
inference(avatar_split_clause,[],[f1275,f4613]) ).
fof(f4613,plain,
( spl171_342
<=> ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_342])]) ).
fof(f1275,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f463]) ).
fof(f463,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f246]) ).
fof(f246,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f4611,plain,
spl171_341,
inference(avatar_split_clause,[],[f1269,f4609]) ).
fof(f4609,plain,
( spl171_341
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_341])]) ).
fof(f1269,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f458]) ).
fof(f458,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f457]) ).
fof(f457,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f213]) ).
fof(f213,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f4607,plain,
spl171_340,
inference(avatar_split_clause,[],[f1268,f4605]) ).
fof(f4605,plain,
( spl171_340
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_340])]) ).
fof(f1268,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f455]) ).
fof(f455,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f278]) ).
fof(f278,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f4603,plain,
spl171_339,
inference(avatar_split_clause,[],[f1208,f4601]) ).
fof(f4601,plain,
( spl171_339
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK73(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_339])]) ).
fof(f1208,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK73(X0,X1),X1) ),
inference(cnf_transformation,[],[f747]) ).
fof(f747,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK73(X0,X1),X1)
& in(sK73(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f423,f746]) ).
fof(f746,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK73(X0,X1),X1)
& in(sK73(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f423,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f4599,plain,
spl171_338,
inference(avatar_split_clause,[],[f1207,f4597]) ).
fof(f4597,plain,
( spl171_338
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| in(sK73(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_338])]) ).
fof(f1207,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK73(X0,X1),X0) ),
inference(cnf_transformation,[],[f747]) ).
fof(f4595,plain,
spl171_337,
inference(avatar_split_clause,[],[f1182,f4593]) ).
fof(f4593,plain,
( spl171_337
<=> ! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_337])]) ).
fof(f1182,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f397]) ).
fof(f397,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f237]) ).
fof(f237,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f4591,plain,
spl171_336,
inference(avatar_split_clause,[],[f1165,f4589]) ).
fof(f4589,plain,
( spl171_336
<=> ! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_336])]) ).
fof(f1165,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f304]) ).
fof(f304,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f4587,plain,
spl171_335,
inference(avatar_split_clause,[],[f1164,f4585]) ).
fof(f4585,plain,
( spl171_335
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_335])]) ).
fof(f1164,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f4582,plain,
( spl171_334
| ~ spl171_34
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2294,f2278,f2186,f4579]) ).
fof(f2294,plain,
( sP1(sK169)
| ~ spl171_34
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2188]) ).
fof(f4577,plain,
spl171_333,
inference(avatar_split_clause,[],[f1154,f4575]) ).
fof(f4575,plain,
( spl171_333
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_333])]) ).
fof(f1154,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f730]) ).
fof(f730,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK69(X0,X1),X1)
& in(sK69(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f367,f729]) ).
fof(f729,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK69(X0,X1),X1)
& in(sK69(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f367,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f4573,plain,
spl171_332,
inference(avatar_split_clause,[],[f1149,f4571]) ).
fof(f4571,plain,
( spl171_332
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_332])]) ).
fof(f1149,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f250]) ).
fof(f250,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f4569,plain,
spl171_331,
inference(avatar_split_clause,[],[f1147,f4567]) ).
fof(f4567,plain,
( spl171_331
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_331])]) ).
fof(f1147,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f243]) ).
fof(f243,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f4565,plain,
spl171_330,
inference(avatar_split_clause,[],[f1143,f4563]) ).
fof(f4563,plain,
( spl171_330
<=> ! [X2,X0] :
( in(powerset(X2),sK67(X0))
| ~ in(X2,sK67(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_330])]) ).
fof(f1143,plain,
! [X2,X0] :
( in(powerset(X2),sK67(X0))
| ~ in(X2,sK67(X0)) ),
inference(cnf_transformation,[],[f726]) ).
fof(f4561,plain,
spl171_329,
inference(avatar_split_clause,[],[f1140,f4559]) ).
fof(f4559,plain,
( spl171_329
<=> ! [X0] :
( ordinal(X0)
| ~ subset(sK66(X0),X0)
| ~ ordinal(sK66(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_329])]) ).
fof(f1140,plain,
! [X0] :
( ordinal(X0)
| ~ subset(sK66(X0),X0)
| ~ ordinal(sK66(X0)) ),
inference(cnf_transformation,[],[f723]) ).
fof(f723,plain,
! [X0] :
( ordinal(X0)
| ( ( ~ subset(sK66(X0),X0)
| ~ ordinal(sK66(X0)) )
& in(sK66(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f363,f722]) ).
fof(f722,plain,
! [X0] :
( ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) )
=> ( ( ~ subset(sK66(X0),X0)
| ~ ordinal(sK66(X0)) )
& in(sK66(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f363,plain,
! [X0] :
( ordinal(X0)
| ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f231]) ).
fof(f231,axiom,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f4557,plain,
spl171_328,
inference(avatar_split_clause,[],[f1121,f4555]) ).
fof(f4555,plain,
( spl171_328
<=> ! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_328])]) ).
fof(f1121,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f357]) ).
fof(f357,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f277]) ).
fof(f277,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f4553,plain,
spl171_327,
inference(avatar_split_clause,[],[f1094,f4551]) ).
fof(f4551,plain,
( spl171_327
<=> ! [X0] :
( antisymmetric(X0)
| sK57(X0) != sK58(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_327])]) ).
fof(f1094,plain,
! [X0] :
( antisymmetric(X0)
| sK57(X0) != sK58(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f701]) ).
fof(f4549,plain,
spl171_326,
inference(avatar_split_clause,[],[f1089,f4547]) ).
fof(f4547,plain,
( spl171_326
<=> ! [X0] :
( reflexive(X0)
| in(sK56(X0),relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_326])]) ).
fof(f1089,plain,
! [X0] :
( reflexive(X0)
| in(sK56(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f697]) ).
fof(f4543,plain,
spl171_325,
inference(avatar_split_clause,[],[f1084,f4541]) ).
fof(f1084,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(flattening,[],[f332]) ).
fof(f332,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f279]) ).
fof(f279,axiom,
! [X0] :
( relation(X0)
=> ( ( empty_set = relation_rng(X0)
| relation_dom(X0) = empty_set )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f4537,plain,
spl171_324,
inference(avatar_split_clause,[],[f1083,f4535]) ).
fof(f1083,plain,
! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f4533,plain,
( spl171_323
| ~ spl171_31
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2293,f2278,f2171,f4530]) ).
fof(f4530,plain,
( spl171_323
<=> sP1(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_323])]) ).
fof(f2293,plain,
( sP1(sK168)
| ~ spl171_31
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2173]) ).
fof(f4528,plain,
spl171_322,
inference(avatar_split_clause,[],[f1080,f4526]) ).
fof(f4526,plain,
( spl171_322
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_322])]) ).
fof(f1080,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f218]) ).
fof(f218,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f4524,plain,
spl171_321,
inference(avatar_split_clause,[],[f1079,f4522]) ).
fof(f1079,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f199]) ).
fof(f199,axiom,
! [X0] :
( relation(X0)
=> relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f4512,plain,
( spl171_320
| ~ spl171_29
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2292,f2278,f2161,f4509]) ).
fof(f4509,plain,
( spl171_320
<=> sP1(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_320])]) ).
fof(f2292,plain,
( sP1(sK167)
| ~ spl171_29
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2163]) ).
fof(f4431,plain,
( spl171_319
| ~ spl171_26
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2291,f2278,f2146,f4428]) ).
fof(f4428,plain,
( spl171_319
<=> sP1(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_319])]) ).
fof(f2291,plain,
( sP1(sK166)
| ~ spl171_26
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2148]) ).
fof(f4342,plain,
( spl171_318
| ~ spl171_24
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2290,f2278,f2136,f4339]) ).
fof(f4339,plain,
( spl171_318
<=> sP1(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_318])]) ).
fof(f2290,plain,
( sP1(sK165)
| ~ spl171_24
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2138]) ).
fof(f4241,plain,
( spl171_317
| ~ spl171_12
| ~ spl171_105
| ~ spl171_270 ),
inference(avatar_split_clause,[],[f4028,f4025,f2639,f2076,f4239]) ).
fof(f4239,plain,
( spl171_317
<=> ! [X0,X1] :
( sK90(X0,X1) != sK160
| sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_317])]) ).
fof(f4025,plain,
( spl171_270
<=> ! [X0,X1] :
( sP13(X0,X1)
| empty_set != sK90(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_270])]) ).
fof(f4028,plain,
( ! [X0,X1] :
( sK90(X0,X1) != sK160
| sP13(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_270 ),
inference(forward_demodulation,[],[f4026,f2706]) ).
fof(f4026,plain,
( ! [X0,X1] :
( sP13(X0,X1)
| empty_set != sK90(X0,X1) )
| ~ spl171_270 ),
inference(avatar_component_clause,[],[f4025]) ).
fof(f4216,plain,
( spl171_316
| ~ spl171_1
| ~ spl171_225 ),
inference(avatar_split_clause,[],[f3803,f3649,f2021,f4213]) ).
fof(f3649,plain,
( spl171_225
<=> ! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_225])]) ).
fof(f3803,plain,
( relation_dom(sK51) = relation_rng(relation_inverse(sK51))
| ~ spl171_1
| ~ spl171_225 ),
inference(resolution,[],[f3650,f2023]) ).
fof(f3650,plain,
( ! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ spl171_225 ),
inference(avatar_component_clause,[],[f3649]) ).
fof(f4211,plain,
spl171_315,
inference(avatar_split_clause,[],[f1998,f4209]) ).
fof(f4209,plain,
( spl171_315
<=> ! [X2,X0,X1] : sP49(X2,X1,X0,unordered_triple(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_315])]) ).
fof(f1998,plain,
! [X2,X0,X1] : sP49(X2,X1,X0,unordered_triple(X0,X1,X2)),
inference(equality_resolution,[],[f1727]) ).
fof(f1727,plain,
! [X2,X3,X0,X1] :
( sP49(X2,X1,X0,X3)
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f1031]) ).
fof(f4207,plain,
spl171_314,
inference(avatar_split_clause,[],[f1997,f4205]) ).
fof(f4205,plain,
( spl171_314
<=> ! [X5,X1,X0,X3] :
( in(X5,X3)
| ~ sP49(X0,X1,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_314])]) ).
fof(f1997,plain,
! [X3,X0,X1,X5] :
( in(X5,X3)
| ~ sP49(X0,X1,X5,X3) ),
inference(equality_resolution,[],[f1720]) ).
fof(f1720,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X2 != X5
| ~ sP49(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f4203,plain,
spl171_313,
inference(avatar_split_clause,[],[f1996,f4201]) ).
fof(f4201,plain,
( spl171_313
<=> ! [X2,X5,X0,X3] :
( in(X5,X3)
| ~ sP49(X0,X5,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_313])]) ).
fof(f1996,plain,
! [X2,X3,X0,X5] :
( in(X5,X3)
| ~ sP49(X0,X5,X2,X3) ),
inference(equality_resolution,[],[f1721]) ).
fof(f1721,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X1 != X5
| ~ sP49(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f4199,plain,
spl171_312,
inference(avatar_split_clause,[],[f1995,f4197]) ).
fof(f4197,plain,
( spl171_312
<=> ! [X3,X5,X2,X1] :
( in(X5,X3)
| ~ sP49(X5,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_312])]) ).
fof(f1995,plain,
! [X2,X3,X1,X5] :
( in(X5,X3)
| ~ sP49(X5,X1,X2,X3) ),
inference(equality_resolution,[],[f1722]) ).
fof(f1722,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X0 != X5
| ~ sP49(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f4195,plain,
spl171_311,
inference(avatar_split_clause,[],[f1975,f4193]) ).
fof(f4193,plain,
( spl171_311
<=> ! [X1] :
( sP37(X1,identity_relation(X1))
| ~ sP38(identity_relation(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_311])]) ).
fof(f1975,plain,
! [X1] :
( sP37(X1,identity_relation(X1))
| ~ sP38(identity_relation(X1),X1) ),
inference(equality_resolution,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1] :
( sP37(X1,X0)
| identity_relation(X1) != X0
| ~ sP38(X0,X1) ),
inference(cnf_transformation,[],[f946]) ).
fof(f4191,plain,
spl171_310,
inference(avatar_split_clause,[],[f1970,f4189]) ).
fof(f4189,plain,
( spl171_310
<=> ! [X1] :
( sP35(X1,set_meet(X1))
| ~ sP36(set_meet(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_310])]) ).
fof(f1970,plain,
! [X1] :
( sP35(X1,set_meet(X1))
| ~ sP36(set_meet(X1),X1) ),
inference(equality_resolution,[],[f1563]) ).
fof(f1563,plain,
! [X0,X1] :
( sP35(X1,X0)
| set_meet(X1) != X0
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f937]) ).
fof(f4187,plain,
spl171_309,
inference(avatar_split_clause,[],[f1967,f4185]) ).
fof(f4185,plain,
( spl171_309
<=> ! [X0,X1] :
( sP33(X0,X1,relation_image(X0,X1))
| ~ sP34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_309])]) ).
fof(f1967,plain,
! [X0,X1] :
( sP33(X0,X1,relation_image(X0,X1))
| ~ sP34(X0) ),
inference(equality_resolution,[],[f1509]) ).
fof(f1509,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| relation_image(X0,X1) != X2
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f900]) ).
fof(f4183,plain,
spl171_308,
inference(avatar_split_clause,[],[f1966,f4181]) ).
fof(f4181,plain,
( spl171_308
<=> ! [X0,X1] :
( sP31(X1,X0,relation_inverse_image(X0,X1))
| ~ sP32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_308])]) ).
fof(f1966,plain,
! [X0,X1] :
( sP31(X1,X0,relation_inverse_image(X0,X1))
| ~ sP32(X0) ),
inference(equality_resolution,[],[f1500]) ).
fof(f1500,plain,
! [X2,X0,X1] :
( sP31(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f894]) ).
fof(f4179,plain,
spl171_307,
inference(avatar_split_clause,[],[f1960,f4177]) ).
fof(f4177,plain,
( spl171_307
<=> ! [X0,X1] :
( sP25(X1,X0,relation_image(X0,X1))
| ~ sP26(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_307])]) ).
fof(f1960,plain,
! [X0,X1] :
( sP25(X1,X0,relation_image(X0,X1))
| ~ sP26(X0) ),
inference(equality_resolution,[],[f1462]) ).
fof(f1462,plain,
! [X2,X0,X1] :
( sP25(X1,X0,X2)
| relation_image(X0,X1) != X2
| ~ sP26(X0) ),
inference(cnf_transformation,[],[f874]) ).
