TSTP Solution File: SEU264+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU264+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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:30:29 EDT 2024
% Result : Theorem 3.68s 0.90s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1398
% Syntax : Number of formulae : 4352 ( 852 unt; 0 def)
% Number of atoms : 14995 (1789 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 17438 (6795 ~;7268 |;1705 &)
% (1243 <=>; 426 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1033 (1031 usr; 945 prp; 0-4 aty)
% Number of functors : 161 ( 161 usr; 17 con; 0-4 aty)
% Number of variables : 7675 (7217 !; 458 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15871,plain,
$false,
inference(avatar_sat_refutation,[],[f2189,f2194,f2199,f2204,f2209,f2214,f2219,f2224,f2229,f2234,f2239,f2244,f2249,f2254,f2259,f2264,f2269,f2274,f2279,f2284,f2289,f2294,f2299,f2304,f2309,f2314,f2319,f2324,f2329,f2334,f2339,f2344,f2349,f2354,f2359,f2364,f2369,f2374,f2379,f2384,f2389,f2394,f2399,f2404,f2408,f2412,f2416,f2420,f2424,f2428,f2432,f2436,f2441,f2446,f2450,f2454,f2469,f2473,f2477,f2481,f2485,f2489,f2493,f2497,f2501,f2505,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2538,f2542,f2546,f2550,f2555,f2559,f2563,f2567,f2571,f2575,f2579,f2583,f2588,f2592,f2596,f2601,f2654,f2719,f2753,f2758,f2762,f2766,f2770,f2774,f2778,f2782,f2788,f2792,f2796,f2800,f2804,f2808,f2812,f2816,f2821,f2825,f2829,f2833,f2837,f2841,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f2967,f2973,f2977,f2982,f2987,f2991,f3004,f3009,f3021,f3025,f3029,f3033,f3037,f3042,f3046,f3050,f3054,f3058,f3062,f3066,f3070,f3074,f3078,f3082,f3086,f3090,f3094,f3098,f3102,f3106,f3110,f3114,f3118,f3122,f3126,f3130,f3135,f3139,f3143,f3147,f3151,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3183,f3187,f3191,f3195,f3221,f3340,f3394,f3423,f3432,f3436,f3440,f3444,f3448,f3452,f3456,f3461,f3465,f3471,f3481,f3486,f3507,f3521,f3525,f3529,f3533,f3537,f3541,f3545,f3550,f3555,f3559,f3563,f3567,f3571,f3575,f3579,f3583,f3587,f3591,f3596,f3601,f3605,f3609,f3613,f3617,f3622,f3626,f3630,f3634,f3641,f3646,f3650,f3654,f3658,f3662,f3666,f3670,f3674,f3678,f3682,f3687,f3692,f3705,f3771,f3775,f3815,f3866,f3870,f3875,f3880,f3884,f3888,f3892,f3896,f3900,f3904,f3908,f3912,f3916,f3921,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3967,f3971,f3976,f3981,f3985,f3989,f3993,f3997,f4001,f4005,f4009,f4014,f4019,f4023,f4027,f4031,f4094,f4131,f4164,f4168,f4177,f4236,f4261,f4265,f4269,f4273,f4277,f4281,f4285,f4289,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4328,f4333,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4381,f4385,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4417,f4421,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4533,f4546,f4555,f4686,f4798,f4851,f4855,f4859,f4865,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4940,f4945,f4990,f4994,f5177,f5181,f5185,f5189,f5193,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5243,f5355,f5359,f5365,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5420,f5424,f5428,f5432,f5436,f5441,f5446,f5450,f5709,f5757,f5761,f5798,f5803,f5807,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5893,f5897,f5901,f5905,f6061,f6065,f6069,f6073,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6119,f6135,f6191,f6481,f6485,f6489,f6494,f6498,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6530,f6534,f6536,f6541,f6545,f6549,f6553,f6557,f6561,f6565,f6569,f6573,f6576,f6701,f6705,f6709,f6713,f6717,f6722,f6726,f6730,f6734,f6740,f6744,f6748,f6752,f6756,f6814,f6818,f7026,f7030,f7034,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7067,f7071,f7075,f7079,f7083,f7087,f7091,f7095,f7099,f7155,f7190,f7194,f7198,f7202,f7206,f7212,f7216,f7220,f7224,f7228,f7232,f7237,f7241,f7245,f7249,f7253,f7370,f7494,f7594,f7598,f7602,f7606,f7610,f7614,f7618,f7622,f7626,f7630,f7634,f7638,f7642,f7652,f7656,f7660,f7664,f7668,f7672,f7676,f7680,f7685,f7689,f7718,f7735,f7907,f7911,f7937,f7941,f7947,f7951,f7955,f7960,f7964,f7968,f7972,f7976,f7980,f7984,f7988,f7992,f7996,f8017,f8021,f8303,f8330,f8335,f8340,f8344,f8348,f8352,f8356,f8360,f8364,f8368,f8538,f8571,f8575,f8579,f8583,f8587,f8591,f8596,f8601,f8609,f8644,f8648,f8652,f8656,f8660,f8664,f8668,f8672,f8677,f8781,f8785,f8946,f8950,f8954,f8958,f8962,f8966,f8970,f8974,f9014,f9018,f9022,f9026,f9030,f9034,f9038,f9043,f9047,f9051,f9055,f9059,f9175,f9273,f9278,f9283,f9287,f9291,f9298,f9302,f9306,f9310,f9314,f9318,f9322,f9326,f9330,f9334,f9339,f9343,f9347,f9351,f9355,f9359,f9363,f9367,f10092,f10096,f10101,f10105,f10109,f10114,f10119,f10124,f10129,f10134,f10138,f10142,f10146,f10160,f10164,f10173,f10239,f10243,f10247,f10251,f10256,f10260,f10346,f10585,f10589,f10593,f10597,f10601,f10605,f10842,f10847,f10851,f10855,f10864,f10868,f10872,f10876,f10881,f11017,f11071,f11243,f11247,f11251,f11255,f11259,f11434,f11438,f11443,f11447,f11451,f11459,f11463,f11468,f11548,f11594,f11619,f11628,f11718,f11722,f11726,f11731,f11736,f11771,f11776,f11781,f11786,f11791,f11871,f11875,f11879,f11883,f11888,f11892,f11896,f11900,f12093,f12097,f12112,f12118,f12140,f12146,f12168,f12173,f12218,f12263,f12267,f12271,f12275,f12365,f12369,f12373,f12377,f12565,f12596,f12600,f12604,f12608,f12761,f12765,f12777,f12781,f12786,f12791,f12795,f12810,f12814,f12932,f12936,f12940,f12945,f12949,f12953,f12959,f12963,f12967,f13080,f13123,f13237,f13241,f13258,f13262,f13267,f13323,f13366,f13377,f13424,f13429,f13434,f13439,f13443,f13447,f13451,f13455,f13616,f13621,f13633,f13637,f13641,f13690,f13691,f13695,f13699,f13703,f13708,f13712,f13717,f13722,f13975,f13997,f14001,f14177,f14182,f14190,f14194,f14198,f14288,f14292,f14345,f14350,f14356,f14361,f14366,f14370,f14374,f14450,f14465,f14491,f14521,f14527,f14533,f14537,f14647,f14653,f14659,f14663,f14767,f14773,f14779,f14785,f14789,f14793,f14797,f15143,f15149,f15154,f15158,f15190,f15196,f15284,f15289,f15306,f15313,f15317,f15337,f15343,f15361,f15366,f15371,f15407,f15413,f15419,f15424,f15430,f15435,f15440,f15445,f15450,f15456,f15462,f15467,f15473,f15478,f15484,f15489,f15494,f15499,f15504,f15510,f15516,f15522,f15527,f15533,f15538,f15543,f15548,f15553,f15559,f15565,f15571,f15578,f15584,f15589,f15594,f15599,f15604,f15610,f15616,f15622,f15627,f15633,f15638,f15643,f15648,f15653,f15659,f15665,f15671,f15676,f15682,f15699,f15704,f15709,f15714,f15720,f15726,f15732,f15737,f15743,f15748,f15749,f15754,f15759,f15764,f15770,f15776,f15782,f15787,f15793,f15798,f15803,f15820,f15825,f15831,f15837,f15843,f15848,f15854,f15859,f15864,f15869,f15870]) ).
fof(f15870,plain,
( spl184_3
| ~ spl184_514
| ~ spl184_860 ),
inference(avatar_split_clause,[],[f15346,f15341,f7064,f2196]) ).
fof(f2196,plain,
( spl184_3
<=> relation_of2_as_subset(sK59,sK58,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_3])]) ).
fof(f7064,plain,
( spl184_514
<=> subset(relation_rng(sK59),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_514])]) ).
fof(f15341,plain,
( spl184_860
<=> ! [X0] :
( ~ subset(relation_rng(sK59),X0)
| relation_of2_as_subset(sK59,sK58,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_860])]) ).
fof(f15346,plain,
( relation_of2_as_subset(sK59,sK58,sK57)
| ~ spl184_514
| ~ spl184_860 ),
inference(resolution,[],[f15342,f7066]) ).
fof(f7066,plain,
( subset(relation_rng(sK59),sK57)
| ~ spl184_514 ),
inference(avatar_component_clause,[],[f7064]) ).
fof(f15342,plain,
( ! [X0] :
( ~ subset(relation_rng(sK59),X0)
| relation_of2_as_subset(sK59,sK58,X0) )
| ~ spl184_860 ),
inference(avatar_component_clause,[],[f15341]) ).
fof(f15869,plain,
( spl184_944
| ~ spl184_32
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2747,f2569,f2341,f15866]) ).
fof(f15866,plain,
( spl184_944
<=> sP32(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_944])]) ).
fof(f2341,plain,
( spl184_32
<=> relation(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_32])]) ).
fof(f2569,plain,
( spl184_82
<=> ! [X0] :
( sP32(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_82])]) ).
fof(f2747,plain,
( sP32(sK181)
| ~ spl184_32
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2343]) ).
fof(f2343,plain,
( relation(sK181)
| ~ spl184_32 ),
inference(avatar_component_clause,[],[f2341]) ).
fof(f2570,plain,
( ! [X0] :
( ~ relation(X0)
| sP32(X0) )
| ~ spl184_82 ),
inference(avatar_component_clause,[],[f2569]) ).
fof(f15864,plain,
( spl184_943
| ~ spl184_30
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2746,f2569,f2331,f15861]) ).
fof(f15861,plain,
( spl184_943
<=> sP32(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_943])]) ).
fof(f2331,plain,
( spl184_30
<=> relation(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_30])]) ).
fof(f2746,plain,
( sP32(sK180)
| ~ spl184_30
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2333]) ).
fof(f2333,plain,
( relation(sK180)
| ~ spl184_30 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f15859,plain,
( spl184_942
| ~ spl184_27
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2745,f2569,f2316,f15856]) ).
fof(f15856,plain,
( spl184_942
<=> sP32(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_942])]) ).
fof(f2316,plain,
( spl184_27
<=> relation(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_27])]) ).
fof(f2745,plain,
( sP32(sK179)
| ~ spl184_27
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2318]) ).
fof(f2318,plain,
( relation(sK179)
| ~ spl184_27 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f15854,plain,
( spl184_941
| ~ spl184_25
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2744,f2569,f2306,f15851]) ).
fof(f15851,plain,
( spl184_941
<=> sP32(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_941])]) ).
fof(f2306,plain,
( spl184_25
<=> relation(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_25])]) ).
fof(f2744,plain,
( sP32(sK178)
| ~ spl184_25
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2308]) ).
fof(f2308,plain,
( relation(sK178)
| ~ spl184_25 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f15848,plain,
( spl184_940
| ~ spl184_24
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2743,f2569,f2301,f15845]) ).
fof(f15845,plain,
( spl184_940
<=> sP32(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_940])]) ).
fof(f2301,plain,
( spl184_24
<=> relation(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_24])]) ).
fof(f2743,plain,
( sP32(sK177)
| ~ spl184_24
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2303]) ).
fof(f2303,plain,
( relation(sK177)
| ~ spl184_24 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f15843,plain,
( spl184_939
| ~ spl184_19
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2742,f2569,f2276,f15840]) ).
fof(f15840,plain,
( spl184_939
<=> sP32(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_939])]) ).
fof(f2276,plain,
( spl184_19
<=> relation(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_19])]) ).
fof(f2742,plain,
( sP32(sK175)
| ~ spl184_19
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2278]) ).
fof(f2278,plain,
( relation(sK175)
| ~ spl184_19 ),
inference(avatar_component_clause,[],[f2276]) ).
fof(f15837,plain,
( spl184_938
| ~ spl184_5
| ~ spl184_82 ),
inference(avatar_split_clause,[],[f2741,f2569,f2206,f15834]) ).
fof(f15834,plain,
( spl184_938
<=> sP32(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_938])]) ).
fof(f2206,plain,
( spl184_5
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_5])]) ).
fof(f2741,plain,
( sP32(empty_set)
| ~ spl184_5
| ~ spl184_82 ),
inference(resolution,[],[f2570,f2208]) ).
fof(f2208,plain,
( relation(empty_set)
| ~ spl184_5 ),
inference(avatar_component_clause,[],[f2206]) ).
fof(f15831,plain,
( spl184_937
| ~ spl184_42
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2739,f2565,f2391,f15828]) ).
fof(f15828,plain,
( spl184_937
<=> sP30(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_937])]) ).
fof(f2391,plain,
( spl184_42
<=> relation(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_42])]) ).
fof(f2565,plain,
( spl184_81
<=> ! [X0] :
( sP30(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_81])]) ).
fof(f2739,plain,
( sP30(sK183)
| ~ spl184_42
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2393]) ).
fof(f2393,plain,
( relation(sK183)
| ~ spl184_42 ),
inference(avatar_component_clause,[],[f2391]) ).
fof(f2566,plain,
( ! [X0] :
( ~ relation(X0)
| sP30(X0) )
| ~ spl184_81 ),
inference(avatar_component_clause,[],[f2565]) ).
fof(f15825,plain,
( spl184_936
| ~ spl184_35
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2738,f2565,f2356,f15822]) ).
fof(f15822,plain,
( spl184_936
<=> sP30(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_936])]) ).
fof(f2356,plain,
( spl184_35
<=> relation(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_35])]) ).
fof(f2738,plain,
( sP30(sK182)
| ~ spl184_35
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2358]) ).
fof(f2358,plain,
( relation(sK182)
| ~ spl184_35 ),
inference(avatar_component_clause,[],[f2356]) ).
fof(f15820,plain,
( spl184_935
| ~ spl184_32
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2737,f2565,f2341,f15817]) ).
fof(f15817,plain,
( spl184_935
<=> sP30(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_935])]) ).
fof(f2737,plain,
( sP30(sK181)
| ~ spl184_32
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2343]) ).
fof(f15803,plain,
( spl184_934
| ~ spl184_30
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2736,f2565,f2331,f15800]) ).
fof(f15800,plain,
( spl184_934
<=> sP30(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_934])]) ).
fof(f2736,plain,
( sP30(sK180)
| ~ spl184_30
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2333]) ).
fof(f15798,plain,
( spl184_933
| ~ spl184_27
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2735,f2565,f2316,f15795]) ).
fof(f15795,plain,
( spl184_933
<=> sP30(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_933])]) ).
fof(f2735,plain,
( sP30(sK179)
| ~ spl184_27
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2318]) ).
fof(f15793,plain,
( spl184_932
| ~ spl184_25
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2734,f2565,f2306,f15790]) ).
fof(f15790,plain,
( spl184_932
<=> sP30(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_932])]) ).
fof(f2734,plain,
( sP30(sK178)
| ~ spl184_25
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2308]) ).
fof(f15787,plain,
( spl184_931
| ~ spl184_24
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2733,f2565,f2301,f15784]) ).
fof(f15784,plain,
( spl184_931
<=> sP30(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_931])]) ).
fof(f2733,plain,
( sP30(sK177)
| ~ spl184_24
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2303]) ).
fof(f15782,plain,
( spl184_930
| ~ spl184_19
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2732,f2565,f2276,f15779]) ).
fof(f15779,plain,
( spl184_930
<=> sP30(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_930])]) ).
fof(f2732,plain,
( sP30(sK175)
| ~ spl184_19
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2278]) ).
fof(f15776,plain,
( spl184_929
| ~ spl184_5
| ~ spl184_81 ),
inference(avatar_split_clause,[],[f2731,f2565,f2206,f15773]) ).
fof(f15773,plain,
( spl184_929
<=> sP30(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_929])]) ).
fof(f2731,plain,
( sP30(empty_set)
| ~ spl184_5
| ~ spl184_81 ),
inference(resolution,[],[f2566,f2208]) ).
fof(f15770,plain,
( spl184_928
| ~ spl184_42
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2729,f2561,f2391,f15767]) ).
fof(f15767,plain,
( spl184_928
<=> sP28(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_928])]) ).
fof(f2561,plain,
( spl184_80
<=> ! [X0] :
( sP28(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_80])]) ).
fof(f2729,plain,
( sP28(sK183)
| ~ spl184_42
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2393]) ).
fof(f2562,plain,
( ! [X0] :
( ~ relation(X0)
| sP28(X0) )
| ~ spl184_80 ),
inference(avatar_component_clause,[],[f2561]) ).
fof(f15764,plain,
( spl184_927
| ~ spl184_35
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2728,f2561,f2356,f15761]) ).
fof(f15761,plain,
( spl184_927
<=> sP28(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_927])]) ).
fof(f2728,plain,
( sP28(sK182)
| ~ spl184_35
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2358]) ).
fof(f15759,plain,
( spl184_926
| ~ spl184_32
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2727,f2561,f2341,f15756]) ).
fof(f15756,plain,
( spl184_926
<=> sP28(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_926])]) ).
fof(f2727,plain,
( sP28(sK181)
| ~ spl184_32
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2343]) ).
fof(f15754,plain,
( spl184_925
| ~ spl184_30
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2726,f2561,f2331,f15751]) ).
fof(f15751,plain,
( spl184_925
<=> sP28(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_925])]) ).
fof(f2726,plain,
( sP28(sK180)
| ~ spl184_30
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2333]) ).
fof(f15749,plain,
( spl184_684
| ~ spl184_225
| ~ spl184_721 ),
inference(avatar_split_clause,[],[f12280,f11625,f3664,f10253]) ).
fof(f10253,plain,
( spl184_684
<=> in(sK159(sK57),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_684])]) ).
fof(f3664,plain,
( spl184_225
<=> ! [X0,X1] :
( in(sK159(X1),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_225])]) ).
fof(f11625,plain,
( spl184_721
<=> in(sK136(sK56),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_721])]) ).
fof(f12280,plain,
( in(sK159(sK57),sK57)
| ~ spl184_225
| ~ spl184_721 ),
inference(resolution,[],[f11627,f3665]) ).
fof(f3665,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| in(sK159(X1),X1) )
| ~ spl184_225 ),
inference(avatar_component_clause,[],[f3664]) ).
fof(f11627,plain,
( in(sK136(sK56),sK57)
| ~ spl184_721 ),
inference(avatar_component_clause,[],[f11625]) ).
fof(f15748,plain,
( spl184_924
| ~ spl184_27
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2725,f2561,f2316,f15745]) ).
fof(f15745,plain,
( spl184_924
<=> sP28(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_924])]) ).
fof(f2725,plain,
( sP28(sK179)
| ~ spl184_27
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2318]) ).
fof(f15743,plain,
( spl184_923
| ~ spl184_25
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2724,f2561,f2306,f15740]) ).
fof(f15740,plain,
( spl184_923
<=> sP28(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_923])]) ).
fof(f2724,plain,
( sP28(sK178)
| ~ spl184_25
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2308]) ).
fof(f15737,plain,
( spl184_922
| ~ spl184_24
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2723,f2561,f2301,f15734]) ).
fof(f15734,plain,
( spl184_922
<=> sP28(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_922])]) ).
fof(f2723,plain,
( sP28(sK177)
| ~ spl184_24
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2303]) ).
fof(f15732,plain,
( spl184_921
| ~ spl184_19
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2722,f2561,f2276,f15729]) ).
fof(f15729,plain,
( spl184_921
<=> sP28(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_921])]) ).
fof(f2722,plain,
( sP28(sK175)
| ~ spl184_19
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2278]) ).
fof(f15726,plain,
( spl184_920
| ~ spl184_5
| ~ spl184_80 ),
inference(avatar_split_clause,[],[f2721,f2561,f2206,f15723]) ).
fof(f15723,plain,
( spl184_920
<=> sP28(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_920])]) ).
fof(f2721,plain,
( sP28(empty_set)
| ~ spl184_5
| ~ spl184_80 ),
inference(resolution,[],[f2562,f2208]) ).
fof(f15720,plain,
( spl184_919
| ~ spl184_42
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2714,f2557,f2391,f15717]) ).
fof(f15717,plain,
( spl184_919
<=> sP24(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_919])]) ).
fof(f2557,plain,
( spl184_79
<=> ! [X0] :
( sP24(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_79])]) ).
fof(f2714,plain,
( sP24(sK183)
| ~ spl184_42
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2393]) ).
fof(f2558,plain,
( ! [X0] :
( ~ relation(X0)
| sP24(X0) )
| ~ spl184_79 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f15714,plain,
( spl184_918
| ~ spl184_35
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2713,f2557,f2356,f15711]) ).
fof(f15711,plain,
( spl184_918
<=> sP24(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_918])]) ).
fof(f2713,plain,
( sP24(sK182)
| ~ spl184_35
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2358]) ).
fof(f15709,plain,
( spl184_917
| ~ spl184_32
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2712,f2557,f2341,f15706]) ).
fof(f15706,plain,
( spl184_917
<=> sP24(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_917])]) ).
fof(f2712,plain,
( sP24(sK181)
| ~ spl184_32
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2343]) ).
fof(f15704,plain,
( spl184_916
| ~ spl184_30
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2711,f2557,f2331,f15701]) ).
fof(f15701,plain,
( spl184_916
<=> sP24(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_916])]) ).
fof(f2711,plain,
( sP24(sK180)
| ~ spl184_30
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2333]) ).
fof(f15699,plain,
( spl184_915
| ~ spl184_27
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2710,f2557,f2316,f15696]) ).
fof(f15696,plain,
( spl184_915
<=> sP24(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_915])]) ).
fof(f2710,plain,
( sP24(sK179)
| ~ spl184_27
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2318]) ).
fof(f15682,plain,
( spl184_914
| ~ spl184_25
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2709,f2557,f2306,f15679]) ).
fof(f15679,plain,
( spl184_914
<=> sP24(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_914])]) ).
fof(f2709,plain,
( sP24(sK178)
| ~ spl184_25
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2308]) ).
fof(f15676,plain,
( spl184_913
| ~ spl184_24
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2708,f2557,f2301,f15673]) ).
fof(f15673,plain,
( spl184_913
<=> sP24(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_913])]) ).
fof(f2708,plain,
( sP24(sK177)
| ~ spl184_24
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2303]) ).
fof(f15671,plain,
( spl184_912
| ~ spl184_19
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2707,f2557,f2276,f15668]) ).
fof(f15668,plain,
( spl184_912
<=> sP24(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_912])]) ).
fof(f2707,plain,
( sP24(sK175)
| ~ spl184_19
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2278]) ).
fof(f15665,plain,
( spl184_911
| ~ spl184_5
| ~ spl184_79 ),
inference(avatar_split_clause,[],[f2706,f2557,f2206,f15662]) ).
fof(f15662,plain,
( spl184_911
<=> sP24(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_911])]) ).
fof(f2706,plain,
( sP24(empty_set)
| ~ spl184_5
| ~ spl184_79 ),
inference(resolution,[],[f2558,f2208]) ).
fof(f15659,plain,
( spl184_910
| ~ spl184_42
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2704,f2548,f2391,f15656]) ).
fof(f15656,plain,
( spl184_910
<=> sP22(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_910])]) ).
fof(f2548,plain,
( spl184_77
<=> ! [X0] :
( sP22(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_77])]) ).
fof(f2704,plain,
( sP22(sK183)
| ~ spl184_42
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2393]) ).
fof(f2549,plain,
( ! [X0] :
( ~ relation(X0)
| sP22(X0) )
| ~ spl184_77 ),
inference(avatar_component_clause,[],[f2548]) ).
fof(f15653,plain,
( spl184_909
| ~ spl184_35
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2703,f2548,f2356,f15650]) ).
fof(f15650,plain,
( spl184_909
<=> sP22(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_909])]) ).
fof(f2703,plain,
( sP22(sK182)
| ~ spl184_35
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2358]) ).
fof(f15648,plain,
( spl184_908
| ~ spl184_32
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2702,f2548,f2341,f15645]) ).
fof(f15645,plain,
( spl184_908
<=> sP22(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_908])]) ).
fof(f2702,plain,
( sP22(sK181)
| ~ spl184_32
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2343]) ).
fof(f15643,plain,
( spl184_907
| ~ spl184_30
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2701,f2548,f2331,f15640]) ).
fof(f15640,plain,
( spl184_907
<=> sP22(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_907])]) ).
fof(f2701,plain,
( sP22(sK180)
| ~ spl184_30
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2333]) ).
fof(f15638,plain,
( spl184_906
| ~ spl184_27
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2700,f2548,f2316,f15635]) ).
fof(f15635,plain,
( spl184_906
<=> sP22(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_906])]) ).