fof(f4175,plain,
( spl171_306
| ~ spl171_1
| ~ spl171_224 ),
inference(avatar_split_clause,[],[f3779,f3645,f2021,f4172]) ).
fof(f4172,plain,
( spl171_306
<=> relation_rng(sK51) = relation_dom(relation_inverse(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_306])]) ).
fof(f3645,plain,
( spl171_224
<=> ! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_224])]) ).
fof(f3779,plain,
( relation_rng(sK51) = relation_dom(relation_inverse(sK51))
| ~ spl171_1
| ~ spl171_224 ),
inference(resolution,[],[f3646,f2023]) ).
fof(f3646,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ spl171_224 ),
inference(avatar_component_clause,[],[f3645]) ).
fof(f4170,plain,
spl171_305,
inference(avatar_split_clause,[],[f1959,f4168]) ).
fof(f4168,plain,
( spl171_305
<=> ! [X0,X1] :
( sP23(X1,X0,relation_inverse_image(X0,X1))
| ~ sP24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_305])]) ).
fof(f1959,plain,
! [X0,X1] :
( sP23(X1,X0,relation_inverse_image(X0,X1))
| ~ sP24(X0) ),
inference(equality_resolution,[],[f1453]) ).
fof(f1453,plain,
! [X2,X0,X1] :
( sP23(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP24(X0) ),
inference(cnf_transformation,[],[f867]) ).
fof(f4166,plain,
spl171_304,
inference(avatar_split_clause,[],[f1932,f4164]) ).
fof(f4164,plain,
( spl171_304
<=> ! [X0] :
( sP3(function_inverse(X0),X0)
| ~ sP4(X0,function_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_304])]) ).
fof(f1932,plain,
! [X0] :
( sP3(function_inverse(X0),X0)
| ~ sP4(X0,function_inverse(X0)) ),
inference(equality_resolution,[],[f1124]) ).
fof(f1124,plain,
! [X0,X1] :
( sP3(X1,X0)
| function_inverse(X0) != X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f713]) ).
fof(f4162,plain,
spl171_303,
inference(avatar_split_clause,[],[f1650,f4160]) ).
fof(f4160,plain,
( spl171_303
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK142(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_303])]) ).
fof(f1650,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK142(X0,X1),X1) ),
inference(cnf_transformation,[],[f976]) ).
fof(f4158,plain,
spl171_302,
inference(avatar_split_clause,[],[f1649,f4156]) ).
fof(f4156,plain,
( spl171_302
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK142(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_302])]) ).
fof(f1649,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK142(X0,X1),X0) ),
inference(cnf_transformation,[],[f976]) ).
fof(f4154,plain,
spl171_301,
inference(avatar_split_clause,[],[f1639,f4152]) ).
fof(f4152,plain,
( spl171_301
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_301])]) ).
fof(f1639,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f588]) ).
fof(f588,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f587]) ).
fof(f587,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f4150,plain,
spl171_300,
inference(avatar_split_clause,[],[f1637,f4148]) ).
fof(f4148,plain,
( spl171_300
<=> ! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_300])]) ).
fof(f1637,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f584]) ).
fof(f584,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f583]) ).
fof(f583,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f4146,plain,
spl171_299,
inference(avatar_split_clause,[],[f1636,f4144]) ).
fof(f4144,plain,
( spl171_299
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_299])]) ).
fof(f1636,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f582,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f581]) ).
fof(f581,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f4142,plain,
spl171_298,
inference(avatar_split_clause,[],[f1635,f4140]) ).
fof(f4140,plain,
( spl171_298
<=> ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_298])]) ).
fof(f1635,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f580]) ).
fof(f580,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f579]) ).
fof(f579,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f4138,plain,
spl171_297,
inference(avatar_split_clause,[],[f1633,f4136]) ).
fof(f4136,plain,
( spl171_297
<=> ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_297])]) ).
fof(f1633,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f578]) ).
fof(f578,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f577]) ).
fof(f577,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f4134,plain,
spl171_296,
inference(avatar_split_clause,[],[f1629,f4132]) ).
fof(f4132,plain,
( spl171_296
<=> ! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_296])]) ).
fof(f1629,plain,
! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f574,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(flattening,[],[f573]) ).
fof(f573,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f4129,plain,
spl171_295,
inference(avatar_split_clause,[],[f1627,f4127]) ).
fof(f4127,plain,
( spl171_295
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_295])]) ).
fof(f1627,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f572]) ).
fof(f572,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f571]) ).
fof(f571,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f4125,plain,
spl171_294,
inference(avatar_split_clause,[],[f1626,f4123]) ).
fof(f4123,plain,
( spl171_294
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_294])]) ).
fof(f1626,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f572]) ).
fof(f4121,plain,
spl171_293,
inference(avatar_split_clause,[],[f1625,f4119]) ).
fof(f4119,plain,
( spl171_293
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_293])]) ).
fof(f1625,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f570]) ).
fof(f570,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f569]) ).
fof(f569,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f4117,plain,
spl171_292,
inference(avatar_split_clause,[],[f1624,f4115]) ).
fof(f4115,plain,
( spl171_292
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_292])]) ).
fof(f1624,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f570]) ).
fof(f4113,plain,
spl171_291,
inference(avatar_split_clause,[],[f1619,f4111]) ).
fof(f4111,plain,
( spl171_291
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_291])]) ).
fof(f1619,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f562]) ).
fof(f562,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f561]) ).
fof(f561,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f4109,plain,
spl171_290,
inference(avatar_split_clause,[],[f1596,f4107]) ).
fof(f4107,plain,
( spl171_290
<=> ! [X2,X0,X1] :
( sP40(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_290])]) ).
fof(f1596,plain,
! [X2,X0,X1] :
( sP40(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f664]) ).
fof(f664,plain,
! [X0,X1] :
( ! [X2] :
( sP40(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f544,f663,f662]) ).
fof(f544,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f4105,plain,
spl171_289,
inference(avatar_split_clause,[],[f1559,f4103]) ).
fof(f4103,plain,
( spl171_289
<=> ! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_289])]) ).
fof(f1559,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f935]) ).
fof(f935,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f536]) ).
fof(f536,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f4101,plain,
spl171_288,
inference(avatar_split_clause,[],[f1531,f4099]) ).
fof(f4099,plain,
( spl171_288
<=> ! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_288])]) ).
fof(f1531,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f915]) ).
fof(f915,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK124(X0),X0)
& in(sK124(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124])],[f913,f914]) ).
fof(f914,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK124(X0),X0)
& in(sK124(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f913,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f912]) ).
fof(f912,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f532]) ).
fof(f532,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f4097,plain,
spl171_287,
inference(avatar_split_clause,[],[f1522,f4095]) ).
fof(f4095,plain,
( spl171_287
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_287])]) ).
fof(f1522,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f529]) ).
fof(f529,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f4093,plain,
spl171_286,
inference(avatar_split_clause,[],[f1452,f4091]) ).
fof(f4091,plain,
( spl171_286
<=> ! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_286])]) ).
fof(f1452,plain,
! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f637]) ).
fof(f637,plain,
! [X0] :
( ! [X1,X2] :
( sP22(X2,X1,X0)
| ~ relation(X2) )
| ~ relation(X0) ),
inference(definition_folding,[],[f504,f636,f635]) ).
fof(f504,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f4089,plain,
spl171_285,
inference(avatar_split_clause,[],[f1431,f4087]) ).
fof(f4087,plain,
( spl171_285
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK98(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_285])]) ).
fof(f1431,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK98(X0,X1),X1) ),
inference(cnf_transformation,[],[f847]) ).
fof(f4085,plain,
spl171_284,
inference(avatar_split_clause,[],[f1430,f4083]) ).
fof(f4083,plain,
( spl171_284
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK97(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_284])]) ).
fof(f1430,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK97(X0,X1),X1) ),
inference(cnf_transformation,[],[f847]) ).
fof(f4081,plain,
spl171_283,
inference(avatar_split_clause,[],[f1429,f4079]) ).
fof(f4079,plain,
( spl171_283
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK96(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_283])]) ).
fof(f1429,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK96(X0,X1),X1) ),
inference(cnf_transformation,[],[f847]) ).
fof(f4077,plain,
spl171_282,
inference(avatar_split_clause,[],[f1427,f4075]) ).
fof(f4075,plain,
( spl171_282
<=> ! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP19(X0,X1)
| ~ sP20(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_282])]) ).
fof(f1427,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP19(X0,X1)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f843]) ).
fof(f843,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ~ sP19(X0,X1) )
& ( sP19(X0,X1)
| ~ is_transitive_in(X0,X1) ) )
| ~ sP20(X0) ),
inference(nnf_transformation,[],[f633]) ).
fof(f633,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> sP19(X0,X1) )
| ~ sP20(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f4073,plain,
spl171_281,
inference(avatar_split_clause,[],[f1426,f4071]) ).
fof(f4071,plain,
( spl171_281
<=> ! [X0,X1] :
( sP19(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP20(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_281])]) ).
fof(f1426,plain,
! [X0,X1] :
( sP19(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f843]) ).
fof(f4069,plain,
spl171_280,
inference(avatar_split_clause,[],[f1421,f4067]) ).
fof(f4067,plain,
( spl171_280
<=> ! [X0,X1] :
( sP17(X0,X1)
| in(sK95(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_280])]) ).
fof(f1421,plain,
! [X0,X1] :
( sP17(X0,X1)
| in(sK95(X0,X1),X1) ),
inference(cnf_transformation,[],[f842]) ).
fof(f4065,plain,
spl171_279,
inference(avatar_split_clause,[],[f1420,f4063]) ).
fof(f4063,plain,
( spl171_279
<=> ! [X0,X1] :
( sP17(X0,X1)
| in(sK94(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_279])]) ).
fof(f1420,plain,
! [X0,X1] :
( sP17(X0,X1)
| in(sK94(X0,X1),X1) ),
inference(cnf_transformation,[],[f842]) ).
fof(f4061,plain,
spl171_278,
inference(avatar_split_clause,[],[f1418,f4059]) ).
fof(f4059,plain,
( spl171_278
<=> ! [X0,X1] :
( is_connected_in(X0,X1)
| ~ sP17(X0,X1)
| ~ sP18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_278])]) ).
fof(f1418,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ sP17(X0,X1)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f838]) ).
fof(f838,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ~ sP17(X0,X1) )
& ( sP17(X0,X1)
| ~ is_connected_in(X0,X1) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f630]) ).
fof(f630,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> sP17(X0,X1) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f4057,plain,
spl171_277,
inference(avatar_split_clause,[],[f1417,f4055]) ).
fof(f4055,plain,
( spl171_277
<=> ! [X0,X1] :
( sP17(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ sP18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_277])]) ).
fof(f1417,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f838]) ).
fof(f4053,plain,
spl171_276,
inference(avatar_split_clause,[],[f1412,f4051]) ).
fof(f4051,plain,
( spl171_276
<=> ! [X0,X1] :
( sP15(X0,X1)
| in(sK93(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_276])]) ).
fof(f1412,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(sK93(X0,X1),X1) ),
inference(cnf_transformation,[],[f837]) ).
fof(f4049,plain,
( ~ spl171_274
| spl171_275
| ~ spl171_106
| ~ spl171_254 ),
inference(avatar_split_clause,[],[f3999,f3944,f2643,f4046,f4042]) ).
fof(f4042,plain,
( spl171_274
<=> empty(relation_inverse(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_274])]) ).
fof(f4046,plain,
( spl171_275
<=> empty(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_275])]) ).
fof(f2643,plain,
( spl171_106
<=> ! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_106])]) ).
fof(f3944,plain,
( spl171_254
<=> sK51 = relation_inverse(relation_inverse(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_254])]) ).
fof(f3999,plain,
( empty(sK51)
| ~ empty(relation_inverse(sK51))
| ~ spl171_106
| ~ spl171_254 ),
inference(superposition,[],[f2644,f3946]) ).
fof(f3946,plain,
( sK51 = relation_inverse(relation_inverse(sK51))
| ~ spl171_254 ),
inference(avatar_component_clause,[],[f3944]) ).
fof(f2644,plain,
( ! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) )
| ~ spl171_106 ),
inference(avatar_component_clause,[],[f2643]) ).
fof(f4040,plain,
spl171_273,
inference(avatar_split_clause,[],[f1411,f4038]) ).
fof(f4038,plain,
( spl171_273
<=> ! [X0,X1] :
( sP15(X0,X1)
| in(sK92(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_273])]) ).
fof(f1411,plain,
! [X0,X1] :
( sP15(X0,X1)
| in(sK92(X0,X1),X1) ),
inference(cnf_transformation,[],[f837]) ).
fof(f4036,plain,
spl171_272,
inference(avatar_split_clause,[],[f1409,f4034]) ).
fof(f4034,plain,
( spl171_272
<=> ! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ sP15(X0,X1)
| ~ sP16(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_272])]) ).
fof(f1409,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ sP15(X0,X1)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f833]) ).
fof(f833,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ~ sP15(X0,X1) )
& ( sP15(X0,X1)
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f627]) ).
fof(f627,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> sP15(X0,X1) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f4032,plain,
spl171_271,
inference(avatar_split_clause,[],[f1408,f4030]) ).
fof(f4030,plain,
( spl171_271
<=> ! [X0,X1] :
( sP15(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ sP16(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_271])]) ).
fof(f1408,plain,
! [X0,X1] :
( sP15(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f833]) ).
fof(f4027,plain,
spl171_270,
inference(avatar_split_clause,[],[f1405,f4025]) ).
fof(f1405,plain,
! [X0,X1] :
( sP13(X0,X1)
| empty_set != sK90(X0,X1) ),
inference(cnf_transformation,[],[f832]) ).
fof(f4023,plain,
spl171_269,
inference(avatar_split_clause,[],[f1404,f4021]) ).
fof(f4021,plain,
( spl171_269
<=> ! [X0,X1] :
( sP13(X0,X1)
| subset(sK90(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_269])]) ).
fof(f1404,plain,
! [X0,X1] :
( sP13(X0,X1)
| subset(sK90(X0,X1),X1) ),
inference(cnf_transformation,[],[f832]) ).
fof(f4019,plain,
spl171_268,
inference(avatar_split_clause,[],[f1401,f4017]) ).
fof(f4017,plain,
( spl171_268
<=> ! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ sP13(X0,X1)
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_268])]) ).
fof(f1401,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ sP13(X0,X1)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ~ sP13(X0,X1) )
& ( sP13(X0,X1)
| ~ is_well_founded_in(X0,X1) ) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f624]) ).
fof(f624,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> sP13(X0,X1) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f4015,plain,
spl171_267,
inference(avatar_split_clause,[],[f1400,f4013]) ).
fof(f4013,plain,
( spl171_267
<=> ! [X0,X1] :
( sP13(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ sP14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_267])]) ).
fof(f1400,plain,
! [X0,X1] :
( sP13(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f827]) ).
fof(f4011,plain,
spl171_266,
inference(avatar_split_clause,[],[f1389,f4009]) ).
fof(f4009,plain,
( spl171_266
<=> ! [X0,X1] :
( well_orders(X0,X1)
| ~ sP11(X1,X0)
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_266])]) ).
fof(f1389,plain,
! [X0,X1] :
( well_orders(X0,X1)
| ~ sP11(X1,X0)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f819]) ).
fof(f819,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| ~ well_orders(X0,X1) ) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f621]) ).
fof(f621,plain,
! [X0] :
( ! [X1] :
( well_orders(X0,X1)
<=> sP11(X1,X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f4007,plain,
spl171_265,
inference(avatar_split_clause,[],[f1388,f4005]) ).
fof(f4005,plain,
( spl171_265
<=> ! [X0,X1] :
( sP11(X1,X0)
| ~ well_orders(X0,X1)
| ~ sP12(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_265])]) ).
fof(f1388,plain,
! [X0,X1] :
( sP11(X1,X0)
| ~ well_orders(X0,X1)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f819]) ).
fof(f4003,plain,
spl171_264,
inference(avatar_split_clause,[],[f1358,f4001]) ).
fof(f4001,plain,
( spl171_264
<=> ! [X0] :
( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_264])]) ).
fof(f1358,plain,
! [X0] :
( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f792,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) )
& ( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f487]) ).
fof(f487,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f3996,plain,
spl171_263,
inference(avatar_split_clause,[],[f1357,f3994]) ).
fof(f3994,plain,
( spl171_263
<=> ! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_263])]) ).
fof(f1357,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f3992,plain,
spl171_262,
inference(avatar_split_clause,[],[f1356,f3990]) ).
fof(f3990,plain,
( spl171_262
<=> ! [X0] :
( connected(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_262])]) ).
fof(f1356,plain,
! [X0] :
( connected(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f486]) ).
fof(f486,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f3988,plain,
spl171_261,
inference(avatar_split_clause,[],[f1355,f3986]) ).
fof(f3986,plain,
( spl171_261
<=> ! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_261])]) ).
fof(f1355,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f791]) ).
fof(f3984,plain,
spl171_260,
inference(avatar_split_clause,[],[f1354,f3982]) ).
fof(f3982,plain,
( spl171_260
<=> ! [X0] :
( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_260])]) ).
fof(f1354,plain,
! [X0] :
( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f790]) ).
fof(f790,plain,
! [X0] :
( ( ( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0)) )
& ( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f485]) ).
fof(f485,plain,
! [X0] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f3980,plain,
spl171_259,
inference(avatar_split_clause,[],[f1353,f3978]) ).
fof(f3978,plain,
( spl171_259
<=> ! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_259])]) ).
fof(f1353,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f790]) ).
fof(f3976,plain,
spl171_258,
inference(avatar_split_clause,[],[f1352,f3974]) ).
fof(f3974,plain,
( spl171_258
<=> ! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_258])]) ).
fof(f1352,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f789]) ).
fof(f789,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f484]) ).
fof(f484,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f3972,plain,
spl171_257,
inference(avatar_split_clause,[],[f1351,f3970]) ).
fof(f3970,plain,
( spl171_257
<=> ! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_257])]) ).
fof(f1351,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f789]) ).
fof(f3968,plain,
spl171_256,
inference(avatar_split_clause,[],[f1127,f3966]) ).
fof(f3966,plain,
( spl171_256
<=> ! [X4,X0,X5,X1] :
( sP2(X4,X5,X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_256])]) ).
fof(f1127,plain,
! [X0,X1,X4,X5] :
( sP2(X4,X5,X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f3964,plain,
spl171_255,
inference(avatar_split_clause,[],[f1126,f3962]) ).
fof(f3962,plain,
( spl171_255
<=> ! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_255])]) ).
fof(f1126,plain,
! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f718]) ).
fof(f3947,plain,
( spl171_254
| ~ spl171_1
| ~ spl171_188 ),
inference(avatar_split_clause,[],[f3495,f3311,f2021,f3944]) ).
fof(f3311,plain,
( spl171_188
<=> ! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_188])]) ).
fof(f3495,plain,
( sK51 = relation_inverse(relation_inverse(sK51))
| ~ spl171_1
| ~ spl171_188 ),
inference(resolution,[],[f3312,f2023]) ).
fof(f3312,plain,
( ! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 )
| ~ spl171_188 ),
inference(avatar_component_clause,[],[f3311]) ).
fof(f3882,plain,
( spl171_253
| ~ spl171_12
| ~ spl171_105
| ~ spl171_239 ),
inference(avatar_split_clause,[],[f3709,f3706,f2639,f2076,f3880]) ).
fof(f3706,plain,
( spl171_239
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_239])]) ).
fof(f3709,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK160
| ~ subset(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_239 ),
inference(forward_demodulation,[],[f3707,f2706]) ).
fof(f3707,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl171_239 ),
inference(avatar_component_clause,[],[f3706]) ).
fof(f3878,plain,
( spl171_252
| ~ spl171_12
| ~ spl171_105
| ~ spl171_238 ),
inference(avatar_split_clause,[],[f3704,f3701,f2639,f2076,f3876]) ).
fof(f3876,plain,
( spl171_252
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK160
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_252])]) ).
fof(f3701,plain,
( spl171_238
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_238])]) ).
fof(f3704,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK160
| subset(X0,X1) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_238 ),
inference(forward_demodulation,[],[f3702,f2706]) ).
fof(f3702,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl171_238 ),
inference(avatar_component_clause,[],[f3701]) ).
fof(f3758,plain,
spl171_251,
inference(avatar_split_clause,[],[f1994,f3756]) ).
fof(f1994,plain,
! [X0,X1] : sP48(X1,X0,set_difference(X0,set_difference(X0,X1))),
inference(equality_resolution,[],[f1930]) ).
fof(f1930,plain,
! [X2,X0,X1] :
( sP48(X1,X0,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f1716,f1148]) ).
fof(f1716,plain,
! [X2,X0,X1] :
( sP48(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1025]) ).
fof(f3754,plain,
spl171_250,
inference(avatar_split_clause,[],[f1984,f3752]) ).
fof(f3752,plain,
( spl171_250
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_250])]) ).
fof(f1984,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f1924]) ).
fof(f1924,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1659,f1065]) ).
fof(f1659,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f987]) ).
fof(f3750,plain,
( spl171_248
| ~ spl171_249
| ~ spl171_94
| ~ spl171_133 ),
inference(avatar_split_clause,[],[f3024,f2866,f2592,f3747,f3743]) ).
fof(f3743,plain,
( spl171_248
<=> sP7(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_248])]) ).
fof(f3747,plain,
( spl171_249
<=> well_founded_relation(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_249])]) ).
fof(f2592,plain,
( spl171_94
<=> sP8(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_94])]) ).
fof(f2866,plain,
( spl171_133
<=> ! [X0] :
( sP7(X0)
| ~ well_founded_relation(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_133])]) ).
fof(f3024,plain,
( ~ well_founded_relation(sK51)
| sP7(sK51)
| ~ spl171_94
| ~ spl171_133 ),
inference(resolution,[],[f2867,f2594]) ).
fof(f2594,plain,
( sP8(sK51)
| ~ spl171_94 ),
inference(avatar_component_clause,[],[f2592]) ).
fof(f2867,plain,
( ! [X0] :
( ~ sP8(X0)
| ~ well_founded_relation(X0)
| sP7(X0) )
| ~ spl171_133 ),
inference(avatar_component_clause,[],[f2866]) ).
fof(f3741,plain,
spl171_247,
inference(avatar_split_clause,[],[f1845,f3739]) ).
fof(f3739,plain,
( spl171_247
<=> ! [X0] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_247])]) ).
fof(f1845,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1321,f1763]) ).
fof(f1321,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f471]) ).
fof(f471,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f3737,plain,
spl171_246,
inference(avatar_split_clause,[],[f1844,f3735]) ).
fof(f3735,plain,
( spl171_246
<=> ! [X0] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_246])]) ).
fof(f1844,plain,
! [X0] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1322,f1763]) ).
fof(f1322,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f471]) ).
fof(f3733,plain,
spl171_245,
inference(avatar_split_clause,[],[f1843,f3731]) ).
fof(f3731,plain,
( spl171_245
<=> ! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_245])]) ).
fof(f1843,plain,
! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1323,f1763]) ).
fof(f1323,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f471]) ).
fof(f3729,plain,
spl171_244,
inference(avatar_split_clause,[],[f1812,f3727]) ).
fof(f3727,plain,
( spl171_244
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_244])]) ).
fof(f1812,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1228,f1065]) ).
fof(f1228,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f425]) ).
fof(f425,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f144]) ).
fof(f144,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f3725,plain,
spl171_243,
inference(avatar_split_clause,[],[f1806,f3723]) ).
fof(f3723,plain,
( spl171_243
<=> ! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_243])]) ).
fof(f1806,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f1218,f1065]) ).
fof(f1218,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f753]) ).
fof(f753,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f241,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f3721,plain,
spl171_242,
inference(avatar_split_clause,[],[f1792,f3719]) ).
fof(f3719,plain,
( spl171_242
<=> ! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_242])]) ).
fof(f1792,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f1174,f1065]) ).
fof(f1174,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f3717,plain,
spl171_241,
inference(avatar_split_clause,[],[f1273,f3715]) ).
fof(f3715,plain,
( spl171_241
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_241])]) ).
fof(f1273,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f777]) ).
fof(f3713,plain,
spl171_240,
inference(avatar_split_clause,[],[f1272,f3711]) ).
fof(f3711,plain,
( spl171_240
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_240])]) ).
fof(f1272,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f777]) ).
fof(f3708,plain,
spl171_239,
inference(avatar_split_clause,[],[f1222,f3706]) ).
fof(f1222,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f755]) ).
fof(f755,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f150]) ).
fof(f150,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f3703,plain,
spl171_238,
inference(avatar_split_clause,[],[f1221,f3701]) ).
fof(f1221,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f755]) ).
fof(f3699,plain,
spl171_237,
inference(avatar_split_clause,[],[f1210,f3697]) ).
fof(f3697,plain,
( spl171_237
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_237])]) ).
fof(f1210,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f748]) ).
fof(f748,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f293]) ).
fof(f293,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f3695,plain,
spl171_236,
inference(avatar_split_clause,[],[f1209,f3693]) ).
fof(f3693,plain,
( spl171_236
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_236])]) ).
fof(f1209,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f748]) ).
fof(f3691,plain,
spl171_235,
inference(avatar_split_clause,[],[f1175,f3689]) ).
fof(f3689,plain,
( spl171_235
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_235])]) ).
fof(f1175,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f390]) ).
fof(f390,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f3687,plain,
spl171_234,
inference(avatar_split_clause,[],[f1163,f3685]) ).
fof(f3685,plain,
( spl171_234
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_234])]) ).
fof(f1163,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f3683,plain,
spl171_233,
inference(avatar_split_clause,[],[f1162,f3681]) ).
fof(f3681,plain,
( spl171_233
<=> ! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_233])]) ).
fof(f1162,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f195]) ).
fof(f195,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f3679,plain,
spl171_232,
inference(avatar_split_clause,[],[f1161,f3677]) ).
fof(f3677,plain,
( spl171_232
<=> ! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_232])]) ).
fof(f1161,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f203]) ).
fof(f203,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f3675,plain,
spl171_231,
inference(avatar_split_clause,[],[f1153,f3673]) ).
fof(f3673,plain,
( spl171_231
<=> ! [X0,X1] :
( in(sK69(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_231])]) ).
fof(f1153,plain,
! [X0,X1] :
( in(sK69(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f730]) ).
fof(f3671,plain,
spl171_230,
inference(avatar_split_clause,[],[f1152,f3669]) ).
fof(f3669,plain,
( spl171_230
<=> ! [X0,X1] :
( in(sK69(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_230])]) ).
fof(f1152,plain,
! [X0,X1] :
( in(sK69(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f730]) ).
fof(f3667,plain,
spl171_229,
inference(avatar_split_clause,[],[f1111,f3665]) ).
fof(f3665,plain,
( spl171_229
<=> ! [X0] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_229])]) ).
fof(f1111,plain,
! [X0] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f712]) ).
fof(f712,plain,
! [X0] :
( ( ( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0) )
& ( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f344]) ).
fof(f344,plain,
! [X0] :
( ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f298]) ).
fof(f298,axiom,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f3663,plain,
spl171_228,
inference(avatar_split_clause,[],[f1110,f3661]) ).
fof(f3661,plain,
( spl171_228
<=> ! [X0] :
( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_228])]) ).
fof(f1110,plain,
! [X0] :
( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f712]) ).
fof(f3659,plain,
spl171_227,
inference(avatar_split_clause,[],[f1087,f3657]) ).
fof(f3657,plain,
( spl171_227
<=> ! [X0] :
( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_227])]) ).
fof(f1087,plain,
! [X0] :
( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f693]) ).
fof(f693,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) )
& ( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f274]) ).
fof(f274,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f3655,plain,
spl171_226,
inference(avatar_split_clause,[],[f1086,f3653]) ).
fof(f3653,plain,
( spl171_226
<=> ! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_226])]) ).
fof(f1086,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f693]) ).
fof(f3651,plain,
spl171_225,
inference(avatar_split_clause,[],[f1082,f3649]) ).
fof(f1082,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f239]) ).
fof(f239,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f3647,plain,
spl171_224,
inference(avatar_split_clause,[],[f1081,f3645]) ).
fof(f1081,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f3643,plain,
spl171_223,
inference(avatar_split_clause,[],[f1074,f3641]) ).
fof(f3641,plain,
( spl171_223
<=> ! [X0] :
( being_limit_ordinal(X0)
| in(sK53(X0),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_223])]) ).
fof(f1074,plain,
! [X0] :
( being_limit_ordinal(X0)
| in(sK53(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f689]) ).
fof(f3619,plain,
( spl171_221
| ~ spl171_222
| ~ spl171_88
| ~ spl171_131 ),
inference(avatar_split_clause,[],[f3022,f2858,f2567,f3616,f3612]) ).
fof(f3612,plain,
( spl171_221
<=> sP5(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_221])]) ).
fof(f3616,plain,
( spl171_222
<=> well_ordering(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_222])]) ).
fof(f2567,plain,
( spl171_88
<=> sP6(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_88])]) ).