fof(f2700,plain,
( sP22(sK179)
| ~ spl184_27
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2318]) ).
fof(f15633,plain,
( spl184_905
| ~ spl184_25
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2699,f2548,f2306,f15630]) ).
fof(f15630,plain,
( spl184_905
<=> sP22(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_905])]) ).
fof(f2699,plain,
( sP22(sK178)
| ~ spl184_25
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2308]) ).
fof(f15627,plain,
( spl184_904
| ~ spl184_24
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2698,f2548,f2301,f15624]) ).
fof(f15624,plain,
( spl184_904
<=> sP22(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_904])]) ).
fof(f2698,plain,
( sP22(sK177)
| ~ spl184_24
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2303]) ).
fof(f15622,plain,
( spl184_903
| ~ spl184_19
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2697,f2548,f2276,f15619]) ).
fof(f15619,plain,
( spl184_903
<=> sP22(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_903])]) ).
fof(f2697,plain,
( sP22(sK175)
| ~ spl184_19
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2278]) ).
fof(f15616,plain,
( spl184_902
| ~ spl184_5
| ~ spl184_77 ),
inference(avatar_split_clause,[],[f2696,f2548,f2206,f15613]) ).
fof(f15613,plain,
( spl184_902
<=> sP22(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_902])]) ).
fof(f2696,plain,
( sP22(empty_set)
| ~ spl184_5
| ~ spl184_77 ),
inference(resolution,[],[f2549,f2208]) ).
fof(f15610,plain,
( spl184_901
| ~ spl184_42
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2694,f2544,f2391,f15607]) ).
fof(f15607,plain,
( spl184_901
<=> sP20(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_901])]) ).
fof(f2544,plain,
( spl184_76
<=> ! [X0] :
( sP20(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_76])]) ).
fof(f2694,plain,
( sP20(sK183)
| ~ spl184_42
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2393]) ).
fof(f2545,plain,
( ! [X0] :
( ~ relation(X0)
| sP20(X0) )
| ~ spl184_76 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f15604,plain,
( spl184_900
| ~ spl184_35
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2693,f2544,f2356,f15601]) ).
fof(f15601,plain,
( spl184_900
<=> sP20(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_900])]) ).
fof(f2693,plain,
( sP20(sK182)
| ~ spl184_35
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2358]) ).
fof(f15599,plain,
( spl184_899
| ~ spl184_32
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2692,f2544,f2341,f15596]) ).
fof(f15596,plain,
( spl184_899
<=> sP20(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_899])]) ).
fof(f2692,plain,
( sP20(sK181)
| ~ spl184_32
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2343]) ).
fof(f15594,plain,
( spl184_898
| ~ spl184_30
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2691,f2544,f2331,f15591]) ).
fof(f15591,plain,
( spl184_898
<=> sP20(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_898])]) ).
fof(f2691,plain,
( sP20(sK180)
| ~ spl184_30
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2333]) ).
fof(f15589,plain,
( spl184_897
| ~ spl184_27
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2690,f2544,f2316,f15586]) ).
fof(f15586,plain,
( spl184_897
<=> sP20(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_897])]) ).
fof(f2690,plain,
( sP20(sK179)
| ~ spl184_27
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2318]) ).
fof(f15584,plain,
( spl184_896
| ~ spl184_25
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2689,f2544,f2306,f15581]) ).
fof(f15581,plain,
( spl184_896
<=> sP20(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_896])]) ).
fof(f2689,plain,
( sP20(sK178)
| ~ spl184_25
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2308]) ).
fof(f15578,plain,
( spl184_895
| ~ spl184_24
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2688,f2544,f2301,f15575]) ).
fof(f15575,plain,
( spl184_895
<=> sP20(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_895])]) ).
fof(f2688,plain,
( sP20(sK177)
| ~ spl184_24
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2303]) ).
fof(f15571,plain,
( spl184_894
| ~ spl184_19
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2687,f2544,f2276,f15568]) ).
fof(f15568,plain,
( spl184_894
<=> sP20(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_894])]) ).
fof(f2687,plain,
( sP20(sK175)
| ~ spl184_19
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2278]) ).
fof(f15565,plain,
( spl184_893
| ~ spl184_5
| ~ spl184_76 ),
inference(avatar_split_clause,[],[f2686,f2544,f2206,f15562]) ).
fof(f15562,plain,
( spl184_893
<=> sP20(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_893])]) ).
fof(f2686,plain,
( sP20(empty_set)
| ~ spl184_5
| ~ spl184_76 ),
inference(resolution,[],[f2545,f2208]) ).
fof(f15559,plain,
( spl184_892
| ~ spl184_42
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2684,f2540,f2391,f15556]) ).
fof(f15556,plain,
( spl184_892
<=> sP18(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_892])]) ).
fof(f2540,plain,
( spl184_75
<=> ! [X0] :
( sP18(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_75])]) ).
fof(f2684,plain,
( sP18(sK183)
| ~ spl184_42
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2393]) ).
fof(f2541,plain,
( ! [X0] :
( ~ relation(X0)
| sP18(X0) )
| ~ spl184_75 ),
inference(avatar_component_clause,[],[f2540]) ).
fof(f15553,plain,
( spl184_891
| ~ spl184_35
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2683,f2540,f2356,f15550]) ).
fof(f15550,plain,
( spl184_891
<=> sP18(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_891])]) ).
fof(f2683,plain,
( sP18(sK182)
| ~ spl184_35
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2358]) ).
fof(f15548,plain,
( spl184_890
| ~ spl184_32
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2682,f2540,f2341,f15545]) ).
fof(f15545,plain,
( spl184_890
<=> sP18(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_890])]) ).
fof(f2682,plain,
( sP18(sK181)
| ~ spl184_32
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2343]) ).
fof(f15543,plain,
( spl184_889
| ~ spl184_30
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2681,f2540,f2331,f15540]) ).
fof(f15540,plain,
( spl184_889
<=> sP18(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_889])]) ).
fof(f2681,plain,
( sP18(sK180)
| ~ spl184_30
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2333]) ).
fof(f15538,plain,
( spl184_888
| ~ spl184_27
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2680,f2540,f2316,f15535]) ).
fof(f15535,plain,
( spl184_888
<=> sP18(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_888])]) ).
fof(f2680,plain,
( sP18(sK179)
| ~ spl184_27
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2318]) ).
fof(f15533,plain,
( spl184_887
| ~ spl184_25
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2679,f2540,f2306,f15530]) ).
fof(f15530,plain,
( spl184_887
<=> sP18(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_887])]) ).
fof(f2679,plain,
( sP18(sK178)
| ~ spl184_25
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2308]) ).
fof(f15527,plain,
( spl184_886
| ~ spl184_24
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2678,f2540,f2301,f15524]) ).
fof(f15524,plain,
( spl184_886
<=> sP18(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_886])]) ).
fof(f2678,plain,
( sP18(sK177)
| ~ spl184_24
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2303]) ).
fof(f15522,plain,
( spl184_885
| ~ spl184_19
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2677,f2540,f2276,f15519]) ).
fof(f15519,plain,
( spl184_885
<=> sP18(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_885])]) ).
fof(f2677,plain,
( sP18(sK175)
| ~ spl184_19
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2278]) ).
fof(f15516,plain,
( spl184_884
| ~ spl184_5
| ~ spl184_75 ),
inference(avatar_split_clause,[],[f2676,f2540,f2206,f15513]) ).
fof(f15513,plain,
( spl184_884
<=> sP18(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_884])]) ).
fof(f2676,plain,
( sP18(empty_set)
| ~ spl184_5
| ~ spl184_75 ),
inference(resolution,[],[f2541,f2208]) ).
fof(f15510,plain,
( spl184_883
| ~ spl184_42
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2674,f2536,f2391,f15507]) ).
fof(f15507,plain,
( spl184_883
<=> sP16(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_883])]) ).
fof(f2536,plain,
( spl184_74
<=> ! [X0] :
( sP16(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_74])]) ).
fof(f2674,plain,
( sP16(sK183)
| ~ spl184_42
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2393]) ).
fof(f2537,plain,
( ! [X0] :
( ~ relation(X0)
| sP16(X0) )
| ~ spl184_74 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f15504,plain,
( spl184_882
| ~ spl184_35
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2673,f2536,f2356,f15501]) ).
fof(f15501,plain,
( spl184_882
<=> sP16(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_882])]) ).
fof(f2673,plain,
( sP16(sK182)
| ~ spl184_35
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2358]) ).
fof(f15499,plain,
( spl184_881
| ~ spl184_32
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2672,f2536,f2341,f15496]) ).
fof(f15496,plain,
( spl184_881
<=> sP16(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_881])]) ).
fof(f2672,plain,
( sP16(sK181)
| ~ spl184_32
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2343]) ).
fof(f15494,plain,
( spl184_880
| ~ spl184_30
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2671,f2536,f2331,f15491]) ).
fof(f15491,plain,
( spl184_880
<=> sP16(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_880])]) ).
fof(f2671,plain,
( sP16(sK180)
| ~ spl184_30
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2333]) ).
fof(f15489,plain,
( spl184_879
| ~ spl184_27
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2670,f2536,f2316,f15486]) ).
fof(f15486,plain,
( spl184_879
<=> sP16(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_879])]) ).
fof(f2670,plain,
( sP16(sK179)
| ~ spl184_27
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2318]) ).
fof(f15484,plain,
( spl184_878
| ~ spl184_25
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2669,f2536,f2306,f15481]) ).
fof(f15481,plain,
( spl184_878
<=> sP16(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_878])]) ).
fof(f2669,plain,
( sP16(sK178)
| ~ spl184_25
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2308]) ).
fof(f15478,plain,
( spl184_877
| ~ spl184_24
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2668,f2536,f2301,f15475]) ).
fof(f15475,plain,
( spl184_877
<=> sP16(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_877])]) ).
fof(f2668,plain,
( sP16(sK177)
| ~ spl184_24
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2303]) ).
fof(f15473,plain,
( spl184_876
| ~ spl184_19
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2667,f2536,f2276,f15470]) ).
fof(f15470,plain,
( spl184_876
<=> sP16(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_876])]) ).
fof(f2667,plain,
( sP16(sK175)
| ~ spl184_19
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2278]) ).
fof(f15467,plain,
( spl184_875
| ~ spl184_5
| ~ spl184_74 ),
inference(avatar_split_clause,[],[f2666,f2536,f2206,f15464]) ).
fof(f15464,plain,
( spl184_875
<=> sP16(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_875])]) ).
fof(f2666,plain,
( sP16(empty_set)
| ~ spl184_5
| ~ spl184_74 ),
inference(resolution,[],[f2537,f2208]) ).
fof(f15462,plain,
( spl184_874
| ~ spl184_73
| ~ spl184_720 ),
inference(avatar_split_clause,[],[f11740,f11621,f2532,f15459]) ).
fof(f15459,plain,
( spl184_874
<=> sP9(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_874])]) ).
fof(f2532,plain,
( spl184_73
<=> ! [X0] :
( sP9(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_73])]) ).
fof(f11621,plain,
( spl184_720
<=> relation(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_720])]) ).
fof(f11740,plain,
( sP9(sK56)
| ~ spl184_73
| ~ spl184_720 ),
inference(resolution,[],[f11623,f2533]) ).
fof(f2533,plain,
( ! [X0] :
( ~ relation(X0)
| sP9(X0) )
| ~ spl184_73 ),
inference(avatar_component_clause,[],[f2532]) ).
fof(f11623,plain,
( relation(sK56)
| ~ spl184_720 ),
inference(avatar_component_clause,[],[f11621]) ).
fof(f15456,plain,
( spl184_873
| ~ spl184_42
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2664,f2532,f2391,f15453]) ).
fof(f15453,plain,
( spl184_873
<=> sP9(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_873])]) ).
fof(f2664,plain,
( sP9(sK183)
| ~ spl184_42
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2393]) ).
fof(f15450,plain,
( spl184_872
| ~ spl184_35
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2663,f2532,f2356,f15447]) ).
fof(f15447,plain,
( spl184_872
<=> sP9(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_872])]) ).
fof(f2663,plain,
( sP9(sK182)
| ~ spl184_35
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2358]) ).
fof(f15445,plain,
( spl184_871
| ~ spl184_32
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2662,f2532,f2341,f15442]) ).
fof(f15442,plain,
( spl184_871
<=> sP9(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_871])]) ).
fof(f2662,plain,
( sP9(sK181)
| ~ spl184_32
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2343]) ).
fof(f15440,plain,
( spl184_870
| ~ spl184_30
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2661,f2532,f2331,f15437]) ).
fof(f15437,plain,
( spl184_870
<=> sP9(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_870])]) ).
fof(f2661,plain,
( sP9(sK180)
| ~ spl184_30
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2333]) ).
fof(f15435,plain,
( spl184_869
| ~ spl184_27
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2660,f2532,f2316,f15432]) ).
fof(f15432,plain,
( spl184_869
<=> sP9(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_869])]) ).
fof(f2660,plain,
( sP9(sK179)
| ~ spl184_27
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2318]) ).
fof(f15430,plain,
( spl184_868
| ~ spl184_25
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2659,f2532,f2306,f15427]) ).
fof(f15427,plain,
( spl184_868
<=> sP9(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_868])]) ).
fof(f2659,plain,
( sP9(sK178)
| ~ spl184_25
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2308]) ).
fof(f15424,plain,
( spl184_867
| ~ spl184_24
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2658,f2532,f2301,f15421]) ).
fof(f15421,plain,
( spl184_867
<=> sP9(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_867])]) ).
fof(f2658,plain,
( sP9(sK177)
| ~ spl184_24
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2303]) ).
fof(f15419,plain,
( spl184_866
| ~ spl184_19
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2657,f2532,f2276,f15416]) ).
fof(f15416,plain,
( spl184_866
<=> sP9(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_866])]) ).
fof(f2657,plain,
( sP9(sK175)
| ~ spl184_19
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2278]) ).
fof(f15413,plain,
( spl184_865
| ~ spl184_5
| ~ spl184_73 ),
inference(avatar_split_clause,[],[f2656,f2532,f2206,f15410]) ).
fof(f15410,plain,
( spl184_865
<=> sP9(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_865])]) ).
fof(f2656,plain,
( sP9(empty_set)
| ~ spl184_5
| ~ spl184_73 ),
inference(resolution,[],[f2533,f2208]) ).
fof(f15407,plain,
( spl184_864
| ~ spl184_42
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2649,f2503,f2391,f15404]) ).
fof(f15404,plain,
( spl184_864
<=> sP7(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_864])]) ).
fof(f2503,plain,
( spl184_66
<=> ! [X0] :
( sP7(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_66])]) ).
fof(f2649,plain,
( sP7(sK183)
| ~ spl184_42
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2393]) ).
fof(f2504,plain,
( ! [X0] :
( ~ relation(X0)
| sP7(X0) )
| ~ spl184_66 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f15371,plain,
( spl184_863
| ~ spl184_35
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2648,f2503,f2356,f15368]) ).
fof(f15368,plain,
( spl184_863
<=> sP7(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_863])]) ).
fof(f2648,plain,
( sP7(sK182)
| ~ spl184_35
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2358]) ).
fof(f15366,plain,
( spl184_862
| ~ spl184_32
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2647,f2503,f2341,f15363]) ).
fof(f15363,plain,
( spl184_862
<=> sP7(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_862])]) ).
fof(f2647,plain,
( sP7(sK181)
| ~ spl184_32
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2343]) ).
fof(f15361,plain,
( spl184_861
| ~ spl184_30
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2646,f2503,f2331,f15358]) ).
fof(f15358,plain,
( spl184_861
<=> sP7(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_861])]) ).
fof(f2646,plain,
( sP7(sK180)
| ~ spl184_30
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2333]) ).
fof(f15343,plain,
( spl184_860
| ~ spl184_2
| ~ spl184_499 ),
inference(avatar_split_clause,[],[f6934,f6746,f2191,f15341]) ).
fof(f2191,plain,
( spl184_2
<=> relation_of2_as_subset(sK59,sK58,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_2])]) ).
fof(f6746,plain,
( spl184_499
<=> ! [X0,X3,X2,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_499])]) ).
fof(f6934,plain,
( ! [X0] :
( ~ subset(relation_rng(sK59),X0)
| relation_of2_as_subset(sK59,sK58,X0) )
| ~ spl184_2
| ~ spl184_499 ),
inference(resolution,[],[f6747,f2193]) ).
fof(f2193,plain,
( relation_of2_as_subset(sK59,sK58,sK56)
| ~ spl184_2 ),
inference(avatar_component_clause,[],[f2191]) ).
fof(f6747,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(relation_rng(X3),X1)
| relation_of2_as_subset(X3,X2,X1) )
| ~ spl184_499 ),
inference(avatar_component_clause,[],[f6746]) ).
fof(f15337,plain,
( ~ spl184_598
| ~ spl184_858
| spl184_859
| ~ spl184_1
| ~ spl184_435 ),
inference(avatar_split_clause,[],[f5971,f5854,f2186,f15334,f15330,f8531]) ).
fof(f8531,plain,
( spl184_598
<=> ordinal(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_598])]) ).
fof(f15330,plain,
( spl184_858
<=> ordinal(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_858])]) ).
fof(f15334,plain,
( spl184_859
<=> ordinal_subset(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_859])]) ).
fof(f2186,plain,
( spl184_1
<=> subset(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_1])]) ).
fof(f5854,plain,
( spl184_435
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_435])]) ).
fof(f5971,plain,
( ordinal_subset(sK56,sK57)
| ~ ordinal(sK57)
| ~ ordinal(sK56)
| ~ spl184_1
| ~ spl184_435 ),
inference(resolution,[],[f5855,f2188]) ).
fof(f2188,plain,
( subset(sK56,sK57)
| ~ spl184_1 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f5855,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl184_435 ),
inference(avatar_component_clause,[],[f5854]) ).
fof(f15317,plain,
( spl184_857
| ~ spl184_214
| ~ spl184_855 ),
inference(avatar_split_clause,[],[f15308,f15304,f3620,f15315]) ).
fof(f15315,plain,
( spl184_857
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_857])]) ).
fof(f3620,plain,
( spl184_214
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_214])]) ).
fof(f15304,plain,
( spl184_855
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_855])]) ).
fof(f15308,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2)) )
| ~ spl184_214
| ~ spl184_855 ),
inference(forward_demodulation,[],[f15307,f3621]) ).
fof(f3621,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl184_214 ),
inference(avatar_component_clause,[],[f3620]) ).
fof(f15307,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_855 ),
inference(forward_demodulation,[],[f15305,f3621]) ).
fof(f15305,plain,
( ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_855 ),
inference(avatar_component_clause,[],[f15304]) ).
fof(f15313,plain,
( spl184_856
| ~ spl184_165
| ~ spl184_684 ),
inference(avatar_split_clause,[],[f13962,f10253,f3165,f15310]) ).
fof(f15310,plain,
( spl184_856
<=> element(sK159(sK57),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_856])]) ).
fof(f3165,plain,
( spl184_165
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_165])]) ).
fof(f13962,plain,
( element(sK159(sK57),sK57)
| ~ spl184_165
| ~ spl184_684 ),
inference(resolution,[],[f10255,f3166]) ).
fof(f3166,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl184_165 ),
inference(avatar_component_clause,[],[f3165]) ).
fof(f10255,plain,
( in(sK159(sK57),sK57)
| ~ spl184_684 ),
inference(avatar_component_clause,[],[f10253]) ).
fof(f15306,plain,
spl184_855,
inference(avatar_split_clause,[],[f2015,f15304]) ).
fof(f2015,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1519,f1913,f1913]) ).
fof(f1913,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1700,f1158]) ).
fof(f1158,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f308]) ).
fof(f308,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f1700,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,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(f1519,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f898,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ( ( ~ in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
& in(sK98(X0,X1,X2),relation_field(X2))
& in(sK97(X0,X1,X2),relation_field(X2)) )
| in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2)) )
& ( ( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& in(X6,relation_field(X2))
& in(X5,relation_field(X2)) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97,sK98])],[f896,f897]) ).
fof(f897,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
| ~ in(X4,relation_field(X2))
| ~ in(X3,relation_field(X2))
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& in(X4,relation_field(X2))
& in(X3,relation_field(X2)) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
| ~ in(sK98(X0,X1,X2),relation_field(X2))
| ~ in(sK97(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
& in(sK98(X0,X1,X2),relation_field(X2))
& in(sK97(X0,X1,X2),relation_field(X2)) )
| in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f896,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
| ~ in(X4,relation_field(X2))
| ~ in(X3,relation_field(X2))
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& in(X4,relation_field(X2))
& in(X3,relation_field(X2)) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2)) )
& ( ( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& in(X6,relation_field(X2))
& in(X5,relation_field(X2)) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f895]) ).
fof(f895,plain,
! [X1,X2,X0] :
( ( sP12(X1,X2,X0)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| in(ordered_pair(X3,X4),X0) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ sP12(X1,X2,X0) ) ),
inference(flattening,[],[f894]) ).
fof(f894,plain,
! [X1,X2,X0] :
( ( sP12(X1,X2,X0)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| in(ordered_pair(X3,X4),X0) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ sP12(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f681]) ).
fof(f681,plain,
! [X1,X2,X0] :
( sP12(X1,X2,X0)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f15289,plain,
( spl184_854
| ~ spl184_214
| ~ spl184_853 ),
inference(avatar_split_clause,[],[f15285,f15282,f3620,f15287]) ).
fof(f15287,plain,
( spl184_854
<=> ! [X0,X5,X2,X1] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| sP10(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_854])]) ).
fof(f15282,plain,
( spl184_853
<=> ! [X0,X5,X2,X1] :
( sP10(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_853])]) ).
fof(f15285,plain,
( ! [X2,X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| sP10(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1) )
| ~ spl184_214
| ~ spl184_853 ),
inference(forward_demodulation,[],[f15283,f3621]) ).
fof(f15283,plain,
( ! [X2,X0,X1,X5] :
( sP10(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) )
| ~ spl184_853 ),
inference(avatar_component_clause,[],[f15282]) ).
fof(f15284,plain,
spl184_853,
inference(avatar_split_clause,[],[f2009,f15282]) ).
fof(f2009,plain,
! [X2,X0,X1,X5] :
( sP10(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1503,f1913,f1913,f1913]) ).
fof(f1503,plain,
! [X2,X0,X1,X5] :
( sP10(X0,X1,X2)
| ~ in(ordered_pair(X5,sK94(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X1)
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f888,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK94(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X0)
& in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X1) )
| in(ordered_pair(sK93(X0,X1,X2),sK94(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(sK96(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP10(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94,sK95,sK96])],[f884,f887,f886,f885]) ).
fof(f885,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,sK94(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK94(X0,X1,X2)),X0)
& in(ordered_pair(sK93(X0,X1,X2),X6),X1) )
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f886,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK94(X0,X1,X2)),X0)
& in(ordered_pair(sK93(X0,X1,X2),X6),X1) )
=> ( in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X0)
& in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f887,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
=> ( in(ordered_pair(sK96(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f884,plain,
! [X0,X1,X2] :
( ( sP10(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) ) )
| ~ sP10(X0,X1,X2) ) ),
inference(rectify,[],[f883]) ).
fof(f883,plain,
! [X1,X0,X2] :
( ( sP10(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) ) )
| ~ sP10(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f678]) ).
fof(f678,plain,
! [X1,X0,X2] :
( sP10(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,[sP10])]) ).
fof(f15196,plain,
( spl184_852
| ~ spl184_214
| ~ spl184_851 ),
inference(avatar_split_clause,[],[f15192,f15188,f3620,f15194]) ).
fof(f15194,plain,
( spl184_852
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_852])]) ).
fof(f15188,plain,
( spl184_851
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_851])]) ).
fof(f15192,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_851 ),
inference(forward_demodulation,[],[f15191,f3621]) ).
fof(f15191,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(apply(X1,sK98(X0,X1,X2)),apply(X1,sK97(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| sP12(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_851 ),
inference(forward_demodulation,[],[f15189,f3621]) ).
fof(f15189,plain,
( ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_851 ),
inference(avatar_component_clause,[],[f15188]) ).
fof(f15190,plain,
spl184_851,
inference(avatar_split_clause,[],[f2016,f15188]) ).
fof(f2016,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(unordered_pair(unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),unordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK97(X0,X1,X2)))),X0)
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1518,f1913,f1913]) ).
fof(f1518,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(ordered_pair(apply(X1,sK97(X0,X1,X2)),apply(X1,sK98(X0,X1,X2))),X0)
| in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f15158,plain,
( spl184_850
| ~ spl184_214
| ~ spl184_847 ),
inference(avatar_split_clause,[],[f15145,f15141,f3620,f15156]) ).
fof(f15156,plain,
( spl184_850
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2)
| ~ in(sK115(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_850])]) ).
fof(f15141,plain,
( spl184_847
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_847])]) ).
fof(f15145,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2)
| ~ in(sK115(X0,X1,X2),X1) )
| ~ spl184_214
| ~ spl184_847 ),
inference(forward_demodulation,[],[f15144,f3621]) ).
fof(f15144,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_847 ),
inference(forward_demodulation,[],[f15142,f3621]) ).
fof(f15142,plain,
( ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) )
| ~ spl184_847 ),
inference(avatar_component_clause,[],[f15141]) ).
fof(f15154,plain,
( ~ spl184_849
| ~ spl184_164
| ~ spl184_684 ),
inference(avatar_split_clause,[],[f13961,f10253,f3161,f15151]) ).