fof(f2858,plain,
( spl171_131
<=> ! [X0] :
( sP5(X0)
| ~ well_ordering(X0)
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_131])]) ).
fof(f3022,plain,
( ~ well_ordering(sK51)
| sP5(sK51)
| ~ spl171_88
| ~ spl171_131 ),
inference(resolution,[],[f2859,f2569]) ).
fof(f2569,plain,
( sP6(sK51)
| ~ spl171_88 ),
inference(avatar_component_clause,[],[f2567]) ).
fof(f2859,plain,
( ! [X0] :
( ~ sP6(X0)
| ~ well_ordering(X0)
| sP5(X0) )
| ~ spl171_131 ),
inference(avatar_component_clause,[],[f2858]) ).
fof(f3549,plain,
( spl171_220
| ~ spl171_12
| ~ spl171_105
| ~ spl171_202 ),
inference(avatar_split_clause,[],[f3371,f3368,f2639,f2076,f3547]) ).
fof(f3547,plain,
( spl171_220
<=> ! [X0] :
( sK160 = X0
| in(sK128(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_220])]) ).
fof(f3368,plain,
( spl171_202
<=> ! [X0] :
( empty_set = X0
| in(sK128(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_202])]) ).
fof(f3371,plain,
( ! [X0] :
( sK160 = X0
| in(sK128(X0),X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_202 ),
inference(forward_demodulation,[],[f3369,f2706]) ).
fof(f3369,plain,
( ! [X0] :
( empty_set = X0
| in(sK128(X0),X0) )
| ~ spl171_202 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f3477,plain,
spl171_219,
inference(avatar_split_clause,[],[f1988,f3475]) ).
fof(f3475,plain,
( spl171_219
<=> ! [X2,X0,X4] :
( in(X4,X2)
| ~ sP44(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_219])]) ).
fof(f1988,plain,
! [X2,X0,X4] :
( in(X4,X2)
| ~ sP44(X0,X4,X2) ),
inference(equality_resolution,[],[f1677]) ).
fof(f1677,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f3473,plain,
spl171_218,
inference(avatar_split_clause,[],[f1987,f3471]) ).
fof(f3471,plain,
( spl171_218
<=> ! [X2,X1,X4] :
( in(X4,X2)
| ~ sP44(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_218])]) ).
fof(f1987,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ sP44(X4,X1,X2) ),
inference(equality_resolution,[],[f1678]) ).
fof(f1678,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f999]) ).
fof(f3469,plain,
spl171_217,
inference(avatar_split_clause,[],[f1986,f3467]) ).
fof(f3467,plain,
( spl171_217
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_217])]) ).
fof(f1986,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f1663]) ).
fof(f1663,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f991]) ).
fof(f3465,plain,
spl171_216,
inference(avatar_split_clause,[],[f1985,f3463]) ).
fof(f3463,plain,
( spl171_216
<=> ! [X0,X3] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_216])]) ).
fof(f1985,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f1664]) ).
fof(f1664,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f991]) ).
fof(f3461,plain,
( spl171_214
| ~ spl171_215
| ~ spl171_57
| ~ spl171_128 ),
inference(avatar_split_clause,[],[f3020,f2845,f2301,f3458,f3454]) ).
fof(f3458,plain,
( spl171_215
<=> connected(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_215])]) ).
fof(f2301,plain,
( spl171_57
<=> sP1(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_57])]) ).
fof(f2845,plain,
( spl171_128
<=> ! [X0] :
( sP0(X0)
| ~ connected(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_128])]) ).
fof(f3020,plain,
( ~ connected(sK51)
| sP0(sK51)
| ~ spl171_57
| ~ spl171_128 ),
inference(resolution,[],[f2846,f2303]) ).
fof(f2303,plain,
( sP1(sK51)
| ~ spl171_57 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f2846,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ connected(X0)
| sP0(X0) )
| ~ spl171_128 ),
inference(avatar_component_clause,[],[f2845]) ).
fof(f3452,plain,
spl171_213,
inference(avatar_split_clause,[],[f1671,f3450]) ).
fof(f3450,plain,
( spl171_213
<=> ! [X0,X1] :
( in(sK148(X1),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_213])]) ).
fof(f1671,plain,
! [X0,X1] :
( in(sK148(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f994]) ).
fof(f3448,plain,
spl171_212,
inference(avatar_split_clause,[],[f1669,f3446]) ).
fof(f3446,plain,
( spl171_212
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_212])]) ).
fof(f1669,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f593]) ).
fof(f593,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f296]) ).
fof(f296,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f3444,plain,
spl171_211,
inference(avatar_split_clause,[],[f1668,f3442]) ).
fof(f3442,plain,
( spl171_211
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_211])]) ).
fof(f1668,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f992]) ).
fof(f992,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f247,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f3440,plain,
spl171_210,
inference(avatar_split_clause,[],[f1667,f3438]) ).
fof(f3438,plain,
( spl171_210
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_210])]) ).
fof(f1667,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f992]) ).
fof(f3436,plain,
spl171_209,
inference(avatar_split_clause,[],[f1658,f3434]) ).
fof(f3434,plain,
( spl171_209
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_209])]) ).
fof(f1658,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f983]) ).
fof(f983,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP43(X0,X1) )
& ( sP43(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f669]) ).
fof(f669,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP43(X0,X1) ),
inference(definition_folding,[],[f49,f668]) ).
fof(f49,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f3402,plain,
( ~ spl171_10
| ~ spl171_207 ),
inference(avatar_contradiction_clause,[],[f3395]) ).
fof(f3395,plain,
( $false
| ~ spl171_10
| ~ spl171_207 ),
inference(resolution,[],[f3390,f2068]) ).
fof(f2068,plain,
( ordinal(empty_set)
| ~ spl171_10 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f2066,plain,
( spl171_10
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_10])]) ).
fof(f3390,plain,
( ! [X1] : ~ ordinal(X1)
| ~ spl171_207 ),
inference(avatar_component_clause,[],[f3389]) ).
fof(f3389,plain,
( spl171_207
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_207])]) ).
fof(f3401,plain,
( ~ spl171_16
| ~ spl171_207 ),
inference(avatar_contradiction_clause,[],[f3396]) ).
fof(f3396,plain,
( $false
| ~ spl171_16
| ~ spl171_207 ),
inference(resolution,[],[f3390,f2098]) ).
fof(f2098,plain,
( ordinal(sK161)
| ~ spl171_16 ),
inference(avatar_component_clause,[],[f2096]) ).
fof(f2096,plain,
( spl171_16
<=> ordinal(sK161) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_16])]) ).
fof(f3400,plain,
( ~ spl171_21
| ~ spl171_207 ),
inference(avatar_contradiction_clause,[],[f3397]) ).
fof(f3397,plain,
( $false
| ~ spl171_21
| ~ spl171_207 ),
inference(resolution,[],[f3390,f2123]) ).
fof(f2123,plain,
( ordinal(sK163)
| ~ spl171_21 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f2121,plain,
( spl171_21
<=> ordinal(sK163) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_21])]) ).
fof(f3399,plain,
( ~ spl171_40
| ~ spl171_207 ),
inference(avatar_contradiction_clause,[],[f3398]) ).
fof(f3398,plain,
( $false
| ~ spl171_40
| ~ spl171_207 ),
inference(resolution,[],[f3390,f2218]) ).
fof(f2218,plain,
( ordinal(sK169)
| ~ spl171_40 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f2216,plain,
( spl171_40
<=> ordinal(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_40])]) ).
fof(f3394,plain,
( spl171_207
| spl171_208 ),
inference(avatar_split_clause,[],[f1620,f3392,f3389]) ).
fof(f3392,plain,
( spl171_208
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_208])]) ).
fof(f1620,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f564]) ).
fof(f564,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f563]) ).
fof(f563,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f178]) ).
fof(f178,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f3387,plain,
spl171_206,
inference(avatar_split_clause,[],[f1562,f3385]) ).
fof(f3385,plain,
( spl171_206
<=> ! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_206])]) ).
fof(f1562,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f935]) ).
fof(f3383,plain,
spl171_205,
inference(avatar_split_clause,[],[f1561,f3381]) ).
fof(f3381,plain,
( spl171_205
<=> ! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_205])]) ).
fof(f1561,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f935]) ).
fof(f3379,plain,
spl171_204,
inference(avatar_split_clause,[],[f1556,f3377]) ).
fof(f1556,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3375,plain,
spl171_203,
inference(avatar_split_clause,[],[f1555,f3373]) ).
fof(f3370,plain,
spl171_202,
inference(avatar_split_clause,[],[f1541,f3368]) ).
fof(f1541,plain,
! [X0] :
( empty_set = X0
| in(sK128(X0),X0) ),
inference(cnf_transformation,[],[f926]) ).
fof(f926,plain,
! [X0] :
( ( empty_set = X0
| in(sK128(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128])],[f924,f925]) ).
fof(f925,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK128(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f924,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f923]) ).
fof(f923,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3366,plain,
spl171_201,
inference(avatar_split_clause,[],[f1530,f3364]) ).
fof(f3364,plain,
( spl171_201
<=> ! [X0] :
( epsilon_connected(X0)
| ~ in(sK123(X0),sK122(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_201])]) ).
fof(f1530,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK123(X0),sK122(X0)) ),
inference(cnf_transformation,[],[f911]) ).
fof(f3362,plain,
spl171_200,
inference(avatar_split_clause,[],[f1529,f3360]) ).
fof(f3360,plain,
( spl171_200
<=> ! [X0] :
( epsilon_connected(X0)
| sK122(X0) != sK123(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_200])]) ).
fof(f1529,plain,
! [X0] :
( epsilon_connected(X0)
| sK122(X0) != sK123(X0) ),
inference(cnf_transformation,[],[f911]) ).
fof(f3358,plain,
spl171_199,
inference(avatar_split_clause,[],[f1528,f3356]) ).
fof(f3356,plain,
( spl171_199
<=> ! [X0] :
( epsilon_connected(X0)
| ~ in(sK122(X0),sK123(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_199])]) ).
fof(f1528,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK122(X0),sK123(X0)) ),
inference(cnf_transformation,[],[f911]) ).
fof(f3354,plain,
spl171_198,
inference(avatar_split_clause,[],[f1485,f3352]) ).
fof(f3352,plain,
( spl171_198
<=> ! [X0] :
( sP27(X0)
| sK113(X0) != sK114(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_198])]) ).
fof(f1485,plain,
! [X0] :
( sP27(X0)
| sK113(X0) != sK114(X0) ),
inference(cnf_transformation,[],[f885]) ).
fof(f3350,plain,
spl171_197,
inference(avatar_split_clause,[],[f1483,f3348]) ).
fof(f3348,plain,
( spl171_197
<=> ! [X0] :
( sP27(X0)
| in(sK114(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_197])]) ).
fof(f1483,plain,
! [X0] :
( sP27(X0)
| in(sK114(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f885]) ).
fof(f3346,plain,
spl171_196,
inference(avatar_split_clause,[],[f1482,f3344]) ).
fof(f3344,plain,
( spl171_196
<=> ! [X0] :
( sP27(X0)
| in(sK113(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_196])]) ).
fof(f1482,plain,
! [X0] :
( sP27(X0)
| in(sK113(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f885]) ).
fof(f3342,plain,
spl171_195,
inference(avatar_split_clause,[],[f1477,f3340]) ).
fof(f3340,plain,
( spl171_195
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_195])]) ).
fof(f1477,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f516]) ).
fof(f516,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f515]) ).
fof(f515,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f3338,plain,
spl171_194,
inference(avatar_split_clause,[],[f1476,f3336]) ).
fof(f3336,plain,
( spl171_194
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_194])]) ).
fof(f1476,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f516]) ).
fof(f3334,plain,
spl171_193,
inference(avatar_split_clause,[],[f1472,f3332]) ).
fof(f3332,plain,
( spl171_193
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_193])]) ).
fof(f1472,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f510]) ).
fof(f510,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f509]) ).
fof(f509,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f3330,plain,
( spl171_191
| ~ spl171_192
| ~ spl171_1
| ~ spl171_145 ),
inference(avatar_split_clause,[],[f3041,f2916,f2021,f3327,f3323]) ).
fof(f3323,plain,
( spl171_191
<=> sP28(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_191])]) ).
fof(f3327,plain,
( spl171_192
<=> function(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_192])]) ).
fof(f2916,plain,
( spl171_145
<=> ! [X0] :
( sP28(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_145])]) ).
fof(f3041,plain,
( ~ function(sK51)
| sP28(sK51)
| ~ spl171_1
| ~ spl171_145 ),
inference(resolution,[],[f2917,f2023]) ).
fof(f2917,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP28(X0) )
| ~ spl171_145 ),
inference(avatar_component_clause,[],[f2916]) ).
fof(f3321,plain,
spl171_190,
inference(avatar_split_clause,[],[f1471,f3319]) ).
fof(f3319,plain,
( spl171_190
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_190])]) ).
fof(f1471,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f508]) ).
fof(f508,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f507]) ).
fof(f507,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f131]) ).
fof(f131,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f3317,plain,
spl171_189,
inference(avatar_split_clause,[],[f1363,f3315]) ).
fof(f3315,plain,
( spl171_189
<=> ! [X0] :
( sP7(X0)
| subset(sK77(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_189])]) ).
fof(f1363,plain,
! [X0] :
( sP7(X0)
| subset(sK77(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f798]) ).
fof(f3313,plain,
spl171_188,
inference(avatar_split_clause,[],[f1340,f3311]) ).
fof(f1340,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f481]) ).
fof(f481,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f3309,plain,
spl171_187,
inference(avatar_split_clause,[],[f1316,f3307]) ).
fof(f3307,plain,
( spl171_187
<=> ! [X0] :
( element(sK76(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_187])]) ).
fof(f1316,plain,
! [X0] :
( element(sK76(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f785]) ).
fof(f785,plain,
! [X0] :
( ( ~ empty(sK76(X0))
& element(sK76(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f469,f784]) ).
fof(f784,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK76(X0))
& element(sK76(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f469,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f3305,plain,
spl171_186,
inference(avatar_split_clause,[],[f1100,f3303]) ).
fof(f3303,plain,
( spl171_186
<=> ! [X0] :
( sP0(X0)
| sK59(X0) != sK60(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_186])]) ).
fof(f1100,plain,
! [X0] :
( sP0(X0)
| sK59(X0) != sK60(X0) ),
inference(cnf_transformation,[],[f706]) ).
fof(f3301,plain,
spl171_185,
inference(avatar_split_clause,[],[f1099,f3299]) ).
fof(f1099,plain,
! [X0] :
( sP0(X0)
| in(sK60(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f706]) ).
fof(f3297,plain,
spl171_184,
inference(avatar_split_clause,[],[f1098,f3295]) ).
fof(f1098,plain,
! [X0] :
( sP0(X0)
| in(sK59(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f706]) ).
fof(f3267,plain,
( spl171_183
| ~ spl171_181
| ~ spl171_182 ),
inference(avatar_split_clause,[],[f3263,f3260,f3250,f3265]) ).
fof(f3250,plain,
( spl171_181
<=> ! [X0] : sK160 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_181])]) ).
fof(f3260,plain,
( spl171_182
<=> ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_182])]) ).
fof(f3263,plain,
( ! [X0] : set_difference(X0,sK160) = X0
| ~ spl171_181
| ~ spl171_182 ),
inference(forward_demodulation,[],[f3261,f3251]) ).
fof(f3251,plain,
( ! [X0] : sK160 = set_difference(X0,X0)
| ~ spl171_181 ),
inference(avatar_component_clause,[],[f3250]) ).
fof(f3261,plain,
( ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0
| ~ spl171_182 ),
inference(avatar_component_clause,[],[f3260]) ).
fof(f3262,plain,
spl171_182,
inference(avatar_split_clause,[],[f1904,f3260]) ).
fof(f1904,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f1554,f1148]) ).
fof(f1554,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f3252,plain,
( spl171_181
| ~ spl171_12
| ~ spl171_100
| ~ spl171_105
| ~ spl171_180 ),
inference(avatar_split_clause,[],[f3248,f3244,f2639,f2619,f2076,f3250]) ).
fof(f2619,plain,
( spl171_100
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_100])]) ).
fof(f3244,plain,
( spl171_180
<=> ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_180])]) ).
fof(f3248,plain,
( ! [X0] : sK160 = set_difference(X0,X0)
| ~ spl171_12
| ~ spl171_100
| ~ spl171_105
| ~ spl171_180 ),
inference(forward_demodulation,[],[f3247,f2706]) ).
fof(f3247,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl171_100
| ~ spl171_180 ),
inference(forward_demodulation,[],[f3245,f2620]) ).
fof(f2620,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl171_100 ),
inference(avatar_component_clause,[],[f2619]) ).
fof(f3245,plain,
( ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set))
| ~ spl171_180 ),
inference(avatar_component_clause,[],[f3244]) ).
fof(f3246,plain,
spl171_180,
inference(avatar_split_clause,[],[f1842,f3244]) ).
fof(f1842,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f1308,f1148]) ).
fof(f1308,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f226]) ).
fof(f226,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f3242,plain,
spl171_179,
inference(avatar_split_clause,[],[f1766,f3240]) ).
fof(f3240,plain,
( spl171_179
<=> ! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_179])]) ).
fof(f1766,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1063,f1763]) ).
fof(f1063,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f182]) ).
fof(f182,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f3238,plain,
spl171_178,
inference(avatar_split_clause,[],[f1178,f3236]) ).
fof(f3236,plain,
( spl171_178
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_178])]) ).
fof(f1178,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f302]) ).
fof(f302,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f3234,plain,
spl171_177,
inference(avatar_split_clause,[],[f1160,f3232]) ).
fof(f3232,plain,
( spl171_177
<=> ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_177])]) ).
fof(f1160,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f295]) ).
fof(f295,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f3230,plain,
spl171_176,
inference(avatar_split_clause,[],[f1159,f3228]) ).
fof(f1159,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f3226,plain,
spl171_175,
inference(avatar_split_clause,[],[f1155,f3224]) ).
fof(f3224,plain,
( spl171_175
<=> ! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_175])]) ).
fof(f1155,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f368]) ).
fof(f368,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f221]) ).
fof(f221,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f3222,plain,
spl171_174,
inference(avatar_split_clause,[],[f1073,f3220]) ).
fof(f3220,plain,
( spl171_174
<=> ! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK53(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_174])]) ).
fof(f1073,plain,
! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK53(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f689]) ).
fof(f3218,plain,
spl171_173,
inference(avatar_split_clause,[],[f1069,f3216]) ).
fof(f3216,plain,
( spl171_173
<=> ! [X0] :
( ordinal(sK52(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_173])]) ).
fof(f1069,plain,
! [X0] :
( ordinal(sK52(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f685]) ).
fof(f3140,plain,
( spl171_172
| ~ spl171_12
| ~ spl171_105
| ~ spl171_156 ),
inference(avatar_split_clause,[],[f2963,f2960,f2639,f2076,f3138]) ).
fof(f3138,plain,
( spl171_172
<=> ! [X0,X1] :
( sK160 = X0
| sP36(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_172])]) ).
fof(f2960,plain,
( spl171_156
<=> ! [X0,X1] :
( sP36(X1,X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_156])]) ).
fof(f2963,plain,
( ! [X0,X1] :
( sK160 = X0
| sP36(X1,X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_156 ),
inference(forward_demodulation,[],[f2961,f2706]) ).
fof(f2961,plain,
( ! [X0,X1] :
( sP36(X1,X0)
| empty_set = X0 )
| ~ spl171_156 ),
inference(avatar_component_clause,[],[f2960]) ).
fof(f3029,plain,
( spl171_171
| ~ spl171_12
| ~ spl171_105
| ~ spl171_135 ),
inference(avatar_split_clause,[],[f2877,f2874,f2639,f2076,f3027]) ).
fof(f3027,plain,
( spl171_171
<=> ! [X0] :
( sK77(X0) != sK160
| sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_171])]) ).
fof(f2874,plain,
( spl171_135
<=> ! [X0] :
( sP7(X0)
| empty_set != sK77(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_135])]) ).
fof(f2877,plain,
( ! [X0] :
( sK77(X0) != sK160
| sP7(X0) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_135 ),
inference(forward_demodulation,[],[f2875,f2706]) ).
fof(f2875,plain,
( ! [X0] :
( sP7(X0)
| empty_set != sK77(X0) )
| ~ spl171_135 ),
inference(avatar_component_clause,[],[f2874]) ).
fof(f3019,plain,
spl171_170,
inference(avatar_split_clause,[],[f1993,f3017]) ).
fof(f1993,plain,
! [X0,X1] : sP47(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f1708]) ).
fof(f1708,plain,
! [X2,X0,X1] :
( sP47(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1019]) ).
fof(f3015,plain,
spl171_169,
inference(avatar_split_clause,[],[f1992,f3013]) ).
fof(f1992,plain,
! [X0,X1] : sP46(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f1700]) ).
fof(f1700,plain,
! [X2,X0,X1] :
( sP46(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1013]) ).
fof(f3011,plain,
spl171_168,
inference(avatar_split_clause,[],[f1991,f3009]) ).
fof(f3009,plain,
( spl171_168
<=> ! [X0,X1] : sP45(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_168])]) ).
fof(f1991,plain,
! [X0,X1] : sP45(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f1692]) ).
fof(f1692,plain,
! [X2,X0,X1] :
( sP45(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1007]) ).
fof(f3007,plain,
spl171_167,
inference(avatar_split_clause,[],[f1989,f3005]) ).
fof(f3005,plain,
( spl171_167
<=> ! [X0,X1] : sP44(X1,X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_167])]) ).
fof(f1989,plain,
! [X0,X1] : sP44(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f1682]) ).
fof(f1682,plain,
! [X2,X0,X1] :
( sP44(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1000]) ).
fof(f3003,plain,
spl171_166,
inference(avatar_split_clause,[],[f1961,f3001]) ).
fof(f1961,plain,
! [X0] :
( sP29(X0,relation_rng(X0))
| ~ sP30(X0) ),
inference(equality_resolution,[],[f1487]) ).
fof(f1487,plain,
! [X0,X1] :
( sP29(X0,X1)
| relation_rng(X0) != X1
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f886]) ).
fof(f2999,plain,
spl171_165,
inference(avatar_split_clause,[],[f1601,f2997]) ).
fof(f1601,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f550]) ).
fof(f550,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f212]) ).
fof(f212,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f2995,plain,
spl171_164,
inference(avatar_split_clause,[],[f1600,f2993]) ).
fof(f1600,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f549]) ).
fof(f549,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2991,plain,
spl171_163,
inference(avatar_split_clause,[],[f1598,f2989]) ).
fof(f2989,plain,
( spl171_163
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_163])]) ).
fof(f1598,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f546]) ).
fof(f546,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f2987,plain,
spl171_162,
inference(avatar_split_clause,[],[f1597,f2985]) ).
fof(f2985,plain,
( spl171_162
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_162])]) ).
fof(f1597,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f545,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f2983,plain,
spl171_161,
inference(avatar_split_clause,[],[f1578,f2981]) ).
fof(f2981,plain,
( spl171_161
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_161])]) ).
fof(f1578,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f2979,plain,
spl171_160,
inference(avatar_split_clause,[],[f1577,f2977]) ).
fof(f1577,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f541]) ).
fof(f541,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f2975,plain,
spl171_159,
inference(avatar_split_clause,[],[f1576,f2973]) ).
fof(f2973,plain,
( spl171_159
<=> ! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_159])]) ).
fof(f1576,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f540]) ).
fof(f540,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f2971,plain,
spl171_158,
inference(avatar_split_clause,[],[f1575,f2969]) ).
fof(f2969,plain,
( spl171_158
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_158])]) ).
fof(f1575,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f539]) ).
fof(f539,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f2967,plain,
spl171_157,
inference(avatar_split_clause,[],[f1574,f2965]) ).
fof(f1574,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f538]) ).
fof(f538,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f2962,plain,
spl171_156,
inference(avatar_split_clause,[],[f1571,f2960]) ).
fof(f1571,plain,
! [X0,X1] :
( sP36(X1,X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f944]) ).
fof(f944,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP36(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f658]) ).
fof(f658,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP36(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f537,f657,f656]) ).
fof(f537,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f2958,plain,
spl171_155,
inference(avatar_split_clause,[],[f1538,f2956]) ).
fof(f2956,plain,
( spl171_155
<=> ! [X0] :
( relation(X0)
| in(sK125(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_155])]) ).
fof(f1538,plain,
! [X0] :
( relation(X0)
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f2954,plain,
spl171_154,
inference(avatar_split_clause,[],[f1533,f2952]) ).
fof(f2952,plain,
( spl171_154
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK124(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_154])]) ).
fof(f1533,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK124(X0),X0) ),
inference(cnf_transformation,[],[f915]) ).
fof(f2950,plain,
spl171_153,
inference(avatar_split_clause,[],[f1532,f2948]) ).
fof(f2948,plain,
( spl171_153
<=> ! [X0] :
( epsilon_transitive(X0)
| in(sK124(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_153])]) ).
fof(f1532,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK124(X0),X0) ),
inference(cnf_transformation,[],[f915]) ).
fof(f2946,plain,
spl171_152,
inference(avatar_split_clause,[],[f1527,f2944]) ).
fof(f2944,plain,
( spl171_152
<=> ! [X0] :
( epsilon_connected(X0)
| in(sK123(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_152])]) ).
fof(f1527,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK123(X0),X0) ),
inference(cnf_transformation,[],[f911]) ).
fof(f2942,plain,
spl171_151,
inference(avatar_split_clause,[],[f1526,f2940]) ).
fof(f2940,plain,
( spl171_151
<=> ! [X0] :
( epsilon_connected(X0)
| in(sK122(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_151])]) ).
fof(f1526,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK122(X0),X0) ),
inference(cnf_transformation,[],[f911]) ).
fof(f2938,plain,
spl171_150,
inference(avatar_split_clause,[],[f1524,f2936]) ).
fof(f2936,plain,
( spl171_150
<=> ! [X0] :
( being_limit_ordinal(X0)
| union(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_150])]) ).
fof(f1524,plain,
! [X0] :
( being_limit_ordinal(X0)
| union(X0) != X0 ),
inference(cnf_transformation,[],[f907]) ).
fof(f907,plain,
! [X0] :
( ( being_limit_ordinal(X0)
| union(X0) != X0 )
& ( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> union(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f2934,plain,
spl171_149,
inference(avatar_split_clause,[],[f1523,f2932]) ).
fof(f2932,plain,
( spl171_149
<=> ! [X0] :
( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_149])]) ).
fof(f1523,plain,
! [X0] :
( union(X0) = X0
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f907]) ).
fof(f2930,plain,
spl171_148,
inference(avatar_split_clause,[],[f1519,f2928]) ).
fof(f2928,plain,
( spl171_148
<=> ! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_148])]) ).
fof(f1519,plain,
! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f655]) ).
fof(f655,plain,
! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f528,f654,f653]) ).
fof(f528,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f527]) ).
fof(f527,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f2926,plain,
spl171_147,
inference(avatar_split_clause,[],[f1508,f2924]) ).
fof(f2924,plain,
( spl171_147
<=> ! [X0] :
( sP32(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_147])]) ).
fof(f1508,plain,
! [X0] :
( sP32(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f652]) ).
fof(f652,plain,
! [X0] :
( sP32(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f526,f651,f650]) ).
fof(f526,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f525]) ).
fof(f525,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f2922,plain,
spl171_146,
inference(avatar_split_clause,[],[f1495,f2920]) ).
fof(f2920,plain,
( spl171_146
<=> ! [X0] :
( sP30(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_146])]) ).
fof(f1495,plain,
! [X0] :
( sP30(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f649]) ).
fof(f649,plain,
! [X0] :
( sP30(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f522,f648,f647]) ).
fof(f522,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f521]) ).
fof(f521,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f2918,plain,
spl171_145,
inference(avatar_split_clause,[],[f1486,f2916]) ).
fof(f1486,plain,
! [X0] :
( sP28(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f646]) ).
fof(f646,plain,
! [X0] :
( sP28(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f520,f645,f644]) ).
fof(f645,plain,
! [X0] :
( ( one_to_one(X0)
<=> sP27(X0) )
| ~ sP28(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f520,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f519]) ).
fof(f519,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f2914,plain,
spl171_144,
inference(avatar_split_clause,[],[f1480,f2912]) ).
fof(f2912,plain,
( spl171_144
<=> ! [X0] :
( one_to_one(X0)
| ~ sP27(X0)
| ~ sP28(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_144])]) ).
fof(f1480,plain,
! [X0] :
( one_to_one(X0)
| ~ sP27(X0)
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f881]) ).
fof(f881,plain,
! [X0] :
( ( ( one_to_one(X0)
| ~ sP27(X0) )
& ( sP27(X0)
| ~ one_to_one(X0) ) )
| ~ sP28(X0) ),
inference(nnf_transformation,[],[f645]) ).