fof(f15151,plain,
( spl184_849
<=> in(sK57,sK159(sK57)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_849])]) ).
fof(f3161,plain,
( spl184_164
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_164])]) ).
fof(f13961,plain,
( ~ in(sK57,sK159(sK57))
| ~ spl184_164
| ~ spl184_684 ),
inference(resolution,[],[f10255,f3162]) ).
fof(f3162,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl184_164 ),
inference(avatar_component_clause,[],[f3161]) ).
fof(f15149,plain,
spl184_848,
inference(avatar_split_clause,[],[f2173,f15147]) ).
fof(f15147,plain,
( spl184_848
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2)
| ~ in(sK150(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_848])]) ).
fof(f2173,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2)
| ~ in(sK150(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f2172,f1697]) ).
fof(f1697,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f2172,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2)
| ~ in(sK150(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f2074,f1697]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| ~ in(sK150(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1737,f1913,f1913]) ).
fof(f1737,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| ~ in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
| ~ in(sK150(X0,X1,X2),X1)
| ~ in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
| ~ in(sK150(X0,X1,X2),X1)
| ~ in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
& in(sK150(X0,X1,X2),X1) )
| in(ordered_pair(sK149(X0,X1,X2),sK150(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) ) )
| ~ sP45(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150])],[f1042,f1043]) ).
fof(f1043,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(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
| ~ in(sK150(X0,X1,X2),X1)
| ~ in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
& in(sK150(X0,X1,X2),X1) )
| in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1042,plain,
! [X0,X1,X2] :
( ( sP45(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) ) )
| ~ sP45(X0,X1,X2) ) ),
inference(rectify,[],[f1041]) ).
fof(f1041,plain,
! [X1,X0,X2] :
( ( sP45(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) ) )
| ~ sP45(X1,X0,X2) ) ),
inference(flattening,[],[f1040]) ).
fof(f1040,plain,
! [X1,X0,X2] :
( ( sP45(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) ) )
| ~ sP45(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f730]) ).
fof(f730,plain,
! [X1,X0,X2] :
( sP45(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,[sP45])]) ).
fof(f15143,plain,
spl184_847,
inference(avatar_split_clause,[],[f2043,f15141]) ).
fof(f2043,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1584,f1913,f1913]) ).
fof(f1584,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f946,plain,
! [X0,X1,X2] :
( ( sP25(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
& in(sK115(X0,X1,X2),X1) )
| in(ordered_pair(sK115(X0,X1,X2),sK116(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) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116])],[f944,f945]) ).
fof(f945,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(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
| ~ in(sK115(X0,X1,X2),X1)
| ~ in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
& in(sK115(X0,X1,X2),X1) )
| in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f944,plain,
! [X0,X1,X2] :
( ( sP25(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) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(rectify,[],[f943]) ).
fof(f943,plain,
! [X0,X1,X2] :
( ( sP25(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) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(flattening,[],[f942]) ).
fof(f942,plain,
! [X0,X1,X2] :
( ( sP25(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) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f700]) ).
fof(f700,plain,
! [X0,X1,X2] :
( sP25(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,[sP25])]) ).
fof(f14797,plain,
( spl184_846
| ~ spl184_214
| ~ spl184_842 ),
inference(avatar_split_clause,[],[f14781,f14777,f3620,f14795]) ).
fof(f14795,plain,
( spl184_846
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_846])]) ).
fof(f14777,plain,
( spl184_842
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_842])]) ).
fof(f14781,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_842 ),
inference(forward_demodulation,[],[f14780,f3621]) ).
fof(f14780,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_842 ),
inference(forward_demodulation,[],[f14778,f3621]) ).
fof(f14778,plain,
( ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) )
| ~ spl184_842 ),
inference(avatar_component_clause,[],[f14777]) ).
fof(f14793,plain,
( spl184_845
| ~ spl184_214
| ~ spl184_841 ),
inference(avatar_split_clause,[],[f14775,f14771,f3620,f14791]) ).
fof(f14791,plain,
( spl184_845
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_845])]) ).
fof(f14771,plain,
( spl184_841
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_841])]) ).
fof(f14775,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| sP10(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_841 ),
inference(forward_demodulation,[],[f14774,f3621]) ).
fof(f14774,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_841 ),
inference(forward_demodulation,[],[f14772,f3621]) ).
fof(f14772,plain,
( ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) )
| ~ spl184_841 ),
inference(avatar_component_clause,[],[f14771]) ).
fof(f14789,plain,
( spl184_844
| ~ spl184_214
| ~ spl184_840 ),
inference(avatar_split_clause,[],[f14769,f14765,f3620,f14787]) ).
fof(f14787,plain,
( spl184_844
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2))),X0)
| sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_844])]) ).
fof(f14765,plain,
( spl184_840
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_840])]) ).
fof(f14769,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK94(X0,X1,X2),sK93(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2))),X0)
| sP10(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_840 ),
inference(forward_demodulation,[],[f14768,f3621]) ).
fof(f14768,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2))),X0)
| sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) )
| ~ spl184_214
| ~ spl184_840 ),
inference(forward_demodulation,[],[f14766,f3621]) ).
fof(f14766,plain,
( ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) )
| ~ spl184_840 ),
inference(avatar_component_clause,[],[f14765]) ).
fof(f14785,plain,
spl184_843,
inference(avatar_split_clause,[],[f2175,f14783]) ).
fof(f14783,plain,
( spl184_843
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_843])]) ).
fof(f2175,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2) ),
inference(forward_demodulation,[],[f2174,f1697]) ).
fof(f2174,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| sP45(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2) ),
inference(forward_demodulation,[],[f2075,f1697]) ).
fof(f2075,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1736,f1913,f1913]) ).
fof(f1736,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X0)
| in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f14779,plain,
spl184_842,
inference(avatar_split_clause,[],[f2044,f14777]) ).
fof(f2044,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1583,f1913,f1913]) ).
fof(f1583,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X0)
| in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f14773,plain,
spl184_841,
inference(avatar_split_clause,[],[f2011,f14771]) ).
fof(f2011,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1501,f1913,f1913]) ).
fof(f1501,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X1)
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f14767,plain,
spl184_840,
inference(avatar_split_clause,[],[f2010,f14765]) ).
fof(f2010,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1502,f1913,f1913]) ).
fof(f1502,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X0)
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f14663,plain,
( spl184_839
| ~ spl184_214
| ~ spl184_837 ),
inference(avatar_split_clause,[],[f14655,f14651,f3620,f14661]) ).
fof(f14661,plain,
( spl184_839
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK91(X0,X1),sK91(X0,X1)),unordered_pair(sK91(X0,X1),sK92(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_839])]) ).
fof(f14651,plain,
( spl184_837
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_837])]) ).
fof(f14655,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK91(X0,X1),sK91(X0,X1)),unordered_pair(sK91(X0,X1),sK92(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_837 ),
inference(forward_demodulation,[],[f14654,f3621]) ).
fof(f14654,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_837 ),
inference(forward_demodulation,[],[f14652,f3621]) ).
fof(f14652,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_837 ),
inference(avatar_component_clause,[],[f14651]) ).
fof(f14659,plain,
( spl184_838
| ~ spl184_214
| ~ spl184_836 ),
inference(avatar_split_clause,[],[f14649,f14645,f3620,f14657]) ).
fof(f14657,plain,
( spl184_838
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK91(X0,X1)),unordered_pair(sK91(X0,X1),sK92(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_838])]) ).
fof(f14645,plain,
( spl184_836
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_836])]) ).
fof(f14649,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK91(X0,X1)),unordered_pair(sK91(X0,X1),sK92(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_836 ),
inference(forward_demodulation,[],[f14648,f3621]) ).
fof(f14648,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_836 ),
inference(forward_demodulation,[],[f14646,f3621]) ).
fof(f14646,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_836 ),
inference(avatar_component_clause,[],[f14645]) ).
fof(f14653,plain,
spl184_837,
inference(avatar_split_clause,[],[f2006,f14651]) ).
fof(f2006,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1494,f1913,f1913]) ).
fof(f1494,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK92(X0,X1),sK91(X0,X1)),X0)
| in(ordered_pair(sK91(X0,X1),sK92(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f880]) ).
fof(f880,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK92(X0,X1),sK91(X0,X1)),X0)
| ~ in(ordered_pair(sK91(X0,X1),sK92(X0,X1)),X1) )
& ( in(ordered_pair(sK92(X0,X1),sK91(X0,X1)),X0)
| in(ordered_pair(sK91(X0,X1),sK92(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,[sK91,sK92])],[f878,f879]) ).
fof(f879,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(sK92(X0,X1),sK91(X0,X1)),X0)
| ~ in(ordered_pair(sK91(X0,X1),sK92(X0,X1)),X1) )
& ( in(ordered_pair(sK92(X0,X1),sK91(X0,X1)),X0)
| in(ordered_pair(sK91(X0,X1),sK92(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f878,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,[],[f877]) ).
fof(f877,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,[],[f546]) ).
fof(f546,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,[],[f64]) ).
fof(f64,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(f14647,plain,
spl184_836,
inference(avatar_split_clause,[],[f2005,f14645]) ).
fof(f2005,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK92(X0,X1),sK91(X0,X1)),unordered_pair(sK92(X0,X1),sK92(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK91(X0,X1),sK92(X0,X1)),unordered_pair(sK91(X0,X1),sK91(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1495,f1913,f1913]) ).
fof(f1495,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK92(X0,X1),sK91(X0,X1)),X0)
| ~ in(ordered_pair(sK91(X0,X1),sK92(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f880]) ).
fof(f14537,plain,
( spl184_835
| ~ spl184_214
| ~ spl184_833 ),
inference(avatar_split_clause,[],[f14529,f14525,f3620,f14535]) ).
fof(f14535,plain,
( spl184_835
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_835])]) ).
fof(f14525,plain,
( spl184_833
<=> ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_833])]) ).
fof(f14529,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_833 ),
inference(forward_demodulation,[],[f14528,f3621]) ).
fof(f14528,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_833 ),
inference(forward_demodulation,[],[f14526,f3621]) ).
fof(f14526,plain,
( ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_833 ),
inference(avatar_component_clause,[],[f14525]) ).
fof(f14533,plain,
( spl184_834
| ~ spl184_214
| ~ spl184_832 ),
inference(avatar_split_clause,[],[f14523,f14519,f3620,f14531]) ).
fof(f14531,plain,
( spl184_834
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_834])]) ).
fof(f14519,plain,
( spl184_832
<=> ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_832])]) ).
fof(f14523,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_832 ),
inference(forward_demodulation,[],[f14522,f3621]) ).
fof(f14522,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_832 ),
inference(forward_demodulation,[],[f14520,f3621]) ).
fof(f14520,plain,
( ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_832 ),
inference(avatar_component_clause,[],[f14519]) ).
fof(f14527,plain,
spl184_833,
inference(avatar_split_clause,[],[f1999,f14525]) ).
fof(f1999,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1487,f1913,f1913]) ).
fof(f1487,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f872]) ).
fof(f872,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X0) )
& ( in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| in(ordered_pair(sK87(X0,X1),sK88(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,[sK87,sK88])],[f870,f871]) ).
fof(f871,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(sK87(X0,X1),sK88(X0,X1)),X1)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X0) )
& ( in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f870,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,[],[f869]) ).
fof(f869,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,[],[f544]) ).
fof(f544,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,[],[f36]) ).
fof(f36,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(f14521,plain,
spl184_832,
inference(avatar_split_clause,[],[f1998,f14519]) ).
fof(f1998,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1488,f1913,f1913]) ).
fof(f1488,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f872]) ).
fof(f14491,plain,
spl184_831,
inference(avatar_split_clause,[],[f2034,f14489]) ).
fof(f14489,plain,
( spl184_831
<=> ! [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)
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_831])]) ).
fof(f2034,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)
| ~ sP23(X0,X1) ),
inference(definition_unfolding,[],[f1561,f1913,f1913,f1913]) ).
fof(f1561,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)
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f927]) ).
fof(f927,plain,
! [X0,X1] :
( ( sP23(X0,X1)
| ( ~ in(ordered_pair(sK106(X0,X1),sK108(X0,X1)),X0)
& in(ordered_pair(sK107(X0,X1),sK108(X0,X1)),X0)
& in(ordered_pair(sK106(X0,X1),sK107(X0,X1)),X0)
& in(sK108(X0,X1),X1)
& in(sK107(X0,X1),X1)
& in(sK106(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) )
| ~ sP23(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107,sK108])],[f925,f926]) ).
fof(f926,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(sK106(X0,X1),sK108(X0,X1)),X0)
& in(ordered_pair(sK107(X0,X1),sK108(X0,X1)),X0)
& in(ordered_pair(sK106(X0,X1),sK107(X0,X1)),X0)
& in(sK108(X0,X1),X1)
& in(sK107(X0,X1),X1)
& in(sK106(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f925,plain,
! [X0,X1] :
( ( sP23(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) )
| ~ sP23(X0,X1) ) ),
inference(rectify,[],[f924]) ).
fof(f924,plain,
! [X0,X1] :
( ( sP23(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) )
| ~ sP23(X0,X1) ) ),
inference(nnf_transformation,[],[f697]) ).
fof(f697,plain,
! [X0,X1] :
( sP23(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,[sP23])]) ).
fof(f14465,plain,
spl184_830,
inference(avatar_split_clause,[],[f2019,f14463]) ).
fof(f14463,plain,
( spl184_830
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2))
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_830])]) ).
fof(f2019,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2))
| ~ sP12(X0,X1,X2) ),
inference(definition_unfolding,[],[f1515,f1913,f1913]) ).
fof(f1515,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f14450,plain,
( spl184_828
| ~ spl184_829
| ~ spl184_130
| ~ spl184_736 ),
inference(avatar_split_clause,[],[f13318,f11885,f3023,f14447,f14443]) ).
fof(f14443,plain,
( spl184_828
<=> connected(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_828])]) ).
fof(f14447,plain,
( spl184_829
<=> sP0(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_829])]) ).
fof(f3023,plain,
( spl184_130
<=> ! [X0] :
( connected(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_130])]) ).
fof(f11885,plain,
( spl184_736
<=> sP1(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_736])]) ).
fof(f13318,plain,
( ~ sP0(sK56)
| connected(sK56)
| ~ spl184_130
| ~ spl184_736 ),
inference(resolution,[],[f11887,f3024]) ).
fof(f3024,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| connected(X0) )
| ~ spl184_130 ),
inference(avatar_component_clause,[],[f3023]) ).
fof(f11887,plain,
( sP1(sK56)
| ~ spl184_736 ),
inference(avatar_component_clause,[],[f11885]) ).
fof(f14374,plain,
( spl184_827
| ~ spl184_214
| ~ spl184_824 ),
inference(avatar_split_clause,[],[f14362,f14359,f3620,f14372]) ).
fof(f14372,plain,
( spl184_827
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,sK117(X0,X1,X2)),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sP27(X0,X1,X2)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_827])]) ).
fof(f14359,plain,
( spl184_824
<=> ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_824])]) ).
fof(f14362,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,sK117(X0,X1,X2)),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sP27(X0,X1,X2)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) )
| ~ spl184_214
| ~ spl184_824 ),
inference(forward_demodulation,[],[f14360,f3621]) ).
fof(f14360,plain,
( ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) )
| ~ spl184_824 ),
inference(avatar_component_clause,[],[f14359]) ).
fof(f14370,plain,
( spl184_826
| ~ spl184_214
| ~ spl184_823 ),
inference(avatar_split_clause,[],[f14357,f14354,f3620,f14368]) ).
fof(f14368,plain,
( spl184_826
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X8,sK96(X0,X1,X7,X8)),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_826])]) ).
fof(f14354,plain,
( spl184_823
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(sK96(X0,X1,X7,X8),X8),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_823])]) ).
fof(f14357,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK96(X0,X1,X7,X8)),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_823 ),
inference(forward_demodulation,[],[f14355,f3621]) ).
fof(f14355,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK96(X0,X1,X7,X8),X8),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) )
| ~ spl184_823 ),
inference(avatar_component_clause,[],[f14354]) ).
fof(f14366,plain,
spl184_825,
inference(avatar_split_clause,[],[f2180,f14364]) ).
fof(f14364,plain,
( spl184_825
<=> ! [X2,X0,X1] :
( sK163(X0,X1,X2) = unordered_pair(unordered_pair(sK165(X0,X1,X2),sK164(X0,X1,X2)),unordered_pair(sK164(X0,X1,X2),sK164(X0,X1,X2)))
| sP51(X0,X1,X2)
| in(sK163(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_825])]) ).
fof(f2180,plain,
! [X2,X0,X1] :
( sK163(X0,X1,X2) = unordered_pair(unordered_pair(sK165(X0,X1,X2),sK164(X0,X1,X2)),unordered_pair(sK164(X0,X1,X2),sK164(X0,X1,X2)))
| sP51(X0,X1,X2)
| in(sK163(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f2088,f1697]) ).
fof(f2088,plain,
! [X2,X0,X1] :
( sP51(X0,X1,X2)
| sK163(X0,X1,X2) = unordered_pair(unordered_pair(sK164(X0,X1,X2),sK165(X0,X1,X2)),unordered_pair(sK164(X0,X1,X2),sK164(X0,X1,X2)))
| in(sK163(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1840,f1913]) ).
fof(f1840,plain,
! [X2,X0,X1] :
( sP51(X0,X1,X2)
| sK163(X0,X1,X2) = ordered_pair(sK164(X0,X1,X2),sK165(X0,X1,X2))
| in(sK163(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,plain,
! [X0,X1,X2] :
( ( sP51(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK163(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK163(X0,X1,X2),X2) )
& ( ( sK163(X0,X1,X2) = ordered_pair(sK164(X0,X1,X2),sK165(X0,X1,X2))
& in(sK165(X0,X1,X2),X0)
& in(sK164(X0,X1,X2),X1) )
| in(sK163(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK166(X0,X1,X8),sK167(X0,X1,X8)) = X8
& in(sK167(X0,X1,X8),X0)
& in(sK166(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP51(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163,sK164,sK165,sK166,sK167])],[f1094,f1097,f1096,f1095]) ).
fof(f1095,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) != sK163(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK163(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK163(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK163(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1096,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK163(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK163(X0,X1,X2) = ordered_pair(sK164(X0,X1,X2),sK165(X0,X1,X2))
& in(sK165(X0,X1,X2),X0)
& in(sK164(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1097,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK166(X0,X1,X8),sK167(X0,X1,X8)) = X8
& in(sK167(X0,X1,X8),X0)
& in(sK166(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1094,plain,
! [X0,X1,X2] :
( ( sP51(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) ) )
| ~ sP51(X0,X1,X2) ) ),
inference(rectify,[],[f1093]) ).
fof(f1093,plain,
! [X1,X0,X2] :
( ( sP51(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) ) )
| ~ sP51(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f740]) ).
fof(f740,plain,
! [X1,X0,X2] :
( sP51(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,[sP51])]) ).
fof(f14361,plain,
spl184_824,
inference(avatar_split_clause,[],[f2049,f14359]) ).
fof(f2049,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1593,f1913]) ).
fof(f1593,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ in(ordered_pair(sK117(X0,X1,X2),X1),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f952,plain,
! [X0,X1,X2] :
( ( sP27(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK117(X0,X1,X2),X1),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK117(X0,X1,X2),X1),X0)
& sK117(X0,X1,X2) != X1 )
| in(sK117(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK117])],[f950,f951]) ).
fof(f951,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) )
=> ( ( ~ in(ordered_pair(sK117(X0,X1,X2),X1),X0)
| sK117(X0,X1,X2) = X1
| ~ in(sK117(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK117(X0,X1,X2),X1),X0)
& sK117(X0,X1,X2) != X1 )
| in(sK117(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f950,plain,
! [X0,X1,X2] :
( ( sP27(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(rectify,[],[f949]) ).
fof(f949,plain,
! [X0,X1,X2] :
( ( sP27(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(flattening,[],[f948]) ).
fof(f948,plain,
! [X0,X1,X2] :
( ( sP27(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f703]) ).
fof(f703,plain,
! [X0,X1,X2] :
( sP27(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f14356,plain,
spl184_823,
inference(avatar_split_clause,[],[f2013,f14354]) ).
fof(f2013,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK96(X0,X1,X7,X8),X8),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ),
inference(definition_unfolding,[],[f1499,f1913,f1913]) ).
fof(f1499,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK96(X0,X1,X7,X8),X8),X0)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f14350,plain,
( spl184_822
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_821 ),
inference(avatar_split_clause,[],[f14346,f14343,f7974,f2764,f2414,f14348]) ).
fof(f14348,plain,
( spl184_822
<=> ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| apply(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_822])]) ).
fof(f2414,plain,
( spl184_47
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_47])]) ).
fof(f2764,plain,
( spl184_95
<=> ! [X0] : relation_rng(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_95])]) ).
fof(f7974,plain,
( spl184_578
<=> ! [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,[spl184_578])]) ).
fof(f14343,plain,
( spl184_821
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK80(X1,X2)) != apply(X1,sK80(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,[spl184_821])]) ).
fof(f14346,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(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_821 ),
inference(forward_demodulation,[],[f14344,f8115]) ).
fof(f8115,plain,
( ! [X0,X1] : set_difference(X1,set_difference(X1,X0)) = relation_rng(relation_rng_restriction(X0,identity_relation(X1)))
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578 ),
inference(forward_demodulation,[],[f8092,f2765]) ).
fof(f2765,plain,
( ! [X0] : relation_rng(identity_relation(X0)) = X0
| ~ spl184_95 ),
inference(avatar_component_clause,[],[f2764]) ).
fof(f8092,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))
| ~ spl184_47
| ~ spl184_578 ),
inference(resolution,[],[f7975,f2415]) ).
fof(f2415,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl184_47 ),
inference(avatar_component_clause,[],[f2414]) ).
fof(f7975,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0)) )
| ~ spl184_578 ),
inference(avatar_component_clause,[],[f7974]) ).
fof(f14344,plain,
( ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl184_821 ),
inference(avatar_component_clause,[],[f14343]) ).
fof(f14345,plain,
spl184_821,
inference(avatar_split_clause,[],[f1947,f14343]) ).
fof(f1947,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK80(X1,X2)) != apply(X1,sK80(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,[],[f1314,f1249]) ).
fof(f1249,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f285]) ).
fof(f285,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(f1314,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f813]) ).
fof(f813,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
& in(sK80(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,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,[sK80])],[f811,f812]) ).
fof(f812,plain,
! [X1,X2] :
( ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X2,sK80(X1,X2)) != apply(X1,sK80(X1,X2))
& in(sK80(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f811,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,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,[],[f810]) ).
fof(f810,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,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,[],[f809]) ).
fof(f809,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,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,[],[f468]) ).
fof(f468,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,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,[],[f467]) ).
fof(f467,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,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,[],[f307]) ).
fof(f307,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(X2,X3) = apply(X1,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f14292,plain,
spl184_820,
inference(avatar_split_clause,[],[f1873,f14290]) ).
fof(f14290,plain,
( spl184_820
<=> ! [X0,X3,X2,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) = X0
| sK171(X0,X1,X2,X3) = X1
| sK171(X0,X1,X2,X3) = X2
| in(sK171(X0,X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_820])]) ).
fof(f1873,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) = X0
| sK171(X0,X1,X2,X3) = X1
| sK171(X0,X1,X2,X3) = X2
| in(sK171(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,plain,
! [X0,X1,X2,X3] :
( ( sP55(X0,X1,X2,X3)
| ( ( ( sK171(X0,X1,X2,X3) != X0
& sK171(X0,X1,X2,X3) != X1
& sK171(X0,X1,X2,X3) != X2 )
| ~ in(sK171(X0,X1,X2,X3),X3) )
& ( sK171(X0,X1,X2,X3) = X0
| sK171(X0,X1,X2,X3) = X1
| sK171(X0,X1,X2,X3) = X2
| in(sK171(X0,X1,X2,X3),X3) ) ) )
& ( ! [X5] :
( ( in(X5,X3)
| ( X0 != X5
& X1 != X5
& X2 != X5 ) )
& ( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3) ) )
| ~ sP55(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f1120,f1121]) ).
fof(f1121,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ( ( X0 != X4
& X1 != X4
& X2 != X4 )
| ~ in(X4,X3) )
& ( X0 = X4
| X1 = X4
| X2 = X4
| in(X4,X3) ) )
=> ( ( ( sK171(X0,X1,X2,X3) != X0
& sK171(X0,X1,X2,X3) != X1
& sK171(X0,X1,X2,X3) != X2 )
| ~ in(sK171(X0,X1,X2,X3),X3) )
& ( sK171(X0,X1,X2,X3) = X0
| sK171(X0,X1,X2,X3) = X1
| sK171(X0,X1,X2,X3) = X2
| in(sK171(X0,X1,X2,X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1120,plain,
! [X0,X1,X2,X3] :
( ( sP55(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) ) )
| ~ sP55(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1119]) ).
fof(f1119,plain,
! [X2,X1,X0,X3] :
( ( sP55(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) ) )
| ~ sP55(X2,X1,X0,X3) ) ),
inference(flattening,[],[f1118]) ).
fof(f1118,plain,
! [X2,X1,X0,X3] :
( ( sP55(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) ) )
| ~ sP55(X2,X1,X0,X3) ) ),
inference(nnf_transformation,[],[f748]) ).