fof(f2910,plain,
spl171_143,
inference(avatar_split_clause,[],[f1479,f2908]) ).
fof(f2908,plain,
( spl171_143
<=> ! [X0] :
( sP27(X0)
| ~ one_to_one(X0)
| ~ sP28(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_143])]) ).
fof(f1479,plain,
! [X0] :
( sP27(X0)
| ~ one_to_one(X0)
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f881]) ).
fof(f2906,plain,
spl171_142,
inference(avatar_split_clause,[],[f1473,f2904]) ).
fof(f2904,plain,
( spl171_142
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_142])]) ).
fof(f1473,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f512]) ).
fof(f512,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f511]) ).
fof(f511,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f2902,plain,
spl171_141,
inference(avatar_split_clause,[],[f1394,f2900]) ).
fof(f2900,plain,
( spl171_141
<=> ! [X0,X1] :
( is_well_founded_in(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_141])]) ).
fof(f1394,plain,
! [X0,X1] :
( is_well_founded_in(X1,X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f2898,plain,
( spl171_140
| ~ spl171_1
| ~ spl171_79 ),
inference(avatar_split_clause,[],[f2557,f2391,f2021,f2895]) ).
fof(f2895,plain,
( spl171_140
<=> sP26(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_140])]) ).
fof(f2557,plain,
( sP26(sK51)
| ~ spl171_1
| ~ spl171_79 ),
inference(resolution,[],[f2392,f2023]) ).
fof(f2893,plain,
spl171_139,
inference(avatar_split_clause,[],[f1393,f2891]) ).
fof(f2891,plain,
( spl171_139
<=> ! [X0,X1] :
( is_connected_in(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_139])]) ).
fof(f1393,plain,
! [X0,X1] :
( is_connected_in(X1,X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f2889,plain,
spl171_138,
inference(avatar_split_clause,[],[f1392,f2887]) ).
fof(f2887,plain,
( spl171_138
<=> ! [X0,X1] :
( is_antisymmetric_in(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_138])]) ).
fof(f1392,plain,
! [X0,X1] :
( is_antisymmetric_in(X1,X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f2885,plain,
spl171_137,
inference(avatar_split_clause,[],[f1391,f2883]) ).
fof(f2883,plain,
( spl171_137
<=> ! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_137])]) ).
fof(f1391,plain,
! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f2881,plain,
spl171_136,
inference(avatar_split_clause,[],[f1390,f2879]) ).
fof(f2879,plain,
( spl171_136
<=> ! [X0,X1] :
( is_reflexive_in(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_136])]) ).
fof(f1390,plain,
! [X0,X1] :
( is_reflexive_in(X1,X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f2876,plain,
spl171_135,
inference(avatar_split_clause,[],[f1364,f2874]) ).
fof(f1364,plain,
! [X0] :
( sP7(X0)
| empty_set != sK77(X0) ),
inference(cnf_transformation,[],[f798]) ).
fof(f2872,plain,
spl171_134,
inference(avatar_split_clause,[],[f1360,f2870]) ).
fof(f2870,plain,
( spl171_134
<=> ! [X0] :
( well_founded_relation(X0)
| ~ sP7(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_134])]) ).
fof(f1360,plain,
! [X0] :
( well_founded_relation(X0)
| ~ sP7(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f793]) ).
fof(f793,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ well_founded_relation(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f615]) ).
fof(f615,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2868,plain,
spl171_133,
inference(avatar_split_clause,[],[f1359,f2866]) ).
fof(f1359,plain,
! [X0] :
( sP7(X0)
| ~ well_founded_relation(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f793]) ).
fof(f2864,plain,
spl171_132,
inference(avatar_split_clause,[],[f1343,f2862]) ).
fof(f2862,plain,
( spl171_132
<=> ! [X0] :
( well_ordering(X0)
| ~ sP5(X0)
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_132])]) ).
fof(f1343,plain,
! [X0] :
( well_ordering(X0)
| ~ sP5(X0)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f786,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ well_ordering(X0) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0] :
( ( well_ordering(X0)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2860,plain,
spl171_131,
inference(avatar_split_clause,[],[f1342,f2858]) ).
fof(f1342,plain,
! [X0] :
( sP5(X0)
| ~ well_ordering(X0)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f2856,plain,
spl171_130,
inference(avatar_split_clause,[],[f1096,f2854]) ).
fof(f2854,plain,
( spl171_130
<=> ! [X0] :
( connected(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_130])]) ).
fof(f1096,plain,
! [X0] :
( connected(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f702,plain,
! [X0] :
( ( ( connected(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ connected(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f605]) ).
fof(f605,plain,
! [X0] :
( ( connected(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f2852,plain,
( spl171_129
| ~ spl171_1
| ~ spl171_77 ),
inference(avatar_split_clause,[],[f2546,f2382,f2021,f2849]) ).
fof(f2849,plain,
( spl171_129
<=> sP24(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_129])]) ).
fof(f2546,plain,
( sP24(sK51)
| ~ spl171_1
| ~ spl171_77 ),
inference(resolution,[],[f2383,f2023]) ).
fof(f2847,plain,
spl171_128,
inference(avatar_split_clause,[],[f1095,f2845]) ).
fof(f1095,plain,
! [X0] :
( sP0(X0)
| ~ connected(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2835,plain,
( spl171_127
| ~ spl171_12
| ~ spl171_105
| ~ spl171_124 ),
inference(avatar_split_clause,[],[f2815,f2811,f2639,f2076,f2832]) ).
fof(f2832,plain,
( spl171_127
<=> powerset(sK160) = unordered_pair(sK160,sK160) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_127])]) ).
fof(f2811,plain,
( spl171_124
<=> powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_124])]) ).
fof(f2815,plain,
( powerset(sK160) = unordered_pair(sK160,sK160)
| ~ spl171_12
| ~ spl171_105
| ~ spl171_124 ),
inference(forward_demodulation,[],[f2813,f2706]) ).
fof(f2813,plain,
( powerset(empty_set) = unordered_pair(empty_set,empty_set)
| ~ spl171_124 ),
inference(avatar_component_clause,[],[f2811]) ).
fof(f2823,plain,
( spl171_126
| ~ spl171_12
| ~ spl171_105
| ~ spl171_120 ),
inference(avatar_split_clause,[],[f2796,f2792,f2639,f2076,f2821]) ).
fof(f2821,plain,
( spl171_126
<=> ! [X0] :
( ~ subset(X0,sK160)
| sK160 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_126])]) ).
fof(f2792,plain,
( spl171_120
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_120])]) ).
fof(f2796,plain,
( ! [X0] :
( ~ subset(X0,sK160)
| sK160 = X0 )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_120 ),
inference(forward_demodulation,[],[f2795,f2706]) ).
fof(f2795,plain,
( ! [X0] :
( sK160 = X0
| ~ subset(X0,empty_set) )
| ~ spl171_12
| ~ spl171_105
| ~ spl171_120 ),
inference(forward_demodulation,[],[f2793,f2706]) ).
fof(f2793,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl171_120 ),
inference(avatar_component_clause,[],[f2792]) ).
fof(f2819,plain,
spl171_125,
inference(avatar_split_clause,[],[f1840,f2817]) ).
fof(f2817,plain,
( spl171_125
<=> ! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_125])]) ).
fof(f1840,plain,
! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1303,f1763]) ).
fof(f1303,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f110]) ).
fof(f110,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f2814,plain,
spl171_124,
inference(avatar_split_clause,[],[f1764,f2811]) ).
fof(f1764,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f1058,f1065]) ).
fof(f1058,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f214]) ).
fof(f214,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f2809,plain,
( spl171_123
| ~ spl171_1
| ~ spl171_76 ),
inference(avatar_split_clause,[],[f2535,f2378,f2021,f2806]) ).
fof(f2806,plain,
( spl171_123
<=> sP20(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_123])]) ).
fof(f2535,plain,
( sP20(sK51)
| ~ spl171_1
| ~ spl171_76 ),
inference(resolution,[],[f2379,f2023]) ).
fof(f2804,plain,
spl171_122,
inference(avatar_split_clause,[],[f1227,f2802]) ).
fof(f1227,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f424]) ).
fof(f424,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f276]) ).
fof(f276,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f2800,plain,
spl171_121,
inference(avatar_split_clause,[],[f1139,f2798]) ).
fof(f2798,plain,
( spl171_121
<=> ! [X0] :
( ordinal(X0)
| in(sK66(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_121])]) ).
fof(f1139,plain,
! [X0] :
( ordinal(X0)
| in(sK66(X0),X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f2794,plain,
spl171_120,
inference(avatar_split_clause,[],[f1120,f2792]) ).
fof(f1120,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f249]) ).
fof(f249,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f2755,plain,
( spl171_119
| ~ spl171_1
| ~ spl171_75 ),
inference(avatar_split_clause,[],[f2524,f2374,f2021,f2752]) ).
fof(f2752,plain,
( spl171_119
<=> sP18(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_119])]) ).
fof(f2524,plain,
( sP18(sK51)
| ~ spl171_1
| ~ spl171_75 ),
inference(resolution,[],[f2375,f2023]) ).
fof(f2697,plain,
( spl171_118
| ~ spl171_1
| ~ spl171_74 ),
inference(avatar_split_clause,[],[f2513,f2370,f2021,f2694]) ).
fof(f2694,plain,
( spl171_118
<=> sP16(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_118])]) ).
fof(f2513,plain,
( sP16(sK51)
| ~ spl171_1
| ~ spl171_74 ),
inference(resolution,[],[f2371,f2023]) ).
fof(f2690,plain,
spl171_117,
inference(avatar_split_clause,[],[f1670,f2688]) ).
fof(f1670,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f594]) ).
fof(f594,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f290]) ).
fof(f290,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f2686,plain,
spl171_116,
inference(avatar_split_clause,[],[f1587,f2684]) ).
fof(f2684,plain,
( spl171_116
<=> ! [X0,X1] :
( sP38(X1,X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_116])]) ).
fof(f1587,plain,
! [X0,X1] :
( sP38(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f661]) ).
fof(f661,plain,
! [X0,X1] :
( sP38(X1,X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f543,f660,f659]) ).
fof(f543,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f2682,plain,
spl171_115,
inference(avatar_split_clause,[],[f1553,f2680]) ).
fof(f2680,plain,
( spl171_115
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_115])]) ).
fof(f1553,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f2678,plain,
spl171_114,
inference(avatar_split_clause,[],[f1547,f2676]) ).
fof(f2676,plain,
( spl171_114
<=> ! [X0] : element(sK132(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_114])]) ).
fof(f1547,plain,
! [X0] : element(sK132(X0),powerset(X0)),
inference(cnf_transformation,[],[f934]) ).
fof(f934,plain,
! [X0] :
( empty(sK132(X0))
& element(sK132(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f168,f933]) ).
fof(f933,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK132(X0))
& element(sK132(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f168,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f2674,plain,
spl171_113,
inference(avatar_split_clause,[],[f1339,f2672]) ).
fof(f2672,plain,
( spl171_113
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_113])]) ).
fof(f1339,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f480]) ).
fof(f480,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f2670,plain,
spl171_112,
inference(avatar_split_clause,[],[f1338,f2668]) ).
fof(f2668,plain,
( spl171_112
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_112])]) ).
fof(f1338,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f479,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f132]) ).
fof(f132,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f2666,plain,
spl171_111,
inference(avatar_split_clause,[],[f1337,f2664]) ).
fof(f2664,plain,
( spl171_111
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_111])]) ).
fof(f1337,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f2662,plain,
spl171_110,
inference(avatar_split_clause,[],[f1336,f2660]) ).
fof(f2660,plain,
( spl171_110
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_110])]) ).
fof(f1336,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f478]) ).
fof(f478,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f2658,plain,
( spl171_109
| ~ spl171_1
| ~ spl171_73 ),
inference(avatar_split_clause,[],[f2502,f2366,f2021,f2655]) ).
fof(f2655,plain,
( spl171_109
<=> sP14(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_109])]) ).
fof(f2502,plain,
( sP14(sK51)
| ~ spl171_1
| ~ spl171_73 ),
inference(resolution,[],[f2367,f2023]) ).
fof(f2653,plain,
spl171_108,
inference(avatar_split_clause,[],[f1335,f2651]) ).
fof(f2651,plain,
( spl171_108
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_108])]) ).
fof(f1335,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f478]) ).
fof(f2649,plain,
spl171_107,
inference(avatar_split_clause,[],[f1334,f2647]) ).
fof(f2647,plain,
( spl171_107
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_107])]) ).
fof(f1334,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f477]) ).
fof(f477,plain,
! [X0] :
( ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f2645,plain,
spl171_106,
inference(avatar_split_clause,[],[f1333,f2643]) ).
fof(f1333,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f477]) ).
fof(f2641,plain,
spl171_105,
inference(avatar_split_clause,[],[f1329,f2639]) ).
fof(f1329,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f475]) ).
fof(f475,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f284]) ).
fof(f284,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f2637,plain,
spl171_104,
inference(avatar_split_clause,[],[f1326,f2635]) ).
fof(f2635,plain,
( spl171_104
<=> ! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_104])]) ).
fof(f1326,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f472]) ).
fof(f472,plain,
! [X0] :
( ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(f2633,plain,
spl171_103,
inference(avatar_split_clause,[],[f1325,f2631]) ).
fof(f2631,plain,
( spl171_103
<=> ! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_103])]) ).
fof(f1325,plain,
! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f472]) ).
fof(f2629,plain,
spl171_102,
inference(avatar_split_clause,[],[f1324,f2627]) ).
fof(f2627,plain,
( spl171_102
<=> ! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_102])]) ).
fof(f1324,plain,
! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f472]) ).
fof(f2625,plain,
spl171_101,
inference(avatar_split_clause,[],[f1317,f2623]) ).
fof(f2623,plain,
( spl171_101
<=> ! [X0] :
( ~ empty(sK76(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_101])]) ).
fof(f1317,plain,
! [X0] :
( ~ empty(sK76(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f785]) ).
fof(f2621,plain,
spl171_100,
inference(avatar_split_clause,[],[f1311,f2619]) ).
fof(f1311,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f245]) ).
fof(f245,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f2617,plain,
spl171_99,
inference(avatar_split_clause,[],[f1310,f2615]) ).
fof(f2615,plain,
( spl171_99
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_99])]) ).
fof(f1310,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f211]) ).
fof(f211,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f2613,plain,
( spl171_98
| ~ spl171_1
| ~ spl171_72 ),
inference(avatar_split_clause,[],[f2491,f2362,f2021,f2610]) ).
fof(f2610,plain,
( spl171_98
<=> sP12(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_98])]) ).
fof(f2491,plain,
( sP12(sK51)
| ~ spl171_1
| ~ spl171_72 ),
inference(resolution,[],[f2363,f2023]) ).
fof(f2608,plain,
spl171_97,
inference(avatar_split_clause,[],[f1309,f2606]) ).
fof(f2606,plain,
( spl171_97
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_97])]) ).
fof(f1309,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f264]) ).
fof(f264,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f2603,plain,
spl171_96,
inference(avatar_split_clause,[],[f1983,f2601]) ).
fof(f2601,plain,
( spl171_96
<=> ! [X3] : in(X3,unordered_pair(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_96])]) ).
fof(f1983,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f1982]) ).
fof(f1982,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f1923]) ).
fof(f1923,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1660,f1065]) ).
fof(f1660,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f987]) ).
fof(f2599,plain,
spl171_95,
inference(avatar_split_clause,[],[f1765,f2597]) ).
fof(f2597,plain,
( spl171_95
<=> ! [X0] : empty_set != unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_95])]) ).
fof(f1765,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f1062,f1065]) ).
fof(f1062,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f142]) ).
fof(f142,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f2595,plain,
( spl171_94
| ~ spl171_1
| ~ spl171_71 ),
inference(avatar_split_clause,[],[f2480,f2358,f2021,f2592]) ).
fof(f2480,plain,
( sP8(sK51)
| ~ spl171_1
| ~ spl171_71 ),
inference(resolution,[],[f2359,f2023]) ).
fof(f2590,plain,
spl171_93,
inference(avatar_split_clause,[],[f1145,f2588]) ).
fof(f2588,plain,
( spl171_93
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_93])]) ).
fof(f1145,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f238]) ).
fof(f238,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f2586,plain,
spl171_92,
inference(avatar_split_clause,[],[f1144,f2584]) ).
fof(f1144,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f292]) ).
fof(f292,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f2582,plain,
spl171_91,
inference(avatar_split_clause,[],[f1067,f2580]) ).
fof(f1067,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f287]) ).
fof(f287,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f2578,plain,
spl171_90,
inference(avatar_split_clause,[],[f1066,f2576]) ).
fof(f2576,plain,
( spl171_90
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_90])]) ).
fof(f1066,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f287]) ).
fof(f2574,plain,
spl171_89,
inference(avatar_split_clause,[],[f1064,f2572]) ).
fof(f2572,plain,
( spl171_89
<=> ! [X0] : union(powerset(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl171_89])]) ).
fof(f1064,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f305]) ).
fof(f305,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f2570,plain,
( spl171_88
| ~ spl171_1
| ~ spl171_70 ),
inference(avatar_split_clause,[],[f2469,f2354,f2021,f2567]) ).
fof(f2469,plain,
( sP6(sK51)
| ~ spl171_1
| ~ spl171_70 ),
inference(resolution,[],[f2355,f2023]) ).
fof(f2466,plain,
( spl171_87
| ~ spl171_23
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2289,f2278,f2131,f2463]) ).
fof(f2463,plain,
( spl171_87
<=> sP1(sK164) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_87])]) ).
fof(f2289,plain,
( sP1(sK164)
| ~ spl171_23
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2133]) ).
fof(f2431,plain,
( spl171_86
| ~ spl171_18
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2288,f2278,f2106,f2428]) ).
fof(f2428,plain,
( spl171_86
<=> sP1(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_86])]) ).
fof(f2288,plain,
( sP1(sK162)
| ~ spl171_18
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2108]) ).
fof(f2418,plain,
spl171_85,
inference(avatar_split_clause,[],[f2002,f2416]) ).
fof(f2416,plain,
( spl171_85
<=> ! [X0] : element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_85])]) ).
fof(f2002,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f1312,f1307]) ).
fof(f1307,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f1312,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f2414,plain,
spl171_84,
inference(avatar_split_clause,[],[f1981,f2412]) ).
fof(f2412,plain,
( spl171_84
<=> ! [X0] : sP43(X0,union(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_84])]) ).
fof(f1981,plain,
! [X0] : sP43(X0,union(X0)),
inference(equality_resolution,[],[f1657]) ).
fof(f1657,plain,
! [X0,X1] :
( sP43(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f983]) ).
fof(f2410,plain,
spl171_83,
inference(avatar_split_clause,[],[f1972,f2407]) ).
fof(f2407,plain,
( spl171_83
<=> empty_set = set_meet(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_83])]) ).
fof(f1972,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f1971]) ).
fof(f1971,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f1573]) ).
fof(f1573,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f944]) ).
fof(f2405,plain,
spl171_82,
inference(avatar_split_clause,[],[f1551,f2403]) ).
fof(f2403,plain,
( spl171_82
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_82])]) ).
fof(f1551,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f2401,plain,
spl171_81,
inference(avatar_split_clause,[],[f1543,f2399]) ).
fof(f1543,plain,
! [X0] : in(X0,sK130(X0)),
inference(cnf_transformation,[],[f932]) ).
fof(f2397,plain,
spl171_80,
inference(avatar_split_clause,[],[f1542,f2395]) ).
fof(f2395,plain,
( spl171_80
<=> ! [X0] : element(sK129(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_80])]) ).
fof(f1542,plain,
! [X0] : element(sK129(X0),X0),
inference(cnf_transformation,[],[f928]) ).
fof(f928,plain,
! [X0] : element(sK129(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129])],[f104,f927]) ).
fof(f927,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK129(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f104,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f2393,plain,
spl171_79,
inference(avatar_split_clause,[],[f1470,f2391]) ).
fof(f1470,plain,
! [X0] :
( sP26(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f643]) ).
fof(f643,plain,
! [X0] :
( sP26(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f506,f642,f641]) ).
fof(f506,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f2389,plain,
( spl171_78
| ~ spl171_4
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2286,f2278,f2036,f2386]) ).
fof(f2386,plain,
( spl171_78
<=> sP1(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_78])]) ).
fof(f2286,plain,
( sP1(empty_set)
| ~ spl171_4
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2038]) ).
fof(f2384,plain,
spl171_77,
inference(avatar_split_clause,[],[f1461,f2382]) ).
fof(f1461,plain,
! [X0] :
( sP24(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f640]) ).
fof(f640,plain,
! [X0] :
( sP24(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f505,f639,f638]) ).
fof(f505,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f2380,plain,
spl171_76,
inference(avatar_split_clause,[],[f1435,f2378]) ).
fof(f1435,plain,
! [X0] :
( sP20(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f634]) ).
fof(f634,plain,
! [X0] :
( sP20(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f501,f633,f632]) ).
fof(f501,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f500]) ).
fof(f500,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f2376,plain,
spl171_75,
inference(avatar_split_clause,[],[f1425,f2374]) ).
fof(f1425,plain,
! [X0] :
( sP18(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f631]) ).
fof(f631,plain,
! [X0] :
( sP18(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f499,f630,f629]) ).
fof(f499,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f2372,plain,
spl171_74,
inference(avatar_split_clause,[],[f1416,f2370]) ).
fof(f1416,plain,
! [X0] :
( sP16(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f628]) ).
fof(f628,plain,
! [X0] :
( sP16(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f498,f627,f626]) ).
fof(f498,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f497]) ).
fof(f497,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f2368,plain,
spl171_73,
inference(avatar_split_clause,[],[f1407,f2366]) ).
fof(f1407,plain,
! [X0] :
( sP14(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0] :
( sP14(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f496,f624,f623]) ).
fof(f496,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f2364,plain,
spl171_72,
inference(avatar_split_clause,[],[f1396,f2362]) ).
fof(f1396,plain,
! [X0] :
( sP12(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f622]) ).
fof(f622,plain,
! [X0] :
( sP12(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f494,f621,f620]) ).
fof(f494,plain,
! [X0] :
( ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
fof(f2360,plain,
spl171_71,
inference(avatar_split_clause,[],[f1366,f2358]) ).
fof(f1366,plain,
! [X0] :
( sP8(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f616]) ).
fof(f616,plain,
! [X0] :
( sP8(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f488,f615,f614]) ).
fof(f488,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( ! [X2] :
~ ( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f2356,plain,
spl171_70,
inference(avatar_split_clause,[],[f1350,f2354]) ).
fof(f1350,plain,
! [X0] :
( sP6(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0] :
( sP6(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f483,f612,f611]) ).
fof(f483,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f2352,plain,
spl171_69,
inference(avatar_split_clause,[],[f1348,f2350]) ).
fof(f2350,plain,
( spl171_69
<=> ! [X0] :
( well_founded_relation(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_69])]) ).
fof(f1348,plain,
! [X0] :
( well_founded_relation(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2348,plain,
spl171_68,
inference(avatar_split_clause,[],[f1347,f2346]) ).
fof(f2346,plain,
( spl171_68
<=> ! [X0] :
( connected(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_68])]) ).
fof(f1347,plain,
! [X0] :
( connected(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2344,plain,
spl171_67,
inference(avatar_split_clause,[],[f1346,f2342]) ).
fof(f2342,plain,
( spl171_67
<=> ! [X0] :
( antisymmetric(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_67])]) ).
fof(f1346,plain,
! [X0] :
( antisymmetric(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2340,plain,
spl171_66,
inference(avatar_split_clause,[],[f1345,f2338]) ).
fof(f2338,plain,
( spl171_66
<=> ! [X0] :
( transitive(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_66])]) ).
fof(f1345,plain,
! [X0] :
( transitive(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2336,plain,
spl171_65,
inference(avatar_split_clause,[],[f1344,f2334]) ).
fof(f2334,plain,
( spl171_65
<=> ! [X0] :
( reflexive(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_65])]) ).
fof(f1344,plain,
! [X0] :
( reflexive(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2332,plain,
spl171_64,
inference(avatar_split_clause,[],[f1332,f2330]) ).
fof(f1332,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f476]) ).
fof(f476,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f2328,plain,
spl171_63,
inference(avatar_split_clause,[],[f1331,f2326]) ).
fof(f1331,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f476]) ).
fof(f2324,plain,
spl171_62,
inference(avatar_split_clause,[],[f1330,f2322]) ).
fof(f1330,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f476]) ).
fof(f2320,plain,
spl171_61,
inference(avatar_split_clause,[],[f1328,f2318]) ).
fof(f1328,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f474]) ).
fof(f474,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f2316,plain,
spl171_60,
inference(avatar_split_clause,[],[f1327,f2314]) ).
fof(f1327,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f473]) ).
fof(f473,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f2312,plain,
spl171_59,
inference(avatar_split_clause,[],[f1319,f2310]) ).
fof(f2310,plain,
( spl171_59
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_59])]) ).
fof(f1319,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f470]) ).
fof(f470,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f2308,plain,
spl171_58,
inference(avatar_split_clause,[],[f1318,f2306]) ).
fof(f2306,plain,
( spl171_58
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_58])]) ).
fof(f1318,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f470]) ).
fof(f2304,plain,
( spl171_57
| ~ spl171_1
| ~ spl171_54 ),
inference(avatar_split_clause,[],[f2287,f2278,f2021,f2301]) ).
fof(f2287,plain,
( sP1(sK51)
| ~ spl171_1
| ~ spl171_54 ),
inference(resolution,[],[f2279,f2023]) ).
fof(f2299,plain,
spl171_56,
inference(avatar_split_clause,[],[f1307,f2297]) ).
fof(f2284,plain,
spl171_55,
inference(avatar_split_clause,[],[f1141,f2282]) ).
fof(f1141,plain,
! [X0] : in(X0,sK67(X0)),
inference(cnf_transformation,[],[f726]) ).
fof(f2280,plain,
spl171_54,
inference(avatar_split_clause,[],[f1103,f2278]) ).
fof(f1103,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f606]) ).
fof(f606,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f340,f605,f604]) ).
fof(f340,plain,
! [X0] :
( ( connected(X0)
<=> ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f154]) ).
fof(f154,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f2276,plain,
spl171_53,
inference(avatar_split_clause,[],[f1060,f2273]) ).
fof(f2273,plain,
( spl171_53
<=> empty_set = relation_rng(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_53])]) ).
fof(f1060,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f275]) ).
fof(f275,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f2271,plain,
spl171_52,
inference(avatar_split_clause,[],[f1059,f2268]) ).
fof(f2268,plain,
( spl171_52
<=> empty_set = relation_dom(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_52])]) ).
fof(f1059,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f275]) ).
fof(f2266,plain,
spl171_51,
inference(avatar_split_clause,[],[f1969,f2264]) ).
fof(f2264,plain,
( spl171_51
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_51])]) ).
fof(f1969,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f1540]) ).
fof(f1540,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f926]) ).
fof(f2262,plain,
spl171_50,
inference(avatar_split_clause,[],[f1550,f2260]) ).
fof(f2260,plain,
( spl171_50
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_50])]) ).
fof(f1550,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f2258,plain,
spl171_49,
inference(avatar_split_clause,[],[f1549,f2256]) ).
fof(f2256,plain,
( spl171_49
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_49])]) ).
fof(f1549,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f2254,plain,
spl171_48,
inference(avatar_split_clause,[],[f1548,f2252]) ).
fof(f2252,plain,
( spl171_48
<=> ! [X0] : empty(sK132(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_48])]) ).
fof(f1548,plain,
! [X0] : empty(sK132(X0)),
inference(cnf_transformation,[],[f934]) ).
fof(f2250,plain,
spl171_47,
inference(avatar_split_clause,[],[f1315,f2248]) ).
fof(f2248,plain,
( spl171_47
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_47])]) ).
fof(f1315,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f115,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f2246,plain,
spl171_46,
inference(avatar_split_clause,[],[f1306,f2244]) ).
fof(f1306,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f96]) ).
fof(f96,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f2242,plain,
spl171_45,
inference(avatar_split_clause,[],[f1305,f2240]) ).
fof(f2240,plain,
( spl171_45
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_45])]) ).
fof(f1305,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f2238,plain,
spl171_44,
inference(avatar_split_clause,[],[f1061,f2236]) ).
fof(f1061,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f229]) ).
fof(f229,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f2234,plain,
spl171_43,
inference(avatar_split_clause,[],[f1761,f2231]) ).
fof(f2231,plain,
( spl171_43
<=> function(sK170) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_43])]) ).
fof(f1761,plain,
function(sK170),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,plain,
( function(sK170)
& empty(sK170)
& relation(sK170) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f165,f1054]) ).
fof(f1054,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK170)
& empty(sK170)
& relation(sK170) ) ),
introduced(choice_axiom,[]) ).
fof(f165,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f2229,plain,
spl171_42,
inference(avatar_split_clause,[],[f1760,f2226]) ).
fof(f1760,plain,
empty(sK170),
inference(cnf_transformation,[],[f1055]) ).