fof(f748,plain,
! [X2,X1,X0,X3] :
( sP55(X2,X1,X0,X3)
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP55])]) ).
fof(f14288,plain,
spl184_819,
inference(avatar_split_clause,[],[f1233,f14286]) ).
fof(f14286,plain,
( spl184_819
<=> ! [X0,X1] :
( sP4(X0,X1)
| sK73(X0,X1) != apply(X0,sK72(X0,X1))
| ~ in(sK72(X0,X1),relation_rng(X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_819])]) ).
fof(f1233,plain,
! [X0,X1] :
( sP4(X0,X1)
| sK73(X0,X1) != apply(X0,sK72(X0,X1))
| ~ in(sK72(X0,X1),relation_rng(X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f788,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( sK73(X0,X1) != apply(X0,sK72(X0,X1))
| ~ in(sK72(X0,X1),relation_rng(X1)) )
& sK72(X0,X1) = apply(X1,sK73(X0,X1))
& in(sK73(X0,X1),relation_dom(X1)) )
| ~ sP3(sK72(X0,X1),sK73(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)) )
& sP3(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f786,f787]) ).
fof(f787,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP3(X2,X3,X1,X0) )
=> ( ( ( sK73(X0,X1) != apply(X0,sK72(X0,X1))
| ~ in(sK72(X0,X1),relation_rng(X1)) )
& sK72(X0,X1) = apply(X1,sK73(X0,X1))
& in(sK73(X0,X1),relation_dom(X1)) )
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f786,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP3(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)) )
& sP3(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f785]) ).
fof(f785,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP3(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)) )
& sP3(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP4(X1,X0) ) ),
inference(flattening,[],[f784]) ).
fof(f784,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP3(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)) )
& sP3(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f669]) ).
fof(f669,plain,
! [X1,X0] :
( sP4(X1,X0)
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP3(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f14198,plain,
( spl184_818
| ~ spl184_214
| ~ spl184_815 ),
inference(avatar_split_clause,[],[f14183,f14180,f3620,f14196]) ).
fof(f14196,plain,
( spl184_818
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_818])]) ).
fof(f14180,plain,
( spl184_815
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_815])]) ).
fof(f14183,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2)) )
| ~ spl184_214
| ~ spl184_815 ),
inference(forward_demodulation,[],[f14181,f3621]) ).
fof(f14181,plain,
( ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_815 ),
inference(avatar_component_clause,[],[f14180]) ).
fof(f14194,plain,
( spl184_817
| ~ spl184_214
| ~ spl184_814 ),
inference(avatar_split_clause,[],[f14178,f14175,f3620,f14192]) ).
fof(f14192,plain,
( spl184_817
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_817])]) ).
fof(f14175,plain,
( spl184_814
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_814])]) ).
fof(f14178,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK98(X0,X1,X2),sK97(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2)
| sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2)) )
| ~ spl184_214
| ~ spl184_814 ),
inference(forward_demodulation,[],[f14176,f3621]) ).
fof(f14176,plain,
( ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) )
| ~ spl184_814 ),
inference(avatar_component_clause,[],[f14175]) ).
fof(f14190,plain,
spl184_816,
inference(avatar_split_clause,[],[f2169,f14188]) ).
fof(f14188,plain,
( spl184_816
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK148(X0,X1),sK148(X0,X1)),unordered_pair(sK148(X0,X1),sK148(X0,X1))),X1)
| sP43(X0,X1)
| sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK148(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_816])]) ).
fof(f2169,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK148(X0,X1),sK148(X0,X1)),unordered_pair(sK148(X0,X1),sK148(X0,X1))),X1)
| sP43(X0,X1)
| sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK148(X0,X1),X0) ),
inference(inner_rewriting,[],[f2168]) ).
fof(f2168,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK148(X0,X1),sK147(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1)
| sP43(X0,X1)
| sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK147(X0,X1),X0) ),
inference(forward_demodulation,[],[f2068,f1697]) ).
fof(f2068,plain,
! [X0,X1] :
( sP43(X0,X1)
| sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK147(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK147(X0,X1),sK148(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1728,f1913]) ).
fof(f1728,plain,
! [X0,X1] :
( sP43(X0,X1)
| sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK147(X0,X1),X0)
| ~ in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,plain,
! [X0,X1] :
( ( sP43(X0,X1)
| ( ( sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK147(X0,X1),X0)
| ~ in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) )
& ( ( sK147(X0,X1) = sK148(X0,X1)
& in(sK147(X0,X1),X0) )
| in(ordered_pair(sK147(X0,X1),sK148(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) ) )
| ~ sP43(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147,sK148])],[f1035,f1036]) ).
fof(f1036,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) ) )
=> ( ( sK147(X0,X1) != sK148(X0,X1)
| ~ in(sK147(X0,X1),X0)
| ~ in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) )
& ( ( sK147(X0,X1) = sK148(X0,X1)
& in(sK147(X0,X1),X0) )
| in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1035,plain,
! [X0,X1] :
( ( sP43(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) ) )
| ~ sP43(X0,X1) ) ),
inference(rectify,[],[f1034]) ).
fof(f1034,plain,
! [X0,X1] :
( ( sP43(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) ) )
| ~ sP43(X0,X1) ) ),
inference(flattening,[],[f1033]) ).
fof(f1033,plain,
! [X0,X1] :
( ( sP43(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) ) )
| ~ sP43(X0,X1) ) ),
inference(nnf_transformation,[],[f727]) ).
fof(f727,plain,
! [X0,X1] :
( sP43(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
fof(f14182,plain,
spl184_815,
inference(avatar_split_clause,[],[f2018,f14180]) ).
fof(f2018,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1516,f1913]) ).
fof(f1516,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK97(X0,X1,X2),relation_field(X2))
| in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f14177,plain,
spl184_814,
inference(avatar_split_clause,[],[f2017,f14175]) ).
fof(f2017,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),unordered_pair(sK97(X0,X1,X2),sK97(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1517,f1913]) ).
fof(f1517,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| in(sK98(X0,X1,X2),relation_field(X2))
| in(ordered_pair(sK97(X0,X1,X2),sK98(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f14001,plain,
( spl184_813
| ~ spl184_214
| ~ spl184_809 ),
inference(avatar_split_clause,[],[f13718,f13715,f3620,f13999]) ).
fof(f13999,plain,
( spl184_813
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK122(X0,X1,X2),sK122(X0,X1,X2)),unordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2))),X1)
| sP31(X0,X1,X2)
| in(sK121(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_813])]) ).
fof(f13715,plain,
( spl184_809
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),unordered_pair(sK122(X0,X1,X2),sK122(X0,X1,X2))),X1)
| in(sK121(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_809])]) ).
fof(f13718,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK122(X0,X1,X2),sK122(X0,X1,X2)),unordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2))),X1)
| sP31(X0,X1,X2)
| in(sK121(X0,X1,X2),X2) )
| ~ spl184_214
| ~ spl184_809 ),
inference(forward_demodulation,[],[f13716,f3621]) ).
fof(f13716,plain,
( ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),unordered_pair(sK122(X0,X1,X2),sK122(X0,X1,X2))),X1)
| in(sK121(X0,X1,X2),X2) )
| ~ spl184_809 ),
inference(avatar_component_clause,[],[f13715]) ).
fof(f13997,plain,
( spl184_812
| ~ spl184_214
| ~ spl184_808 ),
inference(avatar_split_clause,[],[f13713,f13710,f3620,f13995]) ).
fof(f13995,plain,
( spl184_812
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK119(X0,X1,X2),sK118(X0,X1,X2)),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| sP29(X0,X1,X2)
| in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_812])]) ).
fof(f13710,plain,
( spl184_808
<=> ! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_808])]) ).
fof(f13713,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK119(X0,X1,X2),sK118(X0,X1,X2)),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| sP29(X0,X1,X2)
| in(sK118(X0,X1,X2),X2) )
| ~ spl184_214
| ~ spl184_808 ),
inference(forward_demodulation,[],[f13711,f3621]) ).
fof(f13711,plain,
( ! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| in(sK118(X0,X1,X2),X2) )
| ~ spl184_808 ),
inference(avatar_component_clause,[],[f13710]) ).
fof(f13975,plain,
( spl184_811
| ~ spl184_214
| ~ spl184_806 ),
inference(avatar_split_clause,[],[f13704,f13701,f3620,f13973]) ).
fof(f13973,plain,
( spl184_811
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_811])]) ).
fof(f13701,plain,
( spl184_806
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_806])]) ).
fof(f13704,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK116(X0,X1,X2),sK115(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2)
| sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1) )
| ~ spl184_214
| ~ spl184_806 ),
inference(forward_demodulation,[],[f13702,f3621]) ).
fof(f13702,plain,
( ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) )
| ~ spl184_806 ),
inference(avatar_component_clause,[],[f13701]) ).
fof(f13722,plain,
spl184_810,
inference(avatar_split_clause,[],[f2176,f13720]) ).
fof(f13720,plain,
( spl184_810
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_810])]) ).
fof(f2176,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK150(X0,X1,X2),sK149(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2)
| sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X1) ),
inference(forward_demodulation,[],[f2076,f1697]) ).
fof(f2076,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),unordered_pair(sK149(X0,X1,X2),sK149(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1735,f1913]) ).
fof(f1735,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| in(sK150(X0,X1,X2),X1)
| in(ordered_pair(sK149(X0,X1,X2),sK150(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f13717,plain,
spl184_809,
inference(avatar_split_clause,[],[f2058,f13715]) ).
fof(f2058,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),unordered_pair(sK122(X0,X1,X2),sK122(X0,X1,X2))),X1)
| in(sK121(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1609,f1913]) ).
fof(f1609,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(ordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),X1)
| in(sK121(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f966,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK121(X0,X1,X2)),X1) )
| ~ in(sK121(X0,X1,X2),X2) )
& ( ( in(sK122(X0,X1,X2),X0)
& in(ordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),X1) )
| in(sK121(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ( in(sK123(X0,X1,X6),X0)
& in(ordered_pair(sK123(X0,X1,X6),X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121,sK122,sK123])],[f962,f965,f964,f963]) ).
fof(f963,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,sK121(X0,X1,X2)),X1) )
| ~ in(sK121(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK121(X0,X1,X2)),X1) )
| in(sK121(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f964,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK121(X0,X1,X2)),X1) )
=> ( in(sK122(X0,X1,X2),X0)
& in(ordered_pair(sK122(X0,X1,X2),sK121(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f965,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
=> ( in(sK123(X0,X1,X6),X0)
& in(ordered_pair(sK123(X0,X1,X6),X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f962,plain,
! [X0,X1,X2] :
( ( sP31(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) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f961]) ).
fof(f961,plain,
! [X1,X0,X2] :
( ( sP31(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) ) )
| ~ sP31(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f709]) ).
fof(f709,plain,
! [X1,X0,X2] :
( sP31(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f13712,plain,
spl184_808,
inference(avatar_split_clause,[],[f2054,f13710]) ).
fof(f2054,plain,
! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| in(sK118(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1600,f1913]) ).
fof(f1600,plain,
! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(ordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),X1)
| in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f959,plain,
! [X0,X1,X2] :
( ( sP29(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(sK118(X0,X1,X2),X4),X1) )
| ~ in(sK118(X0,X1,X2),X2) )
& ( ( in(sK119(X0,X1,X2),X0)
& in(ordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),X1) )
| in(sK118(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1) ) )
& ( ( in(sK120(X0,X1,X6),X0)
& in(ordered_pair(X6,sK120(X0,X1,X6)),X1) )
| ~ in(X6,X2) ) )
| ~ sP29(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119,sK120])],[f955,f958,f957,f956]) ).
fof(f956,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(sK118(X0,X1,X2),X4),X1) )
| ~ in(sK118(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK118(X0,X1,X2),X5),X1) )
| in(sK118(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f957,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(sK118(X0,X1,X2),X5),X1) )
=> ( in(sK119(X0,X1,X2),X0)
& in(ordered_pair(sK118(X0,X1,X2),sK119(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f958,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X6,X8),X1) )
=> ( in(sK120(X0,X1,X6),X0)
& in(ordered_pair(X6,sK120(X0,X1,X6)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f955,plain,
! [X0,X1,X2] :
( ( sP29(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) ) )
| ~ sP29(X0,X1,X2) ) ),
inference(rectify,[],[f954]) ).
fof(f954,plain,
! [X1,X0,X2] :
( ( sP29(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) ) )
| ~ sP29(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f706]) ).
fof(f706,plain,
! [X1,X0,X2] :
( sP29(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f13708,plain,
spl184_807,
inference(avatar_split_clause,[],[f2053,f13706]) ).
fof(f13706,plain,
( spl184_807
<=> ! [X4,X0,X2,X1] :
( sP29(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK118(X0,X1,X2),X4),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| ~ in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_807])]) ).
fof(f2053,plain,
! [X2,X0,X1,X4] :
( sP29(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(sK118(X0,X1,X2),X4),unordered_pair(sK118(X0,X1,X2),sK118(X0,X1,X2))),X1)
| ~ in(sK118(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1602,f1913]) ).
fof(f1602,plain,
! [X2,X0,X1,X4] :
( sP29(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(sK118(X0,X1,X2),X4),X1)
| ~ in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f13703,plain,
spl184_806,
inference(avatar_split_clause,[],[f2045,f13701]) ).
fof(f2045,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),unordered_pair(sK115(X0,X1,X2),sK115(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1582,f1913]) ).
fof(f1582,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| in(sK115(X0,X1,X2),X1)
| in(ordered_pair(sK115(X0,X1,X2),sK116(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f13699,plain,
spl184_805,
inference(avatar_split_clause,[],[f2012,f13697]) ).
fof(f13697,plain,
( spl184_805
<=> ! [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)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_805])]) ).
fof(f2012,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)
| ~ sP10(X0,X1,X2) ),
inference(definition_unfolding,[],[f1500,f1913,f1913,f1913]) ).
fof(f1500,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)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f13695,plain,
spl184_804,
inference(avatar_split_clause,[],[f1935,f13693]) ).
fof(f13693,plain,
( spl184_804
<=> ! [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,[spl184_804])]) ).
fof(f1935,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,[],[f1197,f1913,f1913,f1913]) ).
fof(f1197,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,[],[f778]) ).
fof(f778,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK69(X0),sK71(X0)),X0)
& in(ordered_pair(sK70(X0),sK71(X0)),X0)
& in(ordered_pair(sK69(X0),sK70(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,[sK69,sK70,sK71])],[f776,f777]) ).
fof(f777,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(sK69(X0),sK71(X0)),X0)
& in(ordered_pair(sK70(X0),sK71(X0)),X0)
& in(ordered_pair(sK69(X0),sK70(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f776,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,[],[f775]) ).
fof(f775,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,[],[f368]) ).
fof(f368,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,[],[f367]) ).
fof(f367,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,[],[f155]) ).
fof(f155,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(f13691,plain,
( spl184_684
| ~ spl184_225
| ~ spl184_721 ),
inference(avatar_split_clause,[],[f12280,f11625,f3664,f10253]) ).
fof(f13690,plain,
spl184_803,
inference(avatar_split_clause,[],[f1931,f13688]) ).
fof(f13688,plain,
( spl184_803
<=> ! [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,[spl184_803])]) ).
fof(f1931,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,[],[f1190,f1913,f1913]) ).
fof(f1190,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,[],[f774]) ).
fof(f774,plain,
! [X0] :
( ( sP0(X0)
| ( ~ in(ordered_pair(sK68(X0),sK67(X0)),X0)
& ~ in(ordered_pair(sK67(X0),sK68(X0)),X0)
& sK67(X0) != sK68(X0)
& in(sK68(X0),relation_field(X0))
& in(sK67(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,[sK67,sK68])],[f772,f773]) ).
fof(f773,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(sK68(X0),sK67(X0)),X0)
& ~ in(ordered_pair(sK67(X0),sK68(X0)),X0)
& sK67(X0) != sK68(X0)
& in(sK68(X0),relation_field(X0))
& in(sK67(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f772,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,[],[f771]) ).
fof(f771,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,[],[f663]) ).
fof(f663,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(f13641,plain,
spl184_802,
inference(avatar_split_clause,[],[f2030,f13639]) ).
fof(f13639,plain,
( spl184_802
<=> ! [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)
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_802])]) ).
fof(f2030,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)
| ~ sP21(X0,X1) ),
inference(definition_unfolding,[],[f1552,f1913,f1913]) ).
fof(f1552,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)
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f922]) ).
fof(f922,plain,
! [X0,X1] :
( ( sP21(X0,X1)
| ( ~ in(ordered_pair(sK105(X0,X1),sK104(X0,X1)),X0)
& ~ in(ordered_pair(sK104(X0,X1),sK105(X0,X1)),X0)
& sK104(X0,X1) != sK105(X0,X1)
& in(sK105(X0,X1),X1)
& in(sK104(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) )
| ~ sP21(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f920,f921]) ).
fof(f921,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(sK105(X0,X1),sK104(X0,X1)),X0)
& ~ in(ordered_pair(sK104(X0,X1),sK105(X0,X1)),X0)
& sK104(X0,X1) != sK105(X0,X1)
& in(sK105(X0,X1),X1)
& in(sK104(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f920,plain,
! [X0,X1] :
( ( sP21(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) )
| ~ sP21(X0,X1) ) ),
inference(rectify,[],[f919]) ).
fof(f919,plain,
! [X0,X1] :
( ( sP21(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) )
| ~ sP21(X0,X1) ) ),
inference(nnf_transformation,[],[f694]) ).
fof(f694,plain,
! [X0,X1] :
( sP21(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,[sP21])]) ).
fof(f13637,plain,
spl184_801,
inference(avatar_split_clause,[],[f2027,f13635]) ).
fof(f13635,plain,
( spl184_801
<=> ! [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)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_801])]) ).
fof(f2027,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)
| ~ sP19(X0,X1) ),
inference(definition_unfolding,[],[f1543,f1913,f1913]) ).
fof(f1543,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)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f917]) ).
fof(f917,plain,
! [X0,X1] :
( ( sP19(X0,X1)
| ( sK102(X0,X1) != sK103(X0,X1)
& in(ordered_pair(sK103(X0,X1),sK102(X0,X1)),X0)
& in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0)
& in(sK103(X0,X1),X1)
& in(sK102(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) )
| ~ sP19(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103])],[f915,f916]) ).
fof(f916,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) )
=> ( sK102(X0,X1) != sK103(X0,X1)
& in(ordered_pair(sK103(X0,X1),sK102(X0,X1)),X0)
& in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0)
& in(sK103(X0,X1),X1)
& in(sK102(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f915,plain,
! [X0,X1] :
( ( sP19(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) )
| ~ sP19(X0,X1) ) ),
inference(rectify,[],[f914]) ).
fof(f914,plain,
! [X0,X1] :
( ( sP19(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) )
| ~ sP19(X0,X1) ) ),
inference(nnf_transformation,[],[f691]) ).
fof(f691,plain,
! [X0,X1] :
( sP19(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,[sP19])]) ).
fof(f13633,plain,
spl184_800,
inference(avatar_split_clause,[],[f2020,f13631]) ).
fof(f13631,plain,
( spl184_800
<=> ! [X2,X6,X0,X5,X1] :
( in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_800])]) ).
fof(f2020,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ),
inference(definition_unfolding,[],[f1514,f1913,f1913]) ).
fof(f1514,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f13621,plain,
( spl184_799
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_798 ),
inference(avatar_split_clause,[],[f13617,f13614,f7974,f2764,f2414,f13619]) ).
fof(f13619,plain,
( spl184_799
<=> ! [X2,X0,X1] :
( relation_dom(X1) != relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X2))))
| relation_dom_restriction(X2,X0) = X1
| in(sK80(X1,X2),relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_799])]) ).
fof(f13614,plain,
( spl184_798
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK80(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,[spl184_798])]) ).
fof(f13617,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(sK80(X1,X2),relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_798 ),
inference(forward_demodulation,[],[f13615,f8115]) ).
fof(f13615,plain,
( ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK80(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) )
| ~ spl184_798 ),
inference(avatar_component_clause,[],[f13614]) ).
fof(f13616,plain,
spl184_798,
inference(avatar_split_clause,[],[f1948,f13614]) ).
fof(f1948,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK80(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,[],[f1313,f1249]) ).
fof(f1313,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK80(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,[],[f813]) ).
fof(f13455,plain,
( spl184_797
| ~ spl184_214
| ~ spl184_792 ),
inference(avatar_split_clause,[],[f13435,f13432,f3620,f13453]) ).
fof(f13453,plain,
( spl184_797
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,sK117(X0,X1,X2)),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sP27(X0,X1,X2)
| in(sK117(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_797])]) ).
fof(f13432,plain,
( spl184_792
<=> ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| in(sK117(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_792])]) ).
fof(f13435,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,sK117(X0,X1,X2)),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| sP27(X0,X1,X2)
| in(sK117(X0,X1,X2),X2) )
| ~ spl184_214
| ~ spl184_792 ),
inference(forward_demodulation,[],[f13433,f3621]) ).
fof(f13433,plain,
( ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| in(sK117(X0,X1,X2),X2) )
| ~ spl184_792 ),
inference(avatar_component_clause,[],[f13432]) ).
fof(f13451,plain,
( spl184_796
| ~ spl184_214
| ~ spl184_791 ),
inference(avatar_split_clause,[],[f13430,f13427,f3620,f13449]) ).
fof(f13449,plain,
( spl184_796
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK113(X0,X1),sK112(X0,X1)),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK112(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_796])]) ).
fof(f13427,plain,
( spl184_791
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK112(X0,X1),sK113(X0,X1)),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| in(sK112(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_791])]) ).
fof(f13430,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK113(X0,X1),sK112(X0,X1)),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK112(X0,X1),X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_791 ),
inference(forward_demodulation,[],[f13428,f3621]) ).
fof(f13428,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK112(X0,X1),sK113(X0,X1)),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| in(sK112(X0,X1),X1)
| ~ relation(X0) )
| ~ spl184_791 ),
inference(avatar_component_clause,[],[f13427]) ).
fof(f13447,plain,
( spl184_795
| ~ spl184_214
| ~ spl184_790 ),
inference(avatar_split_clause,[],[f13425,f13422,f3620,f13445]) ).
fof(f13445,plain,
( spl184_795
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK110(X0,X1),sK110(X0,X1)),unordered_pair(sK110(X0,X1),sK109(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK109(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_795])]) ).
fof(f13422,plain,
( spl184_790
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK110(X0,X1),sK109(X0,X1)),unordered_pair(sK110(X0,X1),sK110(X0,X1))),X0)
| in(sK109(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_790])]) ).
fof(f13425,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK110(X0,X1),sK110(X0,X1)),unordered_pair(sK110(X0,X1),sK109(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK109(X0,X1),X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_790 ),
inference(forward_demodulation,[],[f13423,f3621]) ).
fof(f13423,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK110(X0,X1),sK109(X0,X1)),unordered_pair(sK110(X0,X1),sK110(X0,X1))),X0)
| in(sK109(X0,X1),X1)
| ~ relation(X0) )
| ~ spl184_790 ),
inference(avatar_component_clause,[],[f13422]) ).
fof(f13443,plain,
spl184_794,
inference(avatar_split_clause,[],[f2181,f13441]) ).
fof(f13441,plain,
( spl184_794
<=> ! [X0,X8,X2,X1] :
( unordered_pair(unordered_pair(sK167(X0,X1,X8),sK166(X0,X1,X8)),unordered_pair(sK166(X0,X1,X8),sK166(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_794])]) ).
fof(f2181,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK167(X0,X1,X8),sK166(X0,X1,X8)),unordered_pair(sK166(X0,X1,X8),sK166(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ),
inference(forward_demodulation,[],[f2090,f1697]) ).
fof(f2090,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK166(X0,X1,X8),sK167(X0,X1,X8)),unordered_pair(sK166(X0,X1,X8),sK166(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ),
inference(definition_unfolding,[],[f1836,f1913]) ).
fof(f1836,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK166(X0,X1,X8),sK167(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f13439,plain,
spl184_793,
inference(avatar_split_clause,[],[f2087,f13437]) ).
fof(f13437,plain,
( spl184_793
<=> ! [X4,X0,X5,X2,X1] :
( sP51(X0,X1,X2)
| sK163(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK163(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_793])]) ).
fof(f2087,plain,
! [X2,X0,X1,X4,X5] :
( sP51(X0,X1,X2)
| sK163(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK163(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1841,f1913]) ).
fof(f1841,plain,
! [X2,X0,X1,X4,X5] :
( sP51(X0,X1,X2)
| ordered_pair(X4,X5) != sK163(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK163(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f13434,plain,
spl184_792,
inference(avatar_split_clause,[],[f2050,f13432]) ).
fof(f2050,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X1),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X0)
| in(sK117(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1592,f1913]) ).
fof(f1592,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| in(ordered_pair(sK117(X0,X1,X2),X1),X0)
| in(sK117(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f13429,plain,
spl184_791,
inference(avatar_split_clause,[],[f2040,f13427]) ).
fof(f2040,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK112(X0,X1),sK113(X0,X1)),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| in(sK112(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1575,f1913]) ).
fof(f1575,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK112(X0,X1),sK113(X0,X1)),X0)
| in(sK112(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f939]) ).
fof(f939,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK112(X0,X1),X3),X0)
| ~ in(sK112(X0,X1),X1) )
& ( in(ordered_pair(sK112(X0,X1),sK113(X0,X1)),X0)
| in(sK112(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK114(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113,sK114])],[f935,f938,f937,f936]) ).
fof(f936,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(sK112(X0,X1),X3),X0)
| ~ in(sK112(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK112(X0,X1),X4),X0)
| in(sK112(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f937,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK112(X0,X1),X4),X0)
=> in(ordered_pair(sK112(X0,X1),sK113(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f938,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK114(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f935,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,[],[f934]) ).
fof(f934,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,[],[f559]) ).
fof(f559,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,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(f13424,plain,
spl184_790,
inference(avatar_split_clause,[],[f2036,f13422]) ).
fof(f2036,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK110(X0,X1),sK109(X0,X1)),unordered_pair(sK110(X0,X1),sK110(X0,X1))),X0)
| in(sK109(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1571,f1913]) ).
fof(f1571,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK110(X0,X1),sK109(X0,X1)),X0)
| in(sK109(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f933,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK109(X0,X1)),X0)
| ~ in(sK109(X0,X1),X1) )
& ( in(ordered_pair(sK110(X0,X1),sK109(X0,X1)),X0)
| in(sK109(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK111(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110,sK111])],[f929,f932,f931,f930]) ).
fof(f930,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,sK109(X0,X1)),X0)
| ~ in(sK109(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK109(X0,X1)),X0)
| in(sK109(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f931,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK109(X0,X1)),X0)
=> in(ordered_pair(sK110(X0,X1),sK109(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f932,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK111(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f929,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,[],[f928]) ).
fof(f928,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,[],[f558]) ).
fof(f558,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,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(f13377,plain,
spl184_789,
inference(avatar_split_clause,[],[f2170,f13375]) ).
fof(f13375,plain,
( spl184_789
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK148(X0,X1),sK147(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1)
| sP43(X0,X1)
| sK147(X0,X1) = sK148(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_789])]) ).
fof(f2170,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK148(X0,X1),sK147(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1)
| sP43(X0,X1)
| sK147(X0,X1) = sK148(X0,X1) ),
inference(forward_demodulation,[],[f2069,f1697]) ).
fof(f2069,plain,
! [X0,X1] :
( sP43(X0,X1)
| sK147(X0,X1) = sK148(X0,X1)
| in(unordered_pair(unordered_pair(sK147(X0,X1),sK148(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1727,f1913]) ).
fof(f1727,plain,
! [X0,X1] :
( sP43(X0,X1)
| sK147(X0,X1) = sK148(X0,X1)
| in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f13366,plain,
spl184_788,
inference(avatar_split_clause,[],[f1232,f13364]) ).
fof(f13364,plain,
( spl184_788
<=> ! [X0,X1] :
( sP4(X0,X1)
| sK72(X0,X1) = apply(X1,sK73(X0,X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_788])]) ).
fof(f1232,plain,
! [X0,X1] :
( sP4(X0,X1)
| sK72(X0,X1) = apply(X1,sK73(X0,X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f13323,plain,
( spl184_787
| ~ spl184_214
| ~ spl184_785 ),
inference(avatar_split_clause,[],[f13263,f13260,f3620,f13321]) ).
fof(f13321,plain,
( spl184_787
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK96(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_787])]) ).
fof(f13260,plain,
( spl184_785
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,sK96(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_785])]) ).
fof(f13263,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK96(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_785 ),
inference(forward_demodulation,[],[f13261,f3621]) ).
fof(f13261,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK96(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) )
| ~ spl184_785 ),
inference(avatar_component_clause,[],[f13260]) ).
fof(f13267,plain,
spl184_786,
inference(avatar_split_clause,[],[f2039,f13265]) ).
fof(f13265,plain,
( spl184_786
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK112(X0,X1),X3),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| ~ in(sK112(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_786])]) ).
fof(f2039,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK112(X0,X1),X3),unordered_pair(sK112(X0,X1),sK112(X0,X1))),X0)
| ~ in(sK112(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1576,f1913]) ).
fof(f1576,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK112(X0,X1),X3),X0)
| ~ in(sK112(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f939]) ).
fof(f13262,plain,
spl184_785,
inference(avatar_split_clause,[],[f2014,f13260]) ).
fof(f2014,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK96(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP10(X0,X1,X2) ),
inference(definition_unfolding,[],[f1498,f1913,f1913]) ).
fof(f1498,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X1)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f888]) ).
fof(f13258,plain,
spl184_784,
inference(avatar_split_clause,[],[f1979,f13256]) ).
fof(f13256,plain,
( spl184_784
<=> ! [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,[spl184_784])]) ).
fof(f1979,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,[],[f1394,f1913,f1913]) ).
fof(f1394,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,[],[f849]) ).
fof(f849,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,[],[f848]) ).
fof(f848,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,[],[f516]) ).
fof(f516,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,[],[f314]) ).
fof(f314,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(f13241,plain,
spl184_783,
inference(avatar_split_clause,[],[f1660,f13239]) ).
fof(f13239,plain,
( spl184_783
<=> ! [X4,X0,X2,X1] :
( sP39(X0,X1,X2)
| apply(X0,X4) != sK130(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK130(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_783])]) ).
fof(f1660,plain,
! [X2,X0,X1,X4] :
( sP39(X0,X1,X2)
| apply(X0,X4) != sK130(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK130(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f992,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ( ( ! [X4] :
( apply(X0,X4) != sK130(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK130(X0,X1,X2),X2) )
& ( ( sK130(X0,X1,X2) = apply(X0,sK131(X0,X1,X2))
& in(sK131(X0,X1,X2),X1)
& in(sK131(X0,X1,X2),relation_dom(X0)) )
| in(sK130(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK132(X0,X1,X6)) = X6
& in(sK132(X0,X1,X6),X1)
& in(sK132(X0,X1,X6),relation_dom(X0)) )
| ~ in(X6,X2) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130,sK131,sK132])],[f988,f991,f990,f989]) ).
fof(f989,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) != sK130(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK130(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK130(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK130(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f990,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK130(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK130(X0,X1,X2) = apply(X0,sK131(X0,X1,X2))
& in(sK131(X0,X1,X2),X1)
& in(sK131(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f991,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK132(X0,X1,X6)) = X6
& in(sK132(X0,X1,X6),X1)
& in(sK132(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f988,plain,
! [X0,X1,X2] :
( ( sP39(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) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(rectify,[],[f987]) ).
fof(f987,plain,
! [X0,X1,X2] :
( ( sP39(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) ) )
| ~ sP39(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f721]) ).
fof(f721,plain,
! [X0,X1,X2] :
( sP39(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,[sP39])]) ).
fof(f13237,plain,
spl184_782,
inference(avatar_split_clause,[],[f1649,f13235]) ).
fof(f13235,plain,
( spl184_782
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ in(apply(X1,sK129(X0,X1,X2)),X0)
| ~ in(sK129(X0,X1,X2),relation_dom(X1))
| ~ in(sK129(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_782])]) ).
fof(f1649,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ in(apply(X1,sK129(X0,X1,X2)),X0)
| ~ in(sK129(X0,X1,X2),relation_dom(X1))
| ~ in(sK129(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f985,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ( ~ in(apply(X1,sK129(X0,X1,X2)),X0)
| ~ in(sK129(X0,X1,X2),relation_dom(X1))
| ~ in(sK129(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK129(X0,X1,X2)),X0)
& in(sK129(X0,X1,X2),relation_dom(X1)) )
| in(sK129(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) ) )
| ~ sP37(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129])],[f983,f984]) ).
fof(f984,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,sK129(X0,X1,X2)),X0)
| ~ in(sK129(X0,X1,X2),relation_dom(X1))
| ~ in(sK129(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK129(X0,X1,X2)),X0)
& in(sK129(X0,X1,X2),relation_dom(X1)) )
| in(sK129(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f983,plain,
! [X0,X1,X2] :
( ( sP37(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) ) )
| ~ sP37(X0,X1,X2) ) ),
inference(rectify,[],[f982]) ).
fof(f982,plain,
! [X1,X0,X2] :
( ( sP37(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) ) )
| ~ sP37(X1,X0,X2) ) ),
inference(flattening,[],[f981]) ).
fof(f981,plain,
! [X1,X0,X2] :
( ( sP37(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) ) )
| ~ sP37(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f718]) ).
fof(f718,plain,
! [X1,X0,X2] :
( sP37(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f13123,plain,
( spl184_781
| ~ spl184_214
| ~ spl184_776 ),
inference(avatar_split_clause,[],[f12954,f12951,f3620,f13121]) ).
fof(f13121,plain,
( spl184_781
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK123(X0,X1,X6)),unordered_pair(sK123(X0,X1,X6),sK123(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_781])]) ).
fof(f12951,plain,
( spl184_776
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(sK123(X0,X1,X6),X6),unordered_pair(sK123(X0,X1,X6),sK123(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_776])]) ).
fof(f12954,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK123(X0,X1,X6)),unordered_pair(sK123(X0,X1,X6),sK123(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_776 ),
inference(forward_demodulation,[],[f12952,f3621]) ).
fof(f12952,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK123(X0,X1,X6),X6),unordered_pair(sK123(X0,X1,X6),sK123(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) )
| ~ spl184_776 ),
inference(avatar_component_clause,[],[f12951]) ).
fof(f13080,plain,
( spl184_780
| ~ spl184_214
| ~ spl184_773 ),
inference(avatar_split_clause,[],[f12941,f12938,f3620,f13078]) ).
fof(f13078,plain,
( spl184_780
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK83(X0,X1,X2)),unordered_pair(sK83(X0,X1,X2),sK83(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_780])]) ).
fof(f12938,plain,
( spl184_773
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1,X2),X0),unordered_pair(sK83(X0,X1,X2),sK83(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_773])]) ).
fof(f12941,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK83(X0,X1,X2)),unordered_pair(sK83(X0,X1,X2),sK83(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl184_214
| ~ spl184_773 ),
inference(forward_demodulation,[],[f12939,f3621]) ).
fof(f12939,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1,X2),X0),unordered_pair(sK83(X0,X1,X2),sK83(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) )
| ~ spl184_773 ),
inference(avatar_component_clause,[],[f12938]) ).
fof(f12967,plain,
spl184_779,
inference(avatar_split_clause,[],[f2171,f12965]) ).
fof(f12965,plain,
( spl184_779
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK148(X0,X1),sK147(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1)
| sP43(X0,X1)
| in(sK147(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_779])]) ).
fof(f2171,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK148(X0,X1),sK147(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1)
| sP43(X0,X1)
| in(sK147(X0,X1),X0) ),
inference(forward_demodulation,[],[f2070,f1697]) ).
fof(f2070,plain,
! [X0,X1] :
( sP43(X0,X1)
| in(sK147(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK147(X0,X1),sK148(X0,X1)),unordered_pair(sK147(X0,X1),sK147(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1726,f1913]) ).
fof(f1726,plain,
! [X0,X1] :
( sP43(X0,X1)
| in(sK147(X0,X1),X0)
| in(ordered_pair(sK147(X0,X1),sK148(X0,X1)),X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f12963,plain,
spl184_778,
inference(avatar_split_clause,[],[f2077,f12961]) ).
fof(f12961,plain,
( spl184_778
<=> ! [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)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_778])]) ).
fof(f2077,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)
| ~ sP45(X0,X1,X2) ),
inference(definition_unfolding,[],[f1734,f1913,f1913]) ).
fof(f1734,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X6,X1)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f12959,plain,
( spl184_777
| ~ spl184_66
| ~ spl184_720 ),
inference(avatar_split_clause,[],[f11739,f11621,f2503,f12956]) ).
fof(f12956,plain,
( spl184_777
<=> sP7(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_777])]) ).
fof(f11739,plain,
( sP7(sK56)
| ~ spl184_66
| ~ spl184_720 ),
inference(resolution,[],[f11623,f2504]) ).
fof(f12953,plain,
spl184_776,
inference(avatar_split_clause,[],[f2060,f12951]) ).
fof(f2060,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK123(X0,X1,X6),X6),unordered_pair(sK123(X0,X1,X6),sK123(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ),
inference(definition_unfolding,[],[f1606,f1913]) ).
fof(f1606,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK123(X0,X1,X6),X6),X1)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f12949,plain,
spl184_775,
inference(avatar_split_clause,[],[f2057,f12947]) ).
fof(f12947,plain,
( spl184_775
<=> ! [X4,X0,X2,X1] :
( sP31(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK121(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK121(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_775])]) ).
fof(f2057,plain,
! [X2,X0,X1,X4] :
( sP31(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,sK121(X0,X1,X2)),unordered_pair(X4,X4)),X1)
| ~ in(sK121(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1611,f1913]) ).
fof(f1611,plain,
! [X2,X0,X1,X4] :
( sP31(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK121(X0,X1,X2)),X1)
| ~ in(sK121(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f12945,plain,
spl184_774,
inference(avatar_split_clause,[],[f2046,f12943]) ).
fof(f12943,plain,
( spl184_774
<=> ! [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)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_774])]) ).
fof(f2046,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)
| ~ sP25(X0,X1,X2) ),
inference(definition_unfolding,[],[f1581,f1913,f1913]) ).
fof(f1581,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f12940,plain,
spl184_773,
inference(avatar_split_clause,[],[f1970,f12938]) ).
fof(f1970,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK83(X0,X1,X2),X0),unordered_pair(sK83(X0,X1,X2),sK83(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1354,f1913]) ).
fof(f1354,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK83(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f835]) ).
fof(f835,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(sK83(X0,X1,X2),X1)
& in(ordered_pair(sK83(X0,X1,X2),X0),X2)
& in(sK83(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f833,f834]) ).
fof(f834,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK83(X0,X1,X2),X1)
& in(ordered_pair(sK83(X0,X1,X2),X0),X2)
& in(sK83(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f833,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,[],[f832]) ).
fof(f832,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,[],[f485]) ).
fof(f485,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,[],[f203]) ).
fof(f203,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(f12936,plain,
spl184_772,
inference(avatar_split_clause,[],[f1928,f12934]) ).
fof(f12934,plain,
( spl184_772
<=> ! [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,[spl184_772])]) ).
fof(f1928,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,[],[f1184,f1913,f1913]) ).
fof(f1184,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,[],[f769]) ).
fof(f769,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ( sK65(X0) != sK66(X0)
& in(ordered_pair(sK66(X0),sK65(X0)),X0)
& in(ordered_pair(sK65(X0),sK66(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,[sK65,sK66])],[f767,f768]) ).
fof(f768,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK65(X0) != sK66(X0)
& in(ordered_pair(sK66(X0),sK65(X0)),X0)
& in(ordered_pair(sK65(X0),sK66(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f767,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,[],[f766]) ).
fof(f766,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,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f364]) ).
fof(f364,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,[],[f159]) ).
fof(f159,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(f12932,plain,
spl184_771,
inference(avatar_split_clause,[],[f1310,f12930]) ).
fof(f12930,plain,
( spl184_771
<=> ! [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,[spl184_771])]) ).
fof(f1310,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,[],[f466]) ).
fof(f466,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,[],[f465]) ).
fof(f465,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,[],[f234]) ).
fof(f234,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(f12814,plain,
( spl184_770
| ~ spl184_214
| ~ spl184_766 ),
inference(avatar_split_clause,[],[f12787,f12784,f3620,f12812]) ).
fof(f12812,plain,
( spl184_770
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK90(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_770])]) ).
fof(f12784,plain,
( spl184_766
<=> ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_766])]) ).
fof(f12787,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK90(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_766 ),
inference(forward_demodulation,[],[f12785,f3621]) ).
fof(f12785,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_766 ),
inference(avatar_component_clause,[],[f12784]) ).
fof(f12810,plain,
( spl184_769
| ~ spl184_214
| ~ spl184_765 ),
inference(avatar_split_clause,[],[f12782,f12779,f3620,f12808]) ).
fof(f12808,plain,
( spl184_769
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK90(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_769])]) ).
fof(f12779,plain,
( spl184_765
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_765])]) ).
fof(f12782,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK90(X0,X1),sK89(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_765 ),
inference(forward_demodulation,[],[f12780,f3621]) ).
fof(f12780,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl184_765 ),
inference(avatar_component_clause,[],[f12779]) ).
fof(f12795,plain,
spl184_768,
inference(avatar_split_clause,[],[f2114,f12793]) ).
fof(f12793,plain,
( spl184_768
<=> ! [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,[spl184_768])]) ).
fof(f2114,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,[],[f2008]) ).
fof(f2008,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,[],[f1492,f1913,f1913]) ).
fof(f1492,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,[],[f880]) ).
fof(f12791,plain,
spl184_767,
inference(avatar_split_clause,[],[f2113,f12789]) ).
fof(f12789,plain,
( spl184_767
<=> ! [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,[spl184_767])]) ).
fof(f2113,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,[],[f2007]) ).
fof(f2007,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,[],[f1493,f1913,f1913]) ).
fof(f1493,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,[],[f880]) ).
fof(f12786,plain,
spl184_766,
inference(avatar_split_clause,[],[f2003,f12784]) ).
fof(f2003,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1490,f1913]) ).
fof(f1490,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK89(X0,X1),sK90(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f876,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK89(X0,X1),sK90(X0,X1)),X1)
& in(ordered_pair(sK89(X0,X1),sK90(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,[sK89,sK90])],[f874,f875]) ).
fof(f875,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK89(X0,X1),sK90(X0,X1)),X1)
& in(ordered_pair(sK89(X0,X1),sK90(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f874,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,[],[f873]) ).
fof(f873,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,[],[f545]) ).
fof(f545,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,[],[f43]) ).
fof(f43,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(f12781,plain,
spl184_765,
inference(avatar_split_clause,[],[f2002,f12779]) ).
fof(f2002,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1),sK90(X0,X1)),unordered_pair(sK89(X0,X1),sK89(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1491,f1913]) ).
fof(f1491,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK89(X0,X1),sK90(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f12777,plain,
spl184_764,
inference(avatar_split_clause,[],[f1317,f12775]) ).
fof(f12775,plain,
( spl184_764
<=> ! [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,[spl184_764])]) ).
fof(f1317,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,[],[f815]) ).
fof(f815,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,[],[f814]) ).
fof(f814,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,[],[f470]) ).
fof(f470,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,[],[f469]) ).
fof(f469,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,[],[f230]) ).
fof(f230,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(f12765,plain,
spl184_763,
inference(avatar_split_clause,[],[f1231,f12763]) ).
fof(f12763,plain,
( spl184_763
<=> ! [X0,X1] :
( sP4(X0,X1)
| in(sK73(X0,X1),relation_dom(X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_763])]) ).
fof(f1231,plain,
! [X0,X1] :
( sP4(X0,X1)
| in(sK73(X0,X1),relation_dom(X1))
| ~ sP3(sK72(X0,X1),sK73(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f12761,plain,
( spl184_762
| ~ spl184_165
| ~ spl184_721 ),
inference(avatar_split_clause,[],[f12278,f11625,f3165,f12758]) ).
fof(f12758,plain,
( spl184_762
<=> element(sK136(sK56),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_762])]) ).
fof(f12278,plain,
( element(sK136(sK56),sK57)
| ~ spl184_165
| ~ spl184_721 ),
inference(resolution,[],[f11627,f3166]) ).
fof(f12608,plain,
spl184_761,
inference(avatar_split_clause,[],[f1980,f12606]) ).
fof(f12606,plain,
( spl184_761
<=> ! [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,[spl184_761])]) ).
fof(f1980,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,[],[f1393,f1913,f1913]) ).
fof(f1393,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,[],[f849]) ).
fof(f12604,plain,
spl184_760,
inference(avatar_split_clause,[],[f1969,f12602]) ).
fof(f12602,plain,
( spl184_760
<=> ! [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,[spl184_760])]) ).
fof(f1969,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,[],[f1356,f1913]) ).
fof(f1356,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,[],[f835]) ).
fof(f12600,plain,
spl184_759,
inference(avatar_split_clause,[],[f1967,f12598]) ).
fof(f12598,plain,
( spl184_759
<=> ! [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,[spl184_759])]) ).
fof(f1967,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,[],[f1352,f1913]) ).
fof(f1352,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,[],[f831]) ).
fof(f831,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(sK82(X0,X1,X2),X1)
& in(ordered_pair(X0,sK82(X0,X1,X2)),X2)
& in(sK82(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f829,f830]) ).
fof(f830,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK82(X0,X1,X2),X1)
& in(ordered_pair(X0,sK82(X0,X1,X2)),X2)
& in(sK82(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f829,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,[],[f828]) ).
fof(f828,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,[],[f484]) ).
fof(f484,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,[],[f212]) ).
fof(f212,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(f12596,plain,
spl184_758,
inference(avatar_split_clause,[],[f1309,f12594]) ).
fof(f12594,plain,
( spl184_758
<=> ! [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,[spl184_758])]) ).
fof(f1309,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,[],[f464]) ).
fof(f464,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,[],[f463]) ).
fof(f463,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,[],[f236]) ).
fof(f236,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(f12565,plain,
( ~ spl184_757
| ~ spl184_164
| ~ spl184_721 ),
inference(avatar_split_clause,[],[f12277,f11625,f3161,f12562]) ).
fof(f12562,plain,
( spl184_757
<=> in(sK57,sK136(sK56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_757])]) ).
fof(f12277,plain,
( ~ in(sK57,sK136(sK56))
| ~ spl184_164
| ~ spl184_721 ),
inference(resolution,[],[f11627,f3162]) ).
fof(f12377,plain,
spl184_756,
inference(avatar_split_clause,[],[f1865,f12375]) ).
fof(f12375,plain,
( spl184_756
<=> ! [X2,X0,X1] :
( sP54(X0,X1,X2)
| ~ in(sK170(X0,X1,X2),X0)
| ~ in(sK170(X0,X1,X2),X1)
| ~ in(sK170(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_756])]) ).
fof(f1865,plain,
! [X2,X0,X1] :
( sP54(X0,X1,X2)
| ~ in(sK170(X0,X1,X2),X0)
| ~ in(sK170(X0,X1,X2),X1)
| ~ in(sK170(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ( sP54(X0,X1,X2)
| ( ( ~ in(sK170(X0,X1,X2),X0)
| ~ in(sK170(X0,X1,X2),X1)
| ~ in(sK170(X0,X1,X2),X2) )
& ( ( in(sK170(X0,X1,X2),X0)
& in(sK170(X0,X1,X2),X1) )
| in(sK170(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP54(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f1114,f1115]) ).
fof(f1115,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK170(X0,X1,X2),X0)
| ~ in(sK170(X0,X1,X2),X1)
| ~ in(sK170(X0,X1,X2),X2) )
& ( ( in(sK170(X0,X1,X2),X0)
& in(sK170(X0,X1,X2),X1) )
| in(sK170(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1114,plain,
! [X0,X1,X2] :
( ( sP54(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) ) )
| ~ sP54(X0,X1,X2) ) ),
inference(rectify,[],[f1113]) ).
fof(f1113,plain,
! [X1,X0,X2] :
( ( sP54(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) ) )
| ~ sP54(X1,X0,X2) ) ),
inference(flattening,[],[f1112]) ).
fof(f1112,plain,
! [X1,X0,X2] :
( ( sP54(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) ) )
| ~ sP54(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f746]) ).
fof(f746,plain,
! [X1,X0,X2] :
( sP54(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP54])]) ).
fof(f12373,plain,
spl184_755,
inference(avatar_split_clause,[],[f1857,f12371]) ).
fof(f12371,plain,
( spl184_755
<=> ! [X2,X0,X1] :
( sP53(X0,X1,X2)
| in(sK169(X0,X1,X2),X0)
| ~ in(sK169(X0,X1,X2),X1)
| ~ in(sK169(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_755])]) ).
fof(f1857,plain,
! [X2,X0,X1] :
( sP53(X0,X1,X2)
| in(sK169(X0,X1,X2),X0)
| ~ in(sK169(X0,X1,X2),X1)
| ~ in(sK169(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,plain,
! [X0,X1,X2] :
( ( sP53(X0,X1,X2)
| ( ( in(sK169(X0,X1,X2),X0)
| ~ in(sK169(X0,X1,X2),X1)
| ~ in(sK169(X0,X1,X2),X2) )
& ( ( ~ in(sK169(X0,X1,X2),X0)
& in(sK169(X0,X1,X2),X1) )
| in(sK169(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP53(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f1108,f1109]) ).
fof(f1109,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK169(X0,X1,X2),X0)
| ~ in(sK169(X0,X1,X2),X1)
| ~ in(sK169(X0,X1,X2),X2) )
& ( ( ~ in(sK169(X0,X1,X2),X0)
& in(sK169(X0,X1,X2),X1) )
| in(sK169(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1108,plain,
! [X0,X1,X2] :
( ( sP53(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) ) )
| ~ sP53(X0,X1,X2) ) ),
inference(rectify,[],[f1107]) ).
fof(f1107,plain,
! [X1,X0,X2] :
( ( sP53(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) ) )
| ~ sP53(X1,X0,X2) ) ),
inference(flattening,[],[f1106]) ).
fof(f1106,plain,
! [X1,X0,X2] :
( ( sP53(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) ) )
| ~ sP53(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f744]) ).
fof(f744,plain,
! [X1,X0,X2] :
( sP53(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP53])]) ).
fof(f12369,plain,
spl184_754,
inference(avatar_split_clause,[],[f1847,f12367]) ).
fof(f12367,plain,
( spl184_754
<=> ! [X2,X0,X1] :
( sP52(X0,X1,X2)
| in(sK168(X0,X1,X2),X0)
| in(sK168(X0,X1,X2),X1)
| in(sK168(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_754])]) ).
fof(f1847,plain,
! [X2,X0,X1] :
( sP52(X0,X1,X2)
| in(sK168(X0,X1,X2),X0)
| in(sK168(X0,X1,X2),X1)
| in(sK168(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,plain,
! [X0,X1,X2] :
( ( sP52(X0,X1,X2)
| ( ( ( ~ in(sK168(X0,X1,X2),X0)
& ~ in(sK168(X0,X1,X2),X1) )
| ~ in(sK168(X0,X1,X2),X2) )
& ( in(sK168(X0,X1,X2),X0)
| in(sK168(X0,X1,X2),X1)
| in(sK168(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP52(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f1102,f1103]) ).
fof(f1103,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK168(X0,X1,X2),X0)
& ~ in(sK168(X0,X1,X2),X1) )
| ~ in(sK168(X0,X1,X2),X2) )
& ( in(sK168(X0,X1,X2),X0)
| in(sK168(X0,X1,X2),X1)
| in(sK168(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1102,plain,
! [X0,X1,X2] :
( ( sP52(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) ) )
| ~ sP52(X0,X1,X2) ) ),
inference(rectify,[],[f1101]) ).
fof(f1101,plain,
! [X1,X0,X2] :
( ( sP52(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) ) )
| ~ sP52(X1,X0,X2) ) ),
inference(flattening,[],[f1100]) ).
fof(f1100,plain,
! [X1,X0,X2] :
( ( sP52(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) ) )
| ~ sP52(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f742]) ).
fof(f742,plain,
! [X1,X0,X2] :
( sP52(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP52])]) ).
fof(f12365,plain,
spl184_753,
inference(avatar_split_clause,[],[f1829,f12363]) ).
fof(f12363,plain,
( spl184_753
<=> ! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) = X0
| sK162(X0,X1,X2) = X1
| in(sK162(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_753])]) ).
fof(f1829,plain,
! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) = X0
| sK162(X0,X1,X2) = X1
| in(sK162(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,plain,
! [X0,X1,X2] :
( ( sP50(X0,X1,X2)
| ( ( ( sK162(X0,X1,X2) != X0
& sK162(X0,X1,X2) != X1 )
| ~ in(sK162(X0,X1,X2),X2) )
& ( sK162(X0,X1,X2) = X0
| sK162(X0,X1,X2) = X1
| in(sK162(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP50(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f1089,f1090]) ).
fof(f1090,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK162(X0,X1,X2) != X0
& sK162(X0,X1,X2) != X1 )
| ~ in(sK162(X0,X1,X2),X2) )
& ( sK162(X0,X1,X2) = X0
| sK162(X0,X1,X2) = X1
| in(sK162(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1089,plain,
! [X0,X1,X2] :
( ( sP50(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) ) )
| ~ sP50(X0,X1,X2) ) ),
inference(rectify,[],[f1088]) ).
fof(f1088,plain,
! [X1,X0,X2] :
( ( sP50(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) ) )
| ~ sP50(X1,X0,X2) ) ),
inference(flattening,[],[f1087]) ).
fof(f1087,plain,
! [X1,X0,X2] :
( ( sP50(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) ) )
| ~ sP50(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f738]) ).
fof(f738,plain,
! [X1,X0,X2] :
( sP50(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP50])]) ).
fof(f12275,plain,
spl184_752,
inference(avatar_split_clause,[],[f2078,f12273]) ).
fof(f12273,plain,
( spl184_752
<=> ! [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)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_752])]) ).
fof(f2078,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)
| ~ sP45(X0,X1,X2) ),
inference(definition_unfolding,[],[f1733,f1913,f1913]) ).
fof(f1733,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f12271,plain,
spl184_751,
inference(avatar_split_clause,[],[f2047,f12269]) ).
fof(f12269,plain,
( spl184_751
<=> ! [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)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_751])]) ).
fof(f2047,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)
| ~ sP25(X0,X1,X2) ),
inference(definition_unfolding,[],[f1580,f1913,f1913]) ).
fof(f1580,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f12267,plain,
spl184_750,
inference(avatar_split_clause,[],[f2035,f12265]) ).
fof(f12265,plain,
( spl184_750
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK109(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK109(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_750])]) ).
fof(f2035,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK109(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK109(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1572,f1913]) ).
fof(f1572,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK109(X0,X1)),X0)
| ~ in(sK109(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f12263,plain,
spl184_749,
inference(avatar_split_clause,[],[f2023,f12261]) ).
fof(f12261,plain,
( spl184_749
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK99(X0,X1),sK99(X0,X1)),unordered_pair(sK99(X0,X1),sK99(X0,X1))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_749])]) ).
fof(f2023,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK99(X0,X1),sK99(X0,X1)),unordered_pair(sK99(X0,X1),sK99(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1532,f1913]) ).
fof(f1532,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK99(X0,X1),sK99(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f906,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK99(X0,X1),sK99(X0,X1)),X0)
& in(sK99(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,[sK99])],[f904,f905]) ).
fof(f905,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK99(X0,X1),sK99(X0,X1)),X0)
& in(sK99(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f904,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,[],[f903]) ).
fof(f903,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,[],[f551]) ).
fof(f551,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,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(f12218,plain,
spl184_748,
inference(avatar_split_clause,[],[f1659,f12216]) ).
fof(f12216,plain,
( spl184_748
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| sK130(X0,X1,X2) = apply(X0,sK131(X0,X1,X2))
| in(sK130(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_748])]) ).
fof(f1659,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| sK130(X0,X1,X2) = apply(X0,sK131(X0,X1,X2))
| in(sK130(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f12173,plain,
( spl184_747
| ~ spl184_214
| ~ spl184_746 ),
inference(avatar_split_clause,[],[f12169,f12166,f3620,f12171]) ).
fof(f12171,plain,
( spl184_747
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK111(X0,X5)),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_747])]) ).
fof(f12166,plain,
( spl184_746
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK111(X0,X5),X5),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_746])]) ).
fof(f12169,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK111(X0,X5)),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_746 ),
inference(forward_demodulation,[],[f12167,f3621]) ).
fof(f12167,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK111(X0,X5),X5),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl184_746 ),
inference(avatar_component_clause,[],[f12166]) ).
fof(f12168,plain,
spl184_746,
inference(avatar_split_clause,[],[f2117,f12166]) ).
fof(f2117,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK111(X0,X5),X5),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2038]) ).
fof(f2038,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK111(X0,X5),X5),unordered_pair(sK111(X0,X5),sK111(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1569,f1913]) ).
fof(f1569,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK111(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f12146,plain,
( spl184_745
| ~ spl184_13
| ~ spl184_58
| ~ spl184_109
| ~ spl184_744 ),
inference(avatar_split_clause,[],[f12142,f12138,f2823,f2471,f2246,f12144]) ).
fof(f12144,plain,
( spl184_745
<=> ! [X0,X1] :
( sK173 = 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,[spl184_745])]) ).
fof(f2246,plain,
( spl184_13
<=> empty(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_13])]) ).
fof(f2471,plain,
( spl184_58
<=> ! [X0] : cast_to_subset(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_58])]) ).
fof(f2823,plain,
( spl184_109
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_109])]) ).
fof(f12138,plain,
( spl184_744
<=> ! [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,[spl184_744])]) ).
fof(f12142,plain,
( ! [X0,X1] :
( sK173 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl184_13
| ~ spl184_58
| ~ spl184_109
| ~ spl184_744 ),
inference(forward_demodulation,[],[f12141,f2880]) ).
fof(f2880,plain,
( empty_set = sK173
| ~ spl184_13
| ~ spl184_109 ),
inference(resolution,[],[f2824,f2248]) ).
fof(f2248,plain,
( empty(sK173)
| ~ spl184_13 ),
inference(avatar_component_clause,[],[f2246]) ).
fof(f2824,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl184_109 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f12141,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))) )
| ~ spl184_58
| ~ spl184_744 ),
inference(forward_demodulation,[],[f12139,f2472]) ).
fof(f2472,plain,
( ! [X0] : cast_to_subset(X0) = X0
| ~ spl184_58 ),
inference(avatar_component_clause,[],[f2471]) ).
fof(f12139,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))) )
| ~ spl184_744 ),
inference(avatar_component_clause,[],[f12138]) ).
fof(f12140,plain,
spl184_744,
inference(avatar_split_clause,[],[f1298,f12138]) ).
fof(f1298,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,[],[f451]) ).
fof(f451,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,[],[f450]) ).
fof(f450,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,[],[f283]) ).
fof(f283,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(f12118,plain,
( spl184_743
| ~ spl184_13
| ~ spl184_58
| ~ spl184_109
| ~ spl184_742 ),
inference(avatar_split_clause,[],[f12114,f12110,f2823,f2471,f2246,f12116]) ).
fof(f12116,plain,
( spl184_743
<=> ! [X0,X1] :
( sK173 = 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,[spl184_743])]) ).
fof(f12110,plain,
( spl184_742
<=> ! [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,[spl184_742])]) ).
fof(f12114,plain,
( ! [X0,X1] :
( sK173 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl184_13
| ~ spl184_58
| ~ spl184_109
| ~ spl184_742 ),
inference(forward_demodulation,[],[f12113,f2880]) ).
fof(f12113,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))) )
| ~ spl184_58
| ~ spl184_742 ),
inference(forward_demodulation,[],[f12111,f2472]) ).
fof(f12111,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))) )
| ~ spl184_742 ),
inference(avatar_component_clause,[],[f12110]) ).
fof(f12112,plain,
spl184_742,
inference(avatar_split_clause,[],[f1297,f12110]) ).
fof(f1297,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,[],[f449]) ).
fof(f449,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,[],[f448]) ).
fof(f448,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,[],[f284]) ).
fof(f284,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(f12097,plain,
spl184_741,
inference(avatar_split_clause,[],[f1623,f12095]) ).
fof(f12095,plain,
( spl184_741
<=> ! [X4,X0,X3] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP33(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_741])]) ).
fof(f1623,plain,
! [X3,X0,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP33(X0) ),
inference(cnf_transformation,[],[f971]) ).
fof(f971,plain,
! [X0] :
( ( sP33(X0)
| ( sK124(X0) != sK125(X0)
& apply(X0,sK124(X0)) = apply(X0,sK125(X0))
& in(sK125(X0),relation_dom(X0))
& in(sK124(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP33(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125])],[f969,f970]) ).
fof(f970,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK124(X0) != sK125(X0)
& apply(X0,sK124(X0)) = apply(X0,sK125(X0))
& in(sK125(X0),relation_dom(X0))
& in(sK124(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f969,plain,
! [X0] :
( ( sP33(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)) )
| ~ sP33(X0) ) ),
inference(rectify,[],[f968]) ).
fof(f968,plain,
! [X0] :
( ( sP33(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)) )
| ~ sP33(X0) ) ),
inference(nnf_transformation,[],[f712]) ).
fof(f712,plain,
! [X0] :
( sP33(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,[sP33])]) ).
fof(f12093,plain,
spl184_740,
inference(avatar_split_clause,[],[f1511,f12091]) ).
fof(f12091,plain,
( spl184_740
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ sP12(X2,X1,X0)
| ~ one_to_one(X1)
| relation_rng(X1) != relation_field(X2)
| relation_field(X0) != relation_dom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_740])]) ).
fof(f1511,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ sP12(X2,X1,X0)
| ~ one_to_one(X1)
| relation_rng(X1) != relation_field(X2)
| relation_field(X0) != relation_dom(X1) ),
inference(cnf_transformation,[],[f893]) ).
fof(f893,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ~ sP12(X2,X1,X0)
| ~ one_to_one(X1)
| relation_rng(X1) != relation_field(X2)
| relation_field(X0) != relation_dom(X1) )
& ( ( sP12(X2,X1,X0)
& one_to_one(X1)
& relation_rng(X1) = relation_field(X2)
& relation_field(X0) = relation_dom(X1) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f892]) ).
fof(f892,plain,
! [X0,X2,X1] :
( ( sP13(X0,X2,X1)
| ~ sP12(X1,X2,X0)
| ~ one_to_one(X2)
| relation_rng(X2) != relation_field(X1)
| relation_field(X0) != relation_dom(X2) )
& ( ( sP12(X1,X2,X0)
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) )
| ~ sP13(X0,X2,X1) ) ),
inference(flattening,[],[f891]) ).
fof(f891,plain,
! [X0,X2,X1] :
( ( sP13(X0,X2,X1)
| ~ sP12(X1,X2,X0)
| ~ one_to_one(X2)
| relation_rng(X2) != relation_field(X1)
| relation_field(X0) != relation_dom(X2) )
& ( ( sP12(X1,X2,X0)
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) )
| ~ sP13(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f682]) ).
fof(f682,plain,
! [X0,X2,X1] :
( sP13(X0,X2,X1)
<=> ( sP12(X1,X2,X0)
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f11900,plain,
( spl184_739
| ~ spl184_214
| ~ spl184_730 ),
inference(avatar_split_clause,[],[f11787,f11784,f3620,f11898]) ).
fof(f11898,plain,
( spl184_739
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK107(X0,X1),sK106(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0)
| sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_739])]) ).
fof(f11784,plain,
( spl184_730
<=> ! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK106(X0,X1),sK107(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_730])]) ).
fof(f11787,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK107(X0,X1),sK106(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0)
| sP23(X0,X1) )
| ~ spl184_214
| ~ spl184_730 ),
inference(forward_demodulation,[],[f11785,f3621]) ).
fof(f11785,plain,
( ! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK106(X0,X1),sK107(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) )
| ~ spl184_730 ),
inference(avatar_component_clause,[],[f11784]) ).
fof(f11896,plain,
( spl184_738
| ~ spl184_214
| ~ spl184_729 ),
inference(avatar_split_clause,[],[f11782,f11779,f3620,f11894]) ).
fof(f11894,plain,
( spl184_738
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK108(X0,X1),sK107(X0,X1)),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X0)
| sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_738])]) ).
fof(f11779,plain,
( spl184_729
<=> ! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK107(X0,X1),sK108(X0,X1)),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_729])]) ).
fof(f11782,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK108(X0,X1),sK107(X0,X1)),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X0)
| sP23(X0,X1) )
| ~ spl184_214
| ~ spl184_729 ),
inference(forward_demodulation,[],[f11780,f3621]) ).
fof(f11780,plain,
( ! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK107(X0,X1),sK108(X0,X1)),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X0) )
| ~ spl184_729 ),
inference(avatar_component_clause,[],[f11779]) ).
fof(f11892,plain,
( spl184_737
| ~ spl184_214
| ~ spl184_728 ),
inference(avatar_split_clause,[],[f11777,f11774,f3620,f11890]) ).
fof(f11890,plain,
( spl184_737
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK108(X0,X1),sK106(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0)
| sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_737])]) ).
fof(f11774,plain,
( spl184_728
<=> ! [X0,X1] :
( sP23(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK106(X0,X1),sK108(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_728])]) ).
fof(f11777,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK108(X0,X1),sK106(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0)
| sP23(X0,X1) )
| ~ spl184_214
| ~ spl184_728 ),
inference(forward_demodulation,[],[f11775,f3621]) ).
fof(f11775,plain,
( ! [X0,X1] :
( sP23(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK106(X0,X1),sK108(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) )
| ~ spl184_728 ),
inference(avatar_component_clause,[],[f11774]) ).
fof(f11888,plain,
( spl184_736
| ~ spl184_55
| ~ spl184_720 ),
inference(avatar_split_clause,[],[f11738,f11621,f2448,f11885]) ).
fof(f2448,plain,
( spl184_55
<=> ! [X0] :
( sP1(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_55])]) ).
fof(f11738,plain,
( sP1(sK56)
| ~ spl184_55
| ~ spl184_720 ),
inference(resolution,[],[f11623,f2449]) ).
fof(f2449,plain,
( ! [X0] :
( ~ relation(X0)
| sP1(X0) )
| ~ spl184_55 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f11883,plain,
( spl184_735
| ~ spl184_214
| ~ spl184_727 ),
inference(avatar_split_clause,[],[f11772,f11769,f3620,f11881]) ).
fof(f11881,plain,
( spl184_735
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK104(X0,X1)),unordered_pair(sK104(X0,X1),sK105(X0,X1))),X0)
| sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_735])]) ).
fof(f11769,plain,
( spl184_727
<=> ! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK105(X0,X1)),unordered_pair(sK104(X0,X1),sK104(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_727])]) ).
fof(f11772,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK104(X0,X1)),unordered_pair(sK104(X0,X1),sK105(X0,X1))),X0)
| sP21(X0,X1) )
| ~ spl184_214
| ~ spl184_727 ),
inference(forward_demodulation,[],[f11770,f3621]) ).
fof(f11770,plain,
( ! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK105(X0,X1)),unordered_pair(sK104(X0,X1),sK104(X0,X1))),X0) )
| ~ spl184_727 ),
inference(avatar_component_clause,[],[f11769]) ).
fof(f11879,plain,
( spl184_734
| ~ spl184_214
| ~ spl184_726 ),
inference(avatar_split_clause,[],[f11737,f11734,f3620,f11877]) ).
fof(f11877,plain,
( spl184_734
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK105(X0,X1)),unordered_pair(sK105(X0,X1),sK105(X0,X1))),X0)
| sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_734])]) ).
fof(f11734,plain,
( spl184_726
<=> ! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1),sK104(X0,X1)),unordered_pair(sK105(X0,X1),sK105(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_726])]) ).
fof(f11737,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK105(X0,X1)),unordered_pair(sK105(X0,X1),sK105(X0,X1))),X0)
| sP21(X0,X1) )
| ~ spl184_214
| ~ spl184_726 ),
inference(forward_demodulation,[],[f11735,f3621]) ).
fof(f11735,plain,
( ! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1),sK104(X0,X1)),unordered_pair(sK105(X0,X1),sK105(X0,X1))),X0) )
| ~ spl184_726 ),
inference(avatar_component_clause,[],[f11734]) ).
fof(f11875,plain,
( spl184_733
| ~ spl184_214
| ~ spl184_725 ),
inference(avatar_split_clause,[],[f11732,f11729,f3620,f11873]) ).
fof(f11873,plain,
( spl184_733
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK102(X0,X1),sK102(X0,X1)),unordered_pair(sK102(X0,X1),sK103(X0,X1))),X0)
| sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_733])]) ).
fof(f11729,plain,
( spl184_725
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_725])]) ).
fof(f11732,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK102(X0,X1),sK102(X0,X1)),unordered_pair(sK102(X0,X1),sK103(X0,X1))),X0)
| sP19(X0,X1) )
| ~ spl184_214
| ~ spl184_725 ),
inference(forward_demodulation,[],[f11730,f3621]) ).
fof(f11730,plain,
( ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0) )
| ~ spl184_725 ),
inference(avatar_component_clause,[],[f11729]) ).
fof(f11871,plain,
( spl184_732
| ~ spl184_214
| ~ spl184_724 ),
inference(avatar_split_clause,[],[f11727,f11724,f3620,f11869]) ).
fof(f11869,plain,
( spl184_732
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK103(X0,X1),sK103(X0,X1))),X0)
| sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_732])]) ).
fof(f11724,plain,
( spl184_724
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK103(X0,X1),sK102(X0,X1)),unordered_pair(sK103(X0,X1),sK103(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_724])]) ).
fof(f11727,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK103(X0,X1),sK103(X0,X1))),X0)
| sP19(X0,X1) )
| ~ spl184_214
| ~ spl184_724 ),
inference(forward_demodulation,[],[f11725,f3621]) ).
fof(f11725,plain,
( ! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK103(X0,X1),sK102(X0,X1)),unordered_pair(sK103(X0,X1),sK103(X0,X1))),X0) )
| ~ spl184_724 ),
inference(avatar_component_clause,[],[f11724]) ).
fof(f11791,plain,
spl184_731,
inference(avatar_split_clause,[],[f2100,f11789]) ).
fof(f11789,plain,
( spl184_731
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK79(relation_dom(X1),X1) != apply(X1,sK79(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_731])]) ).
fof(f2100,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK79(relation_dom(X1),X1) != apply(X1,sK79(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1308]) ).
fof(f1308,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK79(X0,X1) != apply(X1,sK79(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f808]) ).
fof(f808,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK79(X0,X1) != apply(X1,sK79(X0,X1))
& in(sK79(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,[sK79])],[f806,f807]) ).
fof(f807,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK79(X0,X1) != apply(X1,sK79(X0,X1))
& in(sK79(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f806,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,[],[f805]) ).
fof(f805,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,[],[f804]) ).
fof(f804,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,[],[f462]) ).
fof(f462,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,[],[f461]) ).
fof(f461,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,[],[f257]) ).
fof(f257,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(f11786,plain,
spl184_730,
inference(avatar_split_clause,[],[f2033,f11784]) ).
fof(f2033,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK106(X0,X1),sK107(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1565,f1913]) ).
fof(f1565,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(ordered_pair(sK106(X0,X1),sK107(X0,X1)),X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f11781,plain,
spl184_729,
inference(avatar_split_clause,[],[f2032,f11779]) ).
fof(f2032,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(unordered_pair(unordered_pair(sK107(X0,X1),sK108(X0,X1)),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1566,f1913]) ).
fof(f1566,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(ordered_pair(sK107(X0,X1),sK108(X0,X1)),X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f11776,plain,
spl184_728,
inference(avatar_split_clause,[],[f2031,f11774]) ).
fof(f2031,plain,
! [X0,X1] :
( sP23(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK106(X0,X1),sK108(X0,X1)),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1567,f1913]) ).
fof(f1567,plain,
! [X0,X1] :
( sP23(X0,X1)
| ~ in(ordered_pair(sK106(X0,X1),sK108(X0,X1)),X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f11771,plain,
spl184_727,
inference(avatar_split_clause,[],[f2029,f11769]) ).
fof(f2029,plain,
! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK104(X0,X1),sK105(X0,X1)),unordered_pair(sK104(X0,X1),sK104(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1556,f1913]) ).
fof(f1556,plain,
! [X0,X1] :
( sP21(X0,X1)
| ~ in(ordered_pair(sK104(X0,X1),sK105(X0,X1)),X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f11736,plain,
spl184_726,
inference(avatar_split_clause,[],[f2028,f11734]) ).
fof(f2028,plain,
! [X0,X1] :
( sP21(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK105(X0,X1),sK104(X0,X1)),unordered_pair(sK105(X0,X1),sK105(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1557,f1913]) ).
fof(f1557,plain,
! [X0,X1] :
( sP21(X0,X1)
| ~ in(ordered_pair(sK105(X0,X1),sK104(X0,X1)),X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f11731,plain,
spl184_725,
inference(avatar_split_clause,[],[f2026,f11729]) ).
fof(f2026,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK102(X0,X1),sK103(X0,X1)),unordered_pair(sK102(X0,X1),sK102(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1546,f1913]) ).
fof(f1546,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(ordered_pair(sK102(X0,X1),sK103(X0,X1)),X0) ),
inference(cnf_transformation,[],[f917]) ).
fof(f11726,plain,
spl184_724,
inference(avatar_split_clause,[],[f2025,f11724]) ).
fof(f2025,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(unordered_pair(unordered_pair(sK103(X0,X1),sK102(X0,X1)),unordered_pair(sK103(X0,X1),sK103(X0,X1))),X0) ),
inference(definition_unfolding,[],[f1547,f1913]) ).
fof(f1547,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(ordered_pair(sK103(X0,X1),sK102(X0,X1)),X0) ),
inference(cnf_transformation,[],[f917]) ).
fof(f11722,plain,
spl184_723,
inference(avatar_split_clause,[],[f1316,f11720]) ).
fof(f11720,plain,
( spl184_723
<=> ! [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,[spl184_723])]) ).
fof(f1316,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,[],[f815]) ).
fof(f11718,plain,
spl184_722,
inference(avatar_split_clause,[],[f1636,f11716]) ).
fof(f11716,plain,
( spl184_722
<=> ! [X0,X1,X3] :
( sP35(X0,X1)
| apply(X0,X3) != sK126(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK126(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_722])]) ).
fof(f1636,plain,
! [X3,X0,X1] :
( sP35(X0,X1)
| apply(X0,X3) != sK126(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK126(X0,X1),X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f978,plain,
! [X0,X1] :
( ( sP35(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK126(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK126(X0,X1),X1) )
& ( ( sK126(X0,X1) = apply(X0,sK127(X0,X1))
& in(sK127(X0,X1),relation_dom(X0)) )
| in(sK126(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK128(X0,X5)) = X5
& in(sK128(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP35(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK126,sK127,sK128])],[f974,f977,f976,f975]) ).
fof(f975,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) != sK126(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK126(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK126(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK126(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f976,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK126(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK126(X0,X1) = apply(X0,sK127(X0,X1))
& in(sK127(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f977,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK128(X0,X5)) = X5
& in(sK128(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f974,plain,
! [X0,X1] :
( ( sP35(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) ) )
| ~ sP35(X0,X1) ) ),
inference(rectify,[],[f973]) ).
fof(f973,plain,
! [X0,X1] :
( ( sP35(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) ) )
| ~ sP35(X0,X1) ) ),
inference(nnf_transformation,[],[f715]) ).
fof(f715,plain,
! [X0,X1] :
( sP35(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP35])]) ).
fof(f11628,plain,
( spl184_720
| spl184_721
| ~ spl184_155
| ~ spl184_503 ),
inference(avatar_split_clause,[],[f7712,f6816,f3124,f11625,f11621]) ).
fof(f3124,plain,
( spl184_155
<=> ! [X0] :
( relation(X0)
| in(sK136(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_155])]) ).
fof(f6816,plain,
( spl184_503
<=> ! [X0] :
( ~ in(X0,sK56)
| in(X0,sK57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_503])]) ).
fof(f7712,plain,
( in(sK136(sK56),sK57)
| relation(sK56)
| ~ spl184_155
| ~ spl184_503 ),
inference(resolution,[],[f6817,f3125]) ).
fof(f3125,plain,
( ! [X0] :
( in(sK136(X0),X0)
| relation(X0) )
| ~ spl184_155 ),
inference(avatar_component_clause,[],[f3124]) ).
fof(f6817,plain,
( ! [X0] :
( ~ in(X0,sK56)
| in(X0,sK57) )
| ~ spl184_503 ),
inference(avatar_component_clause,[],[f6816]) ).
fof(f11619,plain,
( spl184_719
| ~ spl184_214
| ~ spl184_715 ),
inference(avatar_split_clause,[],[f11464,f11461,f3620,f11617]) ).
fof(f11617,plain,
( spl184_719
<=> ! [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,[spl184_719])]) ).
fof(f11461,plain,
( spl184_715
<=> ! [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,[spl184_715])]) ).
fof(f11464,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) )
| ~ spl184_214
| ~ spl184_715 ),
inference(forward_demodulation,[],[f11462,f3621]) ).
fof(f11462,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) )
| ~ spl184_715 ),
inference(avatar_component_clause,[],[f11461]) ).
fof(f11594,plain,
( spl184_718
| ~ spl184_214
| ~ spl184_713 ),
inference(avatar_split_clause,[],[f11452,f11449,f3620,f11592]) ).
fof(f11592,plain,
( spl184_718
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK120(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_718])]) ).
fof(f11449,plain,
( spl184_713
<=> ! [X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X6,sK120(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_713])]) ).
fof(f11452,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,sK120(X0,X1,X6))),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) )
| ~ spl184_214
| ~ spl184_713 ),
inference(forward_demodulation,[],[f11450,f3621]) ).
fof(f11450,plain,
( ! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK120(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) )
| ~ spl184_713 ),
inference(avatar_component_clause,[],[f11449]) ).
fof(f11548,plain,
( spl184_717
| ~ spl184_214
| ~ spl184_710 ),
inference(avatar_split_clause,[],[f11439,f11436,f3620,f11546]) ).
fof(f11546,plain,
( spl184_717
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK82(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_717])]) ).
fof(f11436,plain,
( spl184_710
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK82(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_710])]) ).
fof(f11439,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK82(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl184_214
| ~ spl184_710 ),
inference(forward_demodulation,[],[f11437,f3621]) ).
fof(f11437,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK82(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl184_710 ),
inference(avatar_component_clause,[],[f11436]) ).
fof(f11468,plain,
spl184_716,
inference(avatar_split_clause,[],[f2154,f11466]) ).
fof(f11466,plain,
( spl184_716
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_716])]) ).
fof(f2154,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP51(X0,X1,X2) ),
inference(equality_resolution,[],[f2089]) ).
fof(f2089,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)
| ~ sP51(X0,X1,X2) ),
inference(definition_unfolding,[],[f1837,f1913]) ).
fof(f1837,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f11463,plain,
spl184_715,
inference(avatar_split_clause,[],[f2110,f11461]) ).
fof(f2110,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,[],[f1975]) ).
fof(f1975,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,[],[f1380,f1913]) ).
fof(f1380,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,[],[f843]) ).
fof(f843,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,[],[f842]) ).
fof(f842,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,[],[f504]) ).
fof(f504,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,[],[f503]) ).
fof(f503,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,[],[f322]) ).
fof(f322,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(f11459,plain,
spl184_714,
inference(avatar_split_clause,[],[f2059,f11457]) ).
fof(f11457,plain,
( spl184_714
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_714])]) ).
fof(f2059,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X1)
| ~ sP31(X0,X1,X2) ),
inference(definition_unfolding,[],[f1608,f1913]) ).
fof(f1608,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1)
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f11451,plain,
spl184_713,
inference(avatar_split_clause,[],[f2056,f11449]) ).
fof(f2056,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK120(X0,X1,X6)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ),
inference(definition_unfolding,[],[f1597,f1913]) ).
fof(f1597,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK120(X0,X1,X6)),X1)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f11447,plain,
spl184_712,
inference(avatar_split_clause,[],[f2055,f11445]) ).
fof(f11445,plain,
( spl184_712
<=> ! [X1,X0,X6,X2,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_712])]) ).
fof(f2055,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)
| ~ sP29(X0,X1,X2) ),
inference(definition_unfolding,[],[f1599,f1913]) ).
fof(f1599,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X0)
| ~ in(ordered_pair(X6,X7),X1)
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f11443,plain,
spl184_711,
inference(avatar_split_clause,[],[f2051,f11441]) ).
fof(f11441,plain,
( spl184_711
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_711])]) ).
fof(f2051,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| ~ sP27(X0,X1,X2) ),
inference(definition_unfolding,[],[f1590,f1913]) ).
fof(f1590,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f11438,plain,
spl184_710,
inference(avatar_split_clause,[],[f1968,f11436]) ).
fof(f1968,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK82(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1350,f1913]) ).
fof(f1350,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK82(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f831]) ).
fof(f11434,plain,
spl184_709,
inference(avatar_split_clause,[],[f1377,f11432]) ).
fof(f11432,plain,
( spl184_709
<=> ! [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,[spl184_709])]) ).
fof(f1377,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,[],[f502]) ).
fof(f502,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,[],[f501]) ).
fof(f501,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,[],[f311]) ).
fof(f311,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(f11259,plain,
spl184_708,
inference(avatar_split_clause,[],[f2098,f11257]) ).
fof(f11257,plain,
( spl184_708
<=> ! [X2,X0,X3] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_708])]) ).
fof(f2098,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f1235]) ).
fof(f1235,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0,X1,X2,X3] :
( ( sP3(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))
| ~ sP3(X0,X1,X2,X3) ) ),
inference(rectify,[],[f790]) ).
fof(f790,plain,
! [X2,X3,X0,X1] :
( ( sP3(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))
| ~ sP3(X2,X3,X0,X1) ) ),
inference(flattening,[],[f789]) ).
fof(f789,plain,
! [X2,X3,X0,X1] :
( ( sP3(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))
| ~ sP3(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f668]) ).
fof(f668,plain,
! [X2,X3,X0,X1] :
( sP3(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,[sP3])]) ).
fof(f11255,plain,
spl184_707,
inference(avatar_split_clause,[],[f1759,f11253]) ).
fof(f11253,plain,
( spl184_707
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| ~ in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| ~ in(sK151(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_707])]) ).
fof(f1759,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| ~ in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| ~ in(sK151(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ( ( ~ in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| ~ in(sK151(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| in(sK151(X0,X1,X2),X2) )
& element(sK151(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)) )
| ~ sP47(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f1049,f1050]) ).
fof(f1050,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,sK151(X0,X1,X2)),X0)
| ~ in(sK151(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| in(sK151(X0,X1,X2),X2) )
& element(sK151(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1049,plain,
! [X0,X1,X2] :
( ( sP47(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)) )
| ~ sP47(X0,X1,X2) ) ),
inference(rectify,[],[f1048]) ).
fof(f1048,plain,
! [X1,X0,X2] :
( ( sP47(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)) )
| ~ sP47(X1,X0,X2) ) ),
inference(flattening,[],[f1047]) ).
fof(f1047,plain,
! [X1,X0,X2] :
( ( sP47(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)) )
| ~ sP47(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f733]) ).
fof(f733,plain,
! [X1,X0,X2] :
( sP47(X1,X0,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
fof(f11251,plain,
spl184_706,
inference(avatar_split_clause,[],[f1758,f11249]) ).
fof(f11249,plain,
( spl184_706
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| in(sK151(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_706])]) ).
fof(f1758,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| in(subset_complement(X1,sK151(X0,X1,X2)),X0)
| in(sK151(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f11247,plain,
spl184_705,
inference(avatar_split_clause,[],[f1648,f11245]) ).
fof(f11245,plain,
( spl184_705
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| in(apply(X1,sK129(X0,X1,X2)),X0)
| in(sK129(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_705])]) ).
fof(f1648,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| in(apply(X1,sK129(X0,X1,X2)),X0)
| in(sK129(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f11243,plain,
spl184_704,
inference(avatar_split_clause,[],[f1528,f11241]) ).
fof(f11241,plain,
( spl184_704
<=> ! [X0,X1] :
( sP15(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,[spl184_704])]) ).
fof(f1528,plain,
! [X0,X1] :
( sP15(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,[],[f902]) ).
fof(f902,plain,
! [X0,X1] :
( ( sP15(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) )
| ~ sP15(X0,X1) ) ),
inference(rectify,[],[f901]) ).
fof(f901,plain,
! [X1,X0] :
( ( sP15(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) )
| ~ sP15(X1,X0) ) ),
inference(flattening,[],[f900]) ).
fof(f900,plain,
! [X1,X0] :
( ( sP15(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) )
| ~ sP15(X1,X0) ) ),
inference(nnf_transformation,[],[f685]) ).
fof(f685,plain,
! [X1,X0] :
( sP15(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,[sP15])]) ).
fof(f11071,plain,
( spl184_703
| ~ spl184_214
| ~ spl184_700 ),
inference(avatar_split_clause,[],[f10877,f10874,f3620,f11069]) ).
fof(f11069,plain,
( spl184_703
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK138(X4),sK137(X4)),unordered_pair(sK137(X4),sK137(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_703])]) ).
fof(f10874,plain,
( spl184_700
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK137(X4),sK138(X4)),unordered_pair(sK137(X4),sK137(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_700])]) ).
fof(f10877,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK138(X4),sK137(X4)),unordered_pair(sK137(X4),sK137(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_700 ),
inference(forward_demodulation,[],[f10875,f3621]) ).
fof(f10875,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK137(X4),sK138(X4)),unordered_pair(sK137(X4),sK137(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl184_700 ),
inference(avatar_component_clause,[],[f10874]) ).
fof(f11017,plain,
( spl184_702
| ~ spl184_13
| ~ spl184_109
| ~ spl184_214
| ~ spl184_696 ),
inference(avatar_split_clause,[],[f10857,f10853,f3620,f2823,f2246,f11015]) ).
fof(f11015,plain,
( spl184_702
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK63(X0),sK62(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| sK173 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_702])]) ).
fof(f10853,plain,
( spl184_696
<=> ! [X0] :
( empty_set = 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,[spl184_696])]) ).
fof(f10857,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK63(X0),sK62(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| sK173 = X0
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_214
| ~ spl184_696 ),
inference(forward_demodulation,[],[f10856,f3621]) ).
fof(f10856,plain,
( ! [X0] :
( sK173 = X0
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_696 ),
inference(forward_demodulation,[],[f10854,f2880]) ).
fof(f10854,plain,
( ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) )
| ~ spl184_696 ),
inference(avatar_component_clause,[],[f10853]) ).
fof(f10881,plain,
( spl184_701
| ~ spl184_13
| ~ spl184_109
| ~ spl184_693 ),
inference(avatar_split_clause,[],[f10843,f10840,f2823,f2246,f10879]) ).
fof(f10879,plain,
( spl184_701
<=> ! [X2,X0,X1] :
( sK173 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_701])]) ).
fof(f10840,plain,
( spl184_693
<=> ! [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,[spl184_693])]) ).
fof(f10843,plain,
( ! [X2,X0,X1] :
( sK173 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_693 ),
inference(forward_demodulation,[],[f10841,f2880]) ).
fof(f10841,plain,
( ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 )
| ~ spl184_693 ),
inference(avatar_component_clause,[],[f10840]) ).
fof(f10876,plain,
spl184_700,
inference(avatar_split_clause,[],[f2064,f10874]) ).
fof(f2064,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK137(X4),sK138(X4)),unordered_pair(sK137(X4),sK137(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1679,f1913]) ).
fof(f1679,plain,
! [X0,X4] :
( ordered_pair(sK137(X4),sK138(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f1008,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK136(X0)
& in(sK136(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK137(X4),sK138(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136,sK137,sK138])],[f1005,f1007,f1006]) ).
fof(f1006,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK136(X0)
& in(sK136(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1007,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK137(X4),sK138(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f1005,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,[],[f1004]) ).
fof(f1004,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,[],[f590]) ).
fof(f590,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,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(f10872,plain,
spl184_699,
inference(avatar_split_clause,[],[f1983,f10870]) ).
fof(f10870,plain,
( spl184_699
<=> ! [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,[spl184_699])]) ).
fof(f1983,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,[],[f1396,f1913,f1913]) ).
fof(f1396,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f519]) ).
fof(f519,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f256]) ).
fof(f256,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(f10868,plain,
spl184_698,
inference(avatar_split_clause,[],[f1982,f10866]) ).
fof(f10866,plain,
( spl184_698
<=> ! [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,[spl184_698])]) ).
fof(f1982,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,[],[f1397,f1913,f1913]) ).
fof(f1397,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f519]) ).
fof(f10864,plain,
spl184_697,
inference(avatar_split_clause,[],[f1976,f10862]) ).
fof(f10862,plain,
( spl184_697
<=> ! [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,[spl184_697])]) ).
fof(f1976,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,[],[f1379,f1913]) ).
fof(f1379,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f843]) ).
fof(f10855,plain,
spl184_696,
inference(avatar_split_clause,[],[f1923,f10853]) ).
fof(f1923,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK62(X0),sK63(X0)),unordered_pair(sK62(X0),sK62(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1178,f1913]) ).
fof(f1178,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK62(X0),sK63(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f760]) ).
fof(f760,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK62(X0),sK63(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f361,f759]) ).
fof(f759,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK62(X0),sK63(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f361,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f360]) ).
fof(f360,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f296]) ).
fof(f296,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(f10851,plain,
spl184_695,
inference(avatar_split_clause,[],[f1304,f10849]) ).
fof(f10849,plain,
( spl184_695
<=> ! [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,[spl184_695])]) ).
fof(f1304,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,[],[f460]) ).
fof(f460,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,[],[f459]) ).
fof(f459,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,[],[f297]) ).
fof(f297,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(f10847,plain,
spl184_694,
inference(avatar_split_clause,[],[f1303,f10845]) ).
fof(f10845,plain,
( spl184_694
<=> ! [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,[spl184_694])]) ).
fof(f1303,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,[],[f460]) ).
fof(f10842,plain,
spl184_693,
inference(avatar_split_clause,[],[f1220,f10840]) ).
fof(f1220,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,[],[f387]) ).
fof(f387,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,[],[f386]) ).
fof(f386,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,[],[f290]) ).
fof(f290,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(f10605,plain,
spl184_692,
inference(avatar_split_clause,[],[f2099,f10603]) ).
fof(f10603,plain,
( spl184_692
<=> ! [X2,X0,X3] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_692])]) ).
fof(f2099,plain,
! [X2,X3,X0] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f1234]) ).
fof(f1234,plain,
! [X2,X3,X0,X1] :
( in(X1,relation_dom(X2))
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP3(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f791]) ).
fof(f10601,plain,
spl184_691,
inference(avatar_split_clause,[],[f1869,f10599]) ).
fof(f10599,plain,
( spl184_691
<=> ! [X3,X0,X5,X2,X1] :
( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3)
| ~ sP55(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_691])]) ).
fof(f1869,plain,
! [X2,X3,X0,X1,X5] :
( X0 = X5
| X1 = X5
| X2 = X5
| ~ in(X5,X3)
| ~ sP55(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f10597,plain,
spl184_690,
inference(avatar_split_clause,[],[f1667,f10595]) ).
fof(f10595,plain,
( spl184_690
<=> ! [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,[spl184_690])]) ).
fof(f1667,plain,
! [X3,X0,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f997,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK134(X0),sK133(X0))
& sK133(X0) != sK134(X0)
& ~ in(sK133(X0),sK134(X0))
& in(sK134(X0),X0)
& in(sK133(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,[sK133,sK134])],[f995,f996]) ).
fof(f996,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK134(X0),sK133(X0))
& sK133(X0) != sK134(X0)
& ~ in(sK133(X0),sK134(X0))
& in(sK134(X0),X0)
& in(sK133(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f995,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,[],[f994]) ).
fof(f994,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,[],[f588]) ).
fof(f588,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,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(f10593,plain,
spl184_689,
inference(avatar_split_clause,[],[f1657,f10591]) ).
fof(f10591,plain,
( spl184_689
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK131(X0,X1,X2),relation_dom(X0))
| in(sK130(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_689])]) ).
fof(f1657,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK131(X0,X1,X2),relation_dom(X0))
| in(sK130(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f10589,plain,
spl184_688,
inference(avatar_split_clause,[],[f1647,f10587]) ).
fof(f10587,plain,
( spl184_688
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| in(sK129(X0,X1,X2),relation_dom(X1))
| in(sK129(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_688])]) ).
fof(f1647,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| in(sK129(X0,X1,X2),relation_dom(X1))
| in(sK129(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f10585,plain,
spl184_687,
inference(avatar_split_clause,[],[f1635,f10583]) ).
fof(f10583,plain,
( spl184_687
<=> ! [X0,X1] :
( sP35(X0,X1)
| sK126(X0,X1) = apply(X0,sK127(X0,X1))
| in(sK126(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_687])]) ).
fof(f1635,plain,
! [X0,X1] :
( sP35(X0,X1)
| sK126(X0,X1) = apply(X0,sK127(X0,X1))
| in(sK126(X0,X1),X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f10346,plain,
( spl184_686
| ~ spl184_214
| ~ spl184_678 ),
inference(avatar_split_clause,[],[f10165,f10162,f3620,f10344]) ).
fof(f10344,plain,
( spl184_686
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK114(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_686])]) ).
fof(f10162,plain,
( spl184_678
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK114(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_678])]) ).
fof(f10165,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK114(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_678 ),
inference(forward_demodulation,[],[f10163,f3621]) ).
fof(f10163,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK114(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl184_678 ),
inference(avatar_component_clause,[],[f10162]) ).
fof(f10260,plain,
( spl184_685
| ~ spl184_214
| ~ spl184_672 ),
inference(avatar_split_clause,[],[f10130,f10127,f3620,f10258]) ).
fof(f10258,plain,
( spl184_685
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK70(X0),sK69(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_685])]) ).
fof(f10127,plain,
( spl184_672
<=> ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK69(X0),sK70(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_672])]) ).
fof(f10130,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK70(X0),sK69(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_672 ),
inference(forward_demodulation,[],[f10128,f3621]) ).
fof(f10128,plain,
( ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK69(X0),sK70(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) )
| ~ spl184_672 ),
inference(avatar_component_clause,[],[f10127]) ).
fof(f10256,plain,
( spl184_684
| ~ spl184_225
| ~ spl184_599 ),
inference(avatar_split_clause,[],[f9006,f8535,f3664,f10253]) ).
fof(f8535,plain,
( spl184_599
<=> in(sK74(sK56),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_599])]) ).
fof(f9006,plain,
( in(sK159(sK57),sK57)
| ~ spl184_225
| ~ spl184_599 ),
inference(resolution,[],[f8537,f3665]) ).
fof(f8537,plain,
( in(sK74(sK56),sK57)
| ~ spl184_599 ),
inference(avatar_component_clause,[],[f8535]) ).
fof(f10251,plain,
( spl184_683
| ~ spl184_214
| ~ spl184_671 ),
inference(avatar_split_clause,[],[f10125,f10122,f3620,f10249]) ).
fof(f10249,plain,
( spl184_683
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK71(X0),sK70(X0)),unordered_pair(sK70(X0),sK70(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_683])]) ).
fof(f10122,plain,
( spl184_671
<=> ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK70(X0),sK71(X0)),unordered_pair(sK70(X0),sK70(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_671])]) ).
fof(f10125,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK71(X0),sK70(X0)),unordered_pair(sK70(X0),sK70(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_671 ),
inference(forward_demodulation,[],[f10123,f3621]) ).
fof(f10123,plain,
( ! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK70(X0),sK71(X0)),unordered_pair(sK70(X0),sK70(X0))),X0)
| ~ relation(X0) )
| ~ spl184_671 ),
inference(avatar_component_clause,[],[f10122]) ).
fof(f10247,plain,
( spl184_682
| ~ spl184_214
| ~ spl184_670 ),
inference(avatar_split_clause,[],[f10120,f10117,f3620,f10245]) ).
fof(f10245,plain,
( spl184_682
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK71(X0),sK69(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_682])]) ).
fof(f10117,plain,
( spl184_670
<=> ! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK69(X0),sK71(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_670])]) ).
fof(f10120,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK71(X0),sK69(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| transitive(X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_670 ),
inference(forward_demodulation,[],[f10118,f3621]) ).
fof(f10118,plain,
( ! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK69(X0),sK71(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) )
| ~ spl184_670 ),
inference(avatar_component_clause,[],[f10117]) ).
fof(f10243,plain,
( spl184_681
| ~ spl184_214
| ~ spl184_669 ),
inference(avatar_split_clause,[],[f10115,f10112,f3620,f10241]) ).
fof(f10241,plain,
( spl184_681
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK65(X0),sK65(X0)),unordered_pair(sK65(X0),sK66(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_681])]) ).
fof(f10112,plain,
( spl184_669
<=> ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK65(X0),sK66(X0)),unordered_pair(sK65(X0),sK65(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_669])]) ).
fof(f10115,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK65(X0),sK65(X0)),unordered_pair(sK65(X0),sK66(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_669 ),
inference(forward_demodulation,[],[f10113,f3621]) ).
fof(f10113,plain,
( ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK65(X0),sK66(X0)),unordered_pair(sK65(X0),sK65(X0))),X0)
| ~ relation(X0) )
| ~ spl184_669 ),
inference(avatar_component_clause,[],[f10112]) ).
fof(f10239,plain,
( spl184_680
| ~ spl184_214
| ~ spl184_668 ),
inference(avatar_split_clause,[],[f10110,f10107,f3620,f10237]) ).
fof(f10237,plain,
( spl184_680
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK65(X0),sK66(X0)),unordered_pair(sK66(X0),sK66(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_680])]) ).
fof(f10107,plain,
( spl184_668
<=> ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK66(X0),sK65(X0)),unordered_pair(sK66(X0),sK66(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_668])]) ).
fof(f10110,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK65(X0),sK66(X0)),unordered_pair(sK66(X0),sK66(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) )
| ~ spl184_214
| ~ spl184_668 ),
inference(forward_demodulation,[],[f10108,f3621]) ).
fof(f10108,plain,
( ! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK66(X0),sK65(X0)),unordered_pair(sK66(X0),sK66(X0))),X0)
| ~ relation(X0) )
| ~ spl184_668 ),
inference(avatar_component_clause,[],[f10107]) ).
fof(f10173,plain,
( spl184_679
| ~ spl184_13
| ~ spl184_109
| ~ spl184_665 ),
inference(avatar_split_clause,[],[f10097,f10094,f2823,f2246,f10171]) ).
fof(f10171,plain,
( spl184_679
<=> ! [X0,X1,X3] :
( sK173 = X0
| ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_679])]) ).
fof(f10094,plain,
( spl184_665
<=> ! [X0,X1,X3] :
( ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_665])]) ).
fof(f10097,plain,
( ! [X3,X0,X1] :
( sK173 = X0
| ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_665 ),
inference(forward_demodulation,[],[f10095,f2880]) ).
fof(f10095,plain,
( ! [X3,X0,X1] :
( ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_665 ),
inference(avatar_component_clause,[],[f10094]) ).
fof(f10164,plain,
spl184_678,
inference(avatar_split_clause,[],[f2119,f10162]) ).
fof(f2119,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK114(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2042]) ).
fof(f2042,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK114(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1573,f1913]) ).
fof(f1573,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK114(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f939]) ).
fof(f10160,plain,
spl184_677,
inference(avatar_split_clause,[],[f2024,f10158]) ).
fof(f10158,plain,
( spl184_677
<=> ! [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,[spl184_677])]) ).
fof(f2024,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,[],[f1530,f1913]) ).
fof(f1530,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f10146,plain,
spl184_676,
inference(avatar_split_clause,[],[f2022,f10144]) ).
fof(f10144,plain,
( spl184_676
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_676])]) ).
fof(f2022,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ),
inference(definition_unfolding,[],[f1512,f1913]) ).
fof(f1512,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,relation_field(X2))
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f10142,plain,
spl184_675,
inference(avatar_split_clause,[],[f2021,f10140]) ).
fof(f10140,plain,
( spl184_675
<=> ! [X5,X0,X6,X2,X1] :
( in(X6,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_675])]) ).
fof(f2021,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP12(X0,X1,X2) ),
inference(definition_unfolding,[],[f1513,f1913]) ).
fof(f1513,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,relation_field(X2))
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f898]) ).
fof(f10138,plain,
spl184_674,
inference(avatar_split_clause,[],[f1984,f10136]) ).
fof(f10136,plain,
( spl184_674
<=> ! [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,[spl184_674])]) ).
fof(f1984,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,[],[f1401,f1913]) ).
fof(f1401,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f851]) ).
fof(f851,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,[],[f850]) ).
fof(f850,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,[],[f164]) ).
fof(f164,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',l55_zfmisc_1) ).
fof(f10134,plain,
spl184_673,
inference(avatar_split_clause,[],[f1981,f10132]) ).
fof(f10132,plain,
( spl184_673
<=> ! [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,[spl184_673])]) ).
fof(f1981,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,[],[f1392,f1913]) ).
fof(f1392,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f849]) ).
fof(f10129,plain,
spl184_672,
inference(avatar_split_clause,[],[f1934,f10127]) ).
fof(f1934,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK69(X0),sK70(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1198,f1913]) ).
fof(f1198,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK69(X0),sK70(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f778]) ).
fof(f10124,plain,
spl184_671,
inference(avatar_split_clause,[],[f1933,f10122]) ).
fof(f1933,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK70(X0),sK71(X0)),unordered_pair(sK70(X0),sK70(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1199,f1913]) ).
fof(f1199,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK70(X0),sK71(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f778]) ).
fof(f10119,plain,
spl184_670,
inference(avatar_split_clause,[],[f1932,f10117]) ).
fof(f1932,plain,
! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK69(X0),sK71(X0)),unordered_pair(sK69(X0),sK69(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1200,f1913]) ).
fof(f1200,plain,
! [X0] :
( transitive(X0)
| ~ in(ordered_pair(sK69(X0),sK71(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f778]) ).
fof(f10114,plain,
spl184_669,
inference(avatar_split_clause,[],[f1927,f10112]) ).
fof(f1927,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK65(X0),sK66(X0)),unordered_pair(sK65(X0),sK65(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1185,f1913]) ).
fof(f1185,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK65(X0),sK66(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f769]) ).
fof(f10109,plain,
spl184_668,
inference(avatar_split_clause,[],[f1926,f10107]) ).
fof(f1926,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK66(X0),sK65(X0)),unordered_pair(sK66(X0),sK66(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1186,f1913]) ).
fof(f1186,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK66(X0),sK65(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f769]) ).
fof(f10105,plain,
spl184_667,
inference(avatar_split_clause,[],[f1925,f10103]) ).
fof(f10103,plain,
( spl184_667
<=> ! [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,[spl184_667])]) ).
fof(f1925,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,[],[f1181,f1913]) ).
fof(f1181,plain,
! [X2,X0] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f765]) ).
fof(f765,plain,
! [X0] :
( ( ( reflexive(X0)
| ( ~ in(ordered_pair(sK64(X0),sK64(X0)),X0)
& in(sK64(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,[sK64])],[f763,f764]) ).
fof(f764,plain,
! [X0] :
( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
=> ( ~ in(ordered_pair(sK64(X0),sK64(X0)),X0)
& in(sK64(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f763,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,[],[f762]) ).
fof(f762,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,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ( reflexive(X0)
<=> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f149]) ).
fof(f149,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(f10101,plain,
spl184_666,
inference(avatar_split_clause,[],[f1924,f10099]) ).
fof(f10099,plain,
( spl184_666
<=> ! [X0] :
( reflexive(X0)
| ~ in(unordered_pair(unordered_pair(sK64(X0),sK64(X0)),unordered_pair(sK64(X0),sK64(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_666])]) ).
fof(f1924,plain,
! [X0] :
( reflexive(X0)
| ~ in(unordered_pair(unordered_pair(sK64(X0),sK64(X0)),unordered_pair(sK64(X0),sK64(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1183,f1913]) ).
fof(f1183,plain,
! [X0] :
( reflexive(X0)
| ~ in(ordered_pair(sK64(X0),sK64(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f765]) ).
fof(f10096,plain,
spl184_665,
inference(avatar_split_clause,[],[f1259,f10094]) ).
fof(f1259,plain,
! [X3,X0,X1] :
( ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f802]) ).
fof(f802,plain,
! [X0,X1] :
( ( ! [X3] :
( ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK78(X0),X0)
& ordinal(sK78(X0)) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f403,f801]) ).
fof(f801,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
=> ( ! [X3] :
( ordinal_subset(sK78(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK78(X0),X0)
& ordinal(sK78(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f403,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,[],[f402]) ).
fof(f402,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,[],[f252]) ).
fof(f252,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(f10092,plain,
spl184_664,
inference(avatar_split_clause,[],[f1212,f10090]) ).
fof(f10090,plain,
( spl184_664
<=> ! [X2,X0,X1] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_664])]) ).
fof(f1212,plain,
! [X2,X0,X1] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f286]) ).
fof(f286,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> relation_isomorphism(X1,X0,function_inverse(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_wellord1) ).
fof(f9367,plain,
( spl184_663
| ~ spl184_13
| ~ spl184_109
| ~ spl184_642 ),
inference(avatar_split_clause,[],[f9279,f9276,f2823,f2246,f9365]) ).
fof(f9365,plain,
( spl184_663
<=> ! [X4,X0,X1] :
( sK173 = X4
| disjoint(fiber(X0,sK101(X0,X4)),X4)
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_663])]) ).
fof(f9276,plain,
( spl184_642
<=> ! [X4,X0,X1] :
( disjoint(fiber(X0,sK101(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_642])]) ).
fof(f9279,plain,
( ! [X0,X1,X4] :
( sK173 = X4
| disjoint(fiber(X0,sK101(X0,X4)),X4)
| ~ subset(X4,X1)
| ~ sP17(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_642 ),
inference(forward_demodulation,[],[f9277,f2880]) ).
fof(f9277,plain,
( ! [X0,X1,X4] :
( disjoint(fiber(X0,sK101(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) )
| ~ spl184_642 ),
inference(avatar_component_clause,[],[f9276]) ).
fof(f9363,plain,
( spl184_662
| ~ spl184_13
| ~ spl184_109
| ~ spl184_641 ),
inference(avatar_split_clause,[],[f9274,f9271,f2823,f2246,f9361]) ).
fof(f9361,plain,
( spl184_662
<=> ! [X0,X3] :
( sK173 = X3
| disjoint(fiber(X0,sK86(X0,X3)),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_662])]) ).
fof(f9271,plain,
( spl184_641
<=> ! [X0,X3] :
( disjoint(fiber(X0,sK86(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_641])]) ).
fof(f9274,plain,
( ! [X3,X0] :
( sK173 = X3
| disjoint(fiber(X0,sK86(X0,X3)),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_641 ),
inference(forward_demodulation,[],[f9272,f2880]) ).
fof(f9272,plain,
( ! [X3,X0] :
( disjoint(fiber(X0,sK86(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) )
| ~ spl184_641 ),
inference(avatar_component_clause,[],[f9271]) ).
fof(f9359,plain,
spl184_661,
inference(avatar_split_clause,[],[f2132,f9357]) ).
fof(f9357,plain,
( spl184_661
<=> ! [X0,X7,X2,X1] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_661])]) ).
fof(f2132,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP39(X0,X1,X2) ),
inference(equality_resolution,[],[f1656]) ).
fof(f1656,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f9355,plain,
spl184_660,
inference(avatar_split_clause,[],[f1864,f9353]) ).
fof(f9353,plain,
( spl184_660
<=> ! [X2,X0,X1] :
( sP54(X0,X1,X2)
| in(sK170(X0,X1,X2),X0)
| in(sK170(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_660])]) ).
fof(f1864,plain,
! [X2,X0,X1] :
( sP54(X0,X1,X2)
| in(sK170(X0,X1,X2),X0)
| in(sK170(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f9351,plain,
spl184_659,
inference(avatar_split_clause,[],[f1863,f9349]) ).
fof(f9349,plain,
( spl184_659
<=> ! [X2,X0,X1] :
( sP54(X0,X1,X2)
| in(sK170(X0,X1,X2),X1)
| in(sK170(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_659])]) ).
fof(f1863,plain,
! [X2,X0,X1] :
( sP54(X0,X1,X2)
| in(sK170(X0,X1,X2),X1)
| in(sK170(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f9347,plain,
spl184_658,
inference(avatar_split_clause,[],[f1856,f9345]) ).
fof(f9345,plain,
( spl184_658
<=> ! [X2,X0,X1] :
( sP53(X0,X1,X2)
| ~ in(sK169(X0,X1,X2),X0)
| in(sK169(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_658])]) ).
fof(f1856,plain,
! [X2,X0,X1] :
( sP53(X0,X1,X2)
| ~ in(sK169(X0,X1,X2),X0)
| in(sK169(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f9343,plain,
spl184_657,
inference(avatar_split_clause,[],[f1855,f9341]) ).
fof(f9341,plain,
( spl184_657
<=> ! [X2,X0,X1] :
( sP53(X0,X1,X2)
| in(sK169(X0,X1,X2),X1)
| in(sK169(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_657])]) ).
fof(f1855,plain,
! [X2,X0,X1] :
( sP53(X0,X1,X2)
| in(sK169(X0,X1,X2),X1)
| in(sK169(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f9339,plain,
( spl184_656
| ~ spl184_59
| ~ spl184_598 ),
inference(avatar_split_clause,[],[f8605,f8531,f2475,f9336]) ).
fof(f9336,plain,
( spl184_656
<=> epsilon_transitive(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_656])]) ).
fof(f2475,plain,
( spl184_59
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_59])]) ).
fof(f8605,plain,
( epsilon_transitive(sK56)
| ~ spl184_59
| ~ spl184_598 ),
inference(resolution,[],[f8533,f2476]) ).
fof(f2476,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) )
| ~ spl184_59 ),
inference(avatar_component_clause,[],[f2475]) ).
fof(f8533,plain,
( ordinal(sK56)
| ~ spl184_598 ),
inference(avatar_component_clause,[],[f8531]) ).
fof(f9334,plain,
spl184_655,
inference(avatar_split_clause,[],[f1849,f9332]) ).
fof(f9332,plain,
( spl184_655
<=> ! [X2,X0,X1] :
( sP52(X0,X1,X2)
| ~ in(sK168(X0,X1,X2),X0)
| ~ in(sK168(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_655])]) ).
fof(f1849,plain,
! [X2,X0,X1] :
( sP52(X0,X1,X2)
| ~ in(sK168(X0,X1,X2),X0)
| ~ in(sK168(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f9330,plain,
spl184_654,
inference(avatar_split_clause,[],[f1848,f9328]) ).
fof(f9328,plain,
( spl184_654
<=> ! [X2,X0,X1] :
( sP52(X0,X1,X2)
| ~ in(sK168(X0,X1,X2),X1)
| ~ in(sK168(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_654])]) ).
fof(f1848,plain,
! [X2,X0,X1] :
( sP52(X0,X1,X2)
| ~ in(sK168(X0,X1,X2),X1)
| ~ in(sK168(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f9326,plain,
spl184_653,
inference(avatar_split_clause,[],[f1839,f9324]) ).
fof(f9324,plain,
( spl184_653
<=> ! [X2,X0,X1] :
( sP51(X0,X1,X2)
| in(sK165(X0,X1,X2),X0)
| in(sK163(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_653])]) ).
fof(f1839,plain,
! [X2,X0,X1] :
( sP51(X0,X1,X2)
| in(sK165(X0,X1,X2),X0)
| in(sK163(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f9322,plain,
spl184_652,
inference(avatar_split_clause,[],[f1838,f9320]) ).
fof(f9320,plain,
( spl184_652
<=> ! [X2,X0,X1] :
( sP51(X0,X1,X2)
| in(sK164(X0,X1,X2),X1)
| in(sK163(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_652])]) ).
fof(f1838,plain,
! [X2,X0,X1] :
( sP51(X0,X1,X2)
| in(sK164(X0,X1,X2),X1)
| in(sK163(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f9318,plain,
spl184_651,
inference(avatar_split_clause,[],[f1821,f9316]) ).
fof(f9316,plain,
( spl184_651
<=> ! [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,[spl184_651])]) ).
fof(f1821,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f660]) ).
fof(f660,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f659]) ).
fof(f659,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,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(f9314,plain,
spl184_650,
inference(avatar_split_clause,[],[f1798,f9312]) ).
fof(f9312,plain,
( spl184_650
<=> ! [X0,X1,X3] :
( sP49(X0,X1)
| ~ in(X3,X0)
| ~ in(sK154(X0,X1),X3)
| ~ in(sK154(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_650])]) ).
fof(f1798,plain,
! [X3,X0,X1] :
( sP49(X0,X1)
| ~ in(X3,X0)
| ~ in(sK154(X0,X1),X3)
| ~ in(sK154(X0,X1),X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,plain,
! [X0,X1] :
( ( sP49(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK154(X0,X1),X3) )
| ~ in(sK154(X0,X1),X1) )
& ( ( in(sK155(X0,X1),X0)
& in(sK154(X0,X1),sK155(X0,X1)) )
| in(sK154(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK156(X0,X5),X0)
& in(X5,sK156(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP49(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155,sK156])],[f1064,f1067,f1066,f1065]) ).
fof(f1065,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(sK154(X0,X1),X3) )
| ~ in(sK154(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK154(X0,X1),X4) )
| in(sK154(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1066,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK154(X0,X1),X4) )
=> ( in(sK155(X0,X1),X0)
& in(sK154(X0,X1),sK155(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1067,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK156(X0,X5),X0)
& in(X5,sK156(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f1064,plain,
! [X0,X1] :
( ( sP49(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) ) )
| ~ sP49(X0,X1) ) ),
inference(rectify,[],[f1063]) ).
fof(f1063,plain,
! [X0,X1] :
( ( sP49(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) ) )
| ~ sP49(X0,X1) ) ),
inference(nnf_transformation,[],[f736]) ).
fof(f736,plain,
! [X0,X1] :
( sP49(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP49])]) ).
fof(f9310,plain,
spl184_649,
inference(avatar_split_clause,[],[f1756,f9308]) ).
fof(f9308,plain,
( spl184_649
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_649])]) ).
fof(f1756,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f9306,plain,
spl184_648,
inference(avatar_split_clause,[],[f1755,f9304]) ).
fof(f9304,plain,
( spl184_648
<=> ! [X2,X4,X0,X1] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_648])]) ).
fof(f1755,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f9302,plain,
spl184_647,
inference(avatar_split_clause,[],[f1710,f9300]) ).
fof(f9300,plain,
( spl184_647
<=> ! [X4,X0,X1] :
( sP41(X0,X1)
| in(sK144(X0,X1),X4)
| ~ in(X4,X0)
| in(sK144(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_647])]) ).
fof(f1710,plain,
! [X0,X1,X4] :
( sP41(X0,X1)
| in(sK144(X0,X1),X4)
| ~ in(X4,X0)
| in(sK144(X0,X1),X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,plain,
! [X0,X1] :
( ( sP41(X0,X1)
| ( ( ( ~ in(sK144(X0,X1),sK145(X0,X1))
& in(sK145(X0,X1),X0) )
| ~ in(sK144(X0,X1),X1) )
& ( ! [X4] :
( in(sK144(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK144(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK146(X0,X5))
& in(sK146(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP41(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK144,sK145,sK146])],[f1025,f1028,f1027,f1026]) ).
fof(f1026,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(sK144(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK144(X0,X1),X1) )
& ( ! [X4] :
( in(sK144(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK144(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1027,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK144(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK144(X0,X1),sK145(X0,X1))
& in(sK145(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1028,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK146(X0,X5))
& in(sK146(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1025,plain,
! [X0,X1] :
( ( sP41(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) ) )
| ~ sP41(X0,X1) ) ),
inference(rectify,[],[f1024]) ).
fof(f1024,plain,
! [X0,X1] :
( ( sP41(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) ) )
| ~ sP41(X0,X1) ) ),
inference(nnf_transformation,[],[f724]) ).
fof(f724,plain,
! [X0,X1] :
( sP41(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f9298,plain,
spl184_646,
inference(avatar_split_clause,[],[f1658,f9296]) ).
fof(f9296,plain,
( spl184_646
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK131(X0,X1,X2),X1)
| in(sK130(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_646])]) ).
fof(f1658,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| in(sK131(X0,X1,X2),X1)
| in(sK130(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f9291,plain,
spl184_645,
inference(avatar_split_clause,[],[f1646,f9289]) ).
fof(f9289,plain,
( spl184_645
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_645])]) ).
fof(f1646,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f9287,plain,
spl184_644,
inference(avatar_split_clause,[],[f1610,f9285]) ).
fof(f9285,plain,
( spl184_644
<=> ! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(sK122(X0,X1,X2),X0)
| in(sK121(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_644])]) ).
fof(f1610,plain,
! [X2,X0,X1] :
( sP31(X0,X1,X2)
| in(sK122(X0,X1,X2),X0)
| in(sK121(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f9283,plain,
spl184_643,
inference(avatar_split_clause,[],[f1601,f9281]) ).
fof(f9281,plain,
( spl184_643
<=> ! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(sK119(X0,X1,X2),X0)
| in(sK118(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_643])]) ).
fof(f1601,plain,
! [X2,X0,X1] :
( sP29(X0,X1,X2)
| in(sK119(X0,X1,X2),X0)
| in(sK118(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f9278,plain,
spl184_642,
inference(avatar_split_clause,[],[f1536,f9276]) ).
fof(f1536,plain,
! [X0,X1,X4] :
( disjoint(fiber(X0,sK101(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f912]) ).
fof(f912,plain,
! [X0,X1] :
( ( sP17(X0,X1)
| ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK100(X0,X1))
| ~ in(X3,sK100(X0,X1)) )
& empty_set != sK100(X0,X1)
& subset(sK100(X0,X1),X1) ) )
& ( ! [X4] :
( ( disjoint(fiber(X0,sK101(X0,X4)),X4)
& in(sK101(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) )
| ~ sP17(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101])],[f909,f911,f910]) ).
fof(f910,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
=> ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK100(X0,X1))
| ~ in(X3,sK100(X0,X1)) )
& empty_set != sK100(X0,X1)
& subset(sK100(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f911,plain,
! [X0,X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
=> ( disjoint(fiber(X0,sK101(X0,X4)),X4)
& in(sK101(X0,X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f909,plain,
! [X0,X1] :
( ( sP17(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) )
| ~ sP17(X0,X1) ) ),
inference(rectify,[],[f908]) ).
fof(f908,plain,
! [X0,X1] :
( ( sP17(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) )
| ~ sP17(X0,X1) ) ),
inference(nnf_transformation,[],[f688]) ).
fof(f688,plain,
! [X0,X1] :
( sP17(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,[sP17])]) ).
fof(f9273,plain,
spl184_641,
inference(avatar_split_clause,[],[f1470,f9271]) ).
fof(f1470,plain,
! [X3,X0] :
( disjoint(fiber(X0,sK86(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f865]) ).
fof(f865,plain,
! [X0] :
( ( sP6(X0)
| ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK85(X0))
| ~ in(X2,sK85(X0)) )
& empty_set != sK85(X0)
& subset(sK85(X0),relation_field(X0)) ) )
& ( ! [X3] :
( ( disjoint(fiber(X0,sK86(X0,X3)),X3)
& in(sK86(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86])],[f862,f864,f863]) ).
fof(f863,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),sK85(X0))
| ~ in(X2,sK85(X0)) )
& empty_set != sK85(X0)
& subset(sK85(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f864,plain,
! [X0,X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
=> ( disjoint(fiber(X0,sK86(X0,X3)),X3)
& in(sK86(X0,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f862,plain,
! [X0] :
( ( sP6(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)) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f861]) ).
fof(f861,plain,
! [X0] :
( ( sP6(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)) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f672]) ).
fof(f672,plain,
! [X0] :
( sP6(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,[sP6])]) ).
fof(f9175,plain,
( spl184_640
| ~ spl184_165
| ~ spl184_599 ),
inference(avatar_split_clause,[],[f9004,f8535,f3165,f9172]) ).
fof(f9172,plain,
( spl184_640
<=> element(sK74(sK56),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_640])]) ).
fof(f9004,plain,
( element(sK74(sK56),sK57)
| ~ spl184_165
| ~ spl184_599 ),
inference(resolution,[],[f8537,f3166]) ).
fof(f9059,plain,
spl184_639,
inference(avatar_split_clause,[],[f2101,f9057]) ).
fof(f9057,plain,
( spl184_639
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK79(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_639])]) ).
fof(f2101,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK79(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1307]) ).
fof(f1307,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK79(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f808]) ).
fof(f9055,plain,
spl184_638,
inference(avatar_split_clause,[],[f2079,f9053]) ).
fof(f9053,plain,
( spl184_638
<=> ! [X5,X0,X6,X2,X1] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_638])]) ).
fof(f2079,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP45(X0,X1,X2) ),
inference(definition_unfolding,[],[f1732,f1913]) ).
fof(f1732,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f9051,plain,
spl184_637,
inference(avatar_split_clause,[],[f2052,f9049]) ).
fof(f9049,plain,
( spl184_637
<=> ! [X2,X4,X0,X1] :
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| ~ in(X4,X2)
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_637])]) ).
fof(f2052,plain,
! [X2,X0,X1,X4] :
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| ~ in(X4,X2)
| ~ sP27(X0,X1,X2) ),
inference(definition_unfolding,[],[f1589,f1913]) ).
fof(f1589,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(X4,X1),X0)
| ~ in(X4,X2)
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f9047,plain,
spl184_636,
inference(avatar_split_clause,[],[f2048,f9045]) ).
fof(f9045,plain,
( spl184_636
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_636])]) ).
fof(f2048,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP25(X0,X1,X2) ),
inference(definition_unfolding,[],[f1579,f1913]) ).
fof(f1579,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f946]) ).
fof(f9043,plain,
( ~ spl184_635
| ~ spl184_164
| ~ spl184_599 ),
inference(avatar_split_clause,[],[f9003,f8535,f3161,f9040]) ).
fof(f9040,plain,
( spl184_635
<=> in(sK57,sK74(sK56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_635])]) ).
fof(f9003,plain,
( ~ in(sK57,sK74(sK56))
| ~ spl184_164
| ~ spl184_599 ),
inference(resolution,[],[f8537,f3162]) ).
fof(f9038,plain,
spl184_634,
inference(avatar_split_clause,[],[f1920,f9036]) ).
fof(f9036,plain,
( spl184_634
<=> ! [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,[spl184_634])]) ).
fof(f1920,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,[],[f1165,f1912]) ).
fof(f1912,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1430,f1158]) ).
fof(f1430,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f1165,plain,
! [X2,X0] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f757]) ).
fof(f757,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK61(X0)),X0)
& in(sK61(X0),X0)
& ordinal(sK61(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f755,f756]) ).
fof(f756,plain,
! [X0] :
( ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) )
=> ( ~ in(succ(sK61(X0)),X0)
& in(sK61(X0),X0)
& ordinal(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f755,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,[],[f754]) ).
fof(f754,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,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f273]) ).
fof(f273,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(f9034,plain,
spl184_633,
inference(avatar_split_clause,[],[f1376,f9032]) ).
fof(f9032,plain,
( spl184_633
<=> ! [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,[spl184_633])]) ).
fof(f1376,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f500,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f499]) ).
fof(f499,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f313]) ).
fof(f313,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(f9030,plain,
spl184_632,
inference(avatar_split_clause,[],[f1296,f9028]) ).
fof(f9028,plain,
( spl184_632
<=> ! [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,[spl184_632])]) ).
fof(f1296,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f803]) ).
fof(f803,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,[],[f447]) ).
fof(f447,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f275,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(f9026,plain,
spl184_631,
inference(avatar_split_clause,[],[f1295,f9024]) ).
fof(f9024,plain,
( spl184_631
<=> ! [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,[spl184_631])]) ).
fof(f1295,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f803]) ).
fof(f9022,plain,
spl184_630,
inference(avatar_split_clause,[],[f1219,f9020]) ).
fof(f9020,plain,
( spl184_630
<=> ! [X2,X0,X1] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_630])]) ).
fof(f1219,plain,
! [X2,X0,X1] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f385]) ).
fof(f385,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f384]) ).
fof(f384,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f294]) ).
fof(f294,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_isomorphism(X0,X1,X2)
& well_ordering(X0) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f9018,plain,
spl184_629,
inference(avatar_split_clause,[],[f1211,f9016]) ).
fof(f9016,plain,
( spl184_629
<=> ! [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,[spl184_629])]) ).
fof(f1211,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,[],[f379]) ).
fof(f379,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,[],[f378]) ).
fof(f378,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,[],[f282]) ).
fof(f282,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(f9014,plain,
spl184_628,
inference(avatar_split_clause,[],[f1210,f9012]) ).
fof(f9012,plain,
( spl184_628
<=> ! [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,[spl184_628])]) ).
fof(f1210,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,[],[f377]) ).
fof(f377,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,[],[f376]) ).
fof(f376,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,[],[f279]) ).
fof(f279,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(f8974,plain,
spl184_627,
inference(avatar_split_clause,[],[f2184,f8972]) ).
fof(f8972,plain,
( spl184_627
<=> ! [X0,X3,X2,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X2
| ~ in(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_627])]) ).
fof(f2184,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X2
| ~ in(X2,X3) ),
inference(inner_rewriting,[],[f1874]) ).
fof(f1874,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X2
| ~ in(sK171(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f8970,plain,
spl184_626,
inference(avatar_split_clause,[],[f2183,f8968]) ).
fof(f8968,plain,
( spl184_626
<=> ! [X0,X3,X2,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X1
| ~ in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_626])]) ).
fof(f2183,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X1
| ~ in(X1,X3) ),
inference(inner_rewriting,[],[f1875]) ).
fof(f1875,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X1
| ~ in(sK171(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f8966,plain,
spl184_625,
inference(avatar_split_clause,[],[f2182,f8964]) ).
fof(f8964,plain,
( spl