fof(f2224,plain,
spl171_41,
inference(avatar_split_clause,[],[f1759,f2221]) ).
fof(f1759,plain,
relation(sK170),
inference(cnf_transformation,[],[f1055]) ).
fof(f2219,plain,
spl171_40,
inference(avatar_split_clause,[],[f1758,f2216]) ).
fof(f1758,plain,
ordinal(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,plain,
( ordinal(sK169)
& epsilon_connected(sK169)
& epsilon_transitive(sK169)
& empty(sK169)
& one_to_one(sK169)
& function(sK169)
& relation(sK169) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f166,f1052]) ).
fof(f1052,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK169)
& epsilon_connected(sK169)
& epsilon_transitive(sK169)
& empty(sK169)
& one_to_one(sK169)
& function(sK169)
& relation(sK169) ) ),
introduced(choice_axiom,[]) ).
fof(f166,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f2214,plain,
spl171_39,
inference(avatar_split_clause,[],[f1757,f2211]) ).
fof(f2211,plain,
( spl171_39
<=> epsilon_connected(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_39])]) ).
fof(f1757,plain,
epsilon_connected(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2209,plain,
spl171_38,
inference(avatar_split_clause,[],[f1756,f2206]) ).
fof(f2206,plain,
( spl171_38
<=> epsilon_transitive(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_38])]) ).
fof(f1756,plain,
epsilon_transitive(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2204,plain,
spl171_37,
inference(avatar_split_clause,[],[f1755,f2201]) ).
fof(f1755,plain,
empty(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2199,plain,
spl171_36,
inference(avatar_split_clause,[],[f1754,f2196]) ).
fof(f2196,plain,
( spl171_36
<=> one_to_one(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_36])]) ).
fof(f1754,plain,
one_to_one(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2194,plain,
spl171_35,
inference(avatar_split_clause,[],[f1753,f2191]) ).
fof(f2191,plain,
( spl171_35
<=> function(sK169) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_35])]) ).
fof(f1753,plain,
function(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2189,plain,
spl171_34,
inference(avatar_split_clause,[],[f1752,f2186]) ).
fof(f1752,plain,
relation(sK169),
inference(cnf_transformation,[],[f1053]) ).
fof(f2184,plain,
spl171_33,
inference(avatar_split_clause,[],[f1751,f2181]) ).
fof(f2181,plain,
( spl171_33
<=> one_to_one(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_33])]) ).
fof(f1751,plain,
one_to_one(sK168),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,plain,
( one_to_one(sK168)
& function(sK168)
& relation(sK168) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f170,f1050]) ).
fof(f1050,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK168)
& function(sK168)
& relation(sK168) ) ),
introduced(choice_axiom,[]) ).
fof(f170,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f2179,plain,
spl171_32,
inference(avatar_split_clause,[],[f1750,f2176]) ).
fof(f2176,plain,
( spl171_32
<=> function(sK168) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_32])]) ).
fof(f1750,plain,
function(sK168),
inference(cnf_transformation,[],[f1051]) ).
fof(f2174,plain,
spl171_31,
inference(avatar_split_clause,[],[f1749,f2171]) ).
fof(f1749,plain,
relation(sK168),
inference(cnf_transformation,[],[f1051]) ).
fof(f2169,plain,
spl171_30,
inference(avatar_split_clause,[],[f1748,f2166]) ).
fof(f2166,plain,
( spl171_30
<=> function(sK167) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_30])]) ).
fof(f1748,plain,
function(sK167),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,plain,
( function(sK167)
& relation(sK167) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f160,f1048]) ).
fof(f1048,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK167)
& relation(sK167) ) ),
introduced(choice_axiom,[]) ).
fof(f160,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f2164,plain,
spl171_29,
inference(avatar_split_clause,[],[f1747,f2161]) ).
fof(f1747,plain,
relation(sK167),
inference(cnf_transformation,[],[f1049]) ).
fof(f2159,plain,
spl171_28,
inference(avatar_split_clause,[],[f1746,f2156]) ).
fof(f2156,plain,
( spl171_28
<=> function(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_28])]) ).
fof(f1746,plain,
function(sK166),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,plain,
( function(sK166)
& relation_empty_yielding(sK166)
& relation(sK166) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f173,f1046]) ).
fof(f1046,plain,
( ? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) )
=> ( function(sK166)
& relation_empty_yielding(sK166)
& relation(sK166) ) ),
introduced(choice_axiom,[]) ).
fof(f173,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f2154,plain,
spl171_27,
inference(avatar_split_clause,[],[f1745,f2151]) ).
fof(f2151,plain,
( spl171_27
<=> relation_empty_yielding(sK166) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_27])]) ).
fof(f1745,plain,
relation_empty_yielding(sK166),
inference(cnf_transformation,[],[f1047]) ).
fof(f2149,plain,
spl171_26,
inference(avatar_split_clause,[],[f1744,f2146]) ).
fof(f1744,plain,
relation(sK166),
inference(cnf_transformation,[],[f1047]) ).
fof(f2144,plain,
spl171_25,
inference(avatar_split_clause,[],[f1743,f2141]) ).
fof(f2141,plain,
( spl171_25
<=> relation_empty_yielding(sK165) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_25])]) ).
fof(f1743,plain,
relation_empty_yielding(sK165),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,plain,
( relation_empty_yielding(sK165)
& relation(sK165) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f172,f1044]) ).
fof(f1044,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK165)
& relation(sK165) ) ),
introduced(choice_axiom,[]) ).
fof(f172,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f2139,plain,
spl171_24,
inference(avatar_split_clause,[],[f1742,f2136]) ).
fof(f1742,plain,
relation(sK165),
inference(cnf_transformation,[],[f1045]) ).
fof(f2134,plain,
spl171_23,
inference(avatar_split_clause,[],[f1741,f2131]) ).
fof(f1741,plain,
relation(sK164),
inference(cnf_transformation,[],[f1043]) ).
fof(f1043,plain,
( relation(sK164)
& empty(sK164) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f162,f1042]) ).
fof(f1042,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK164)
& empty(sK164) ) ),
introduced(choice_axiom,[]) ).
fof(f162,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f2129,plain,
spl171_22,
inference(avatar_split_clause,[],[f1740,f2126]) ).
fof(f1740,plain,
empty(sK164),
inference(cnf_transformation,[],[f1043]) ).
fof(f2124,plain,
spl171_21,
inference(avatar_split_clause,[],[f1739,f2121]) ).
fof(f1739,plain,
ordinal(sK163),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,plain,
( ordinal(sK163)
& epsilon_connected(sK163)
& epsilon_transitive(sK163) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f161,f1040]) ).
fof(f1040,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK163)
& epsilon_connected(sK163)
& epsilon_transitive(sK163) ) ),
introduced(choice_axiom,[]) ).
fof(f161,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f2119,plain,
spl171_20,
inference(avatar_split_clause,[],[f1738,f2116]) ).
fof(f2116,plain,
( spl171_20
<=> epsilon_connected(sK163) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_20])]) ).
fof(f1738,plain,
epsilon_connected(sK163),
inference(cnf_transformation,[],[f1041]) ).
fof(f2114,plain,
spl171_19,
inference(avatar_split_clause,[],[f1737,f2111]) ).
fof(f2111,plain,
( spl171_19
<=> epsilon_transitive(sK163) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_19])]) ).
fof(f1737,plain,
epsilon_transitive(sK163),
inference(cnf_transformation,[],[f1041]) ).
fof(f2109,plain,
spl171_18,
inference(avatar_split_clause,[],[f1736,f2106]) ).
fof(f1736,plain,
relation(sK162),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,plain,
( relation(sK162)
& ~ empty(sK162) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f167,f1038]) ).
fof(f1038,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK162)
& ~ empty(sK162) ) ),
introduced(choice_axiom,[]) ).
fof(f167,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f2104,plain,
~ spl171_17,
inference(avatar_split_clause,[],[f1735,f2101]) ).
fof(f2101,plain,
( spl171_17
<=> empty(sK162) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_17])]) ).
fof(f1735,plain,
~ empty(sK162),
inference(cnf_transformation,[],[f1039]) ).
fof(f2099,plain,
spl171_16,
inference(avatar_split_clause,[],[f1734,f2096]) ).
fof(f1734,plain,
ordinal(sK161),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,plain,
( ordinal(sK161)
& epsilon_connected(sK161)
& epsilon_transitive(sK161)
& ~ empty(sK161) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f171,f1036]) ).
fof(f1036,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK161)
& epsilon_connected(sK161)
& epsilon_transitive(sK161)
& ~ empty(sK161) ) ),
introduced(choice_axiom,[]) ).
fof(f171,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f2094,plain,
spl171_15,
inference(avatar_split_clause,[],[f1733,f2091]) ).
fof(f2091,plain,
( spl171_15
<=> epsilon_connected(sK161) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_15])]) ).
fof(f1733,plain,
epsilon_connected(sK161),
inference(cnf_transformation,[],[f1037]) ).
fof(f2089,plain,
spl171_14,
inference(avatar_split_clause,[],[f1732,f2086]) ).
fof(f2086,plain,
( spl171_14
<=> epsilon_transitive(sK161) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_14])]) ).
fof(f1732,plain,
epsilon_transitive(sK161),
inference(cnf_transformation,[],[f1037]) ).
fof(f2084,plain,
~ spl171_13,
inference(avatar_split_clause,[],[f1731,f2081]) ).
fof(f2081,plain,
( spl171_13
<=> empty(sK161) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_13])]) ).
fof(f1731,plain,
~ empty(sK161),
inference(cnf_transformation,[],[f1037]) ).
fof(f2079,plain,
spl171_12,
inference(avatar_split_clause,[],[f1730,f2076]) ).
fof(f1730,plain,
empty(sK160),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,plain,
empty(sK160),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f164,f1034]) ).
fof(f1034,plain,
( ? [X0] : empty(X0)
=> empty(sK160) ),
introduced(choice_axiom,[]) ).
fof(f164,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f2074,plain,
~ spl171_11,
inference(avatar_split_clause,[],[f1729,f2071]) ).
fof(f2071,plain,
( spl171_11
<=> empty(sK159) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_11])]) ).
fof(f1729,plain,
~ empty(sK159),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,plain,
~ empty(sK159),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f169,f1032]) ).
fof(f1032,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK159) ),
introduced(choice_axiom,[]) ).
fof(f169,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f2069,plain,
spl171_10,
inference(avatar_split_clause,[],[f1302,f2066]) ).
fof(f1302,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f116]) ).
fof(f116,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f2064,plain,
spl171_9,
inference(avatar_split_clause,[],[f1301,f2061]) ).
fof(f2061,plain,
( spl171_9
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_9])]) ).
fof(f1301,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f116]) ).
fof(f2059,plain,
spl171_8,
inference(avatar_split_clause,[],[f1300,f2056]) ).
fof(f2056,plain,
( spl171_8
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_8])]) ).
fof(f1300,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f116]) ).
fof(f2054,plain,
spl171_7,
inference(avatar_split_clause,[],[f1298,f2051]) ).
fof(f2051,plain,
( spl171_7
<=> one_to_one(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_7])]) ).
fof(f1298,plain,
one_to_one(empty_set),
inference(cnf_transformation,[],[f116]) ).
fof(f2049,plain,
spl171_6,
inference(avatar_split_clause,[],[f1297,f2046]) ).
fof(f2046,plain,
( spl171_6
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_6])]) ).
fof(f1297,plain,
function(empty_set),
inference(cnf_transformation,[],[f116]) ).
fof(f2044,plain,
spl171_5,
inference(avatar_split_clause,[],[f1294,f2041]) ).
fof(f2041,plain,
( spl171_5
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_5])]) ).
fof(f1294,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f107]) ).
fof(f107,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f2039,plain,
spl171_4,
inference(avatar_split_clause,[],[f1291,f2036]) ).
fof(f1291,plain,
relation(empty_set),
inference(cnf_transformation,[],[f127]) ).
fof(f127,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f2034,plain,
spl171_3,
inference(avatar_split_clause,[],[f1289,f2031]) ).
fof(f2031,plain,
( spl171_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl171_3])]) ).
fof(f1289,plain,
empty(empty_set),
inference(cnf_transformation,[],[f113]) ).
fof(f113,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f2029,plain,
~ spl171_2,
inference(avatar_split_clause,[],[f1057,f2026]) ).
fof(f1057,plain,
~ subset(relation_dom(relation_rng_restriction(sK50,sK51)),relation_dom(sK51)),
inference(cnf_transformation,[],[f683]) ).
fof(f683,plain,
( ~ subset(relation_dom(relation_rng_restriction(sK50,sK51)),relation_dom(sK51))
& relation(sK51) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f320,f682]) ).
fof(f682,plain,
( ? [X0,X1] :
( ~ subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
& relation(X1) )
=> ( ~ subset(relation_dom(relation_rng_restriction(sK50,sK51)),relation_dom(sK51))
& relation(sK51) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
? [X0,X1] :
( ~ subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f147]) ).
fof(f147,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(negated_conjecture,[],[f146]) ).
fof(f146,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
fof(f2024,plain,
spl171_1,
inference(avatar_split_clause,[],[f1056,f2021]) ).
fof(f1056,plain,
relation(sK51),
inference(cnf_transformation,[],[f683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26 % Computer : n014.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:33:49 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % (14157)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28 % (14163)WARNING: value z3 for option sas not known
% 0.07/0.28 % (14161)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (14162)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (14164)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (14165)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.28 % (14166)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.28 % (14163)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.28 % (14167)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.32 TRYING [1]
% 0.11/0.32 TRYING [2]
% 0.11/0.36 TRYING [3]
% 0.11/0.42 TRYING [1]
% 0.11/0.44 TRYING [2]
% 0.11/0.69 TRYING [4]
% 3.19/0.75 % (14165)First to succeed.
% 3.19/0.77 TRYING [3]
% 3.19/0.79 % (14165)Refutation found. Thanks to Tanya!
% 3.19/0.79 % SZS status Theorem for theBenchmark
% 3.19/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/0.81 % (14165)------------------------------
% 3.70/0.81 % (14165)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.70/0.81 % (14165)Termination reason: Refutation
% 3.70/0.81
% 3.70/0.81 % (14165)Memory used [KB]: 11737
% 3.70/0.81 % (14165)Time elapsed: 0.510 s
% 3.70/0.81 % (14165)Instructions burned: 1407 (million)
% 3.70/0.81 % (14165)------------------------------
% 3.70/0.81 % (14165)------------------------------
% 3.70/0.81 % (14157)Success in time 0.529 s
%------------------------------------------------------------------------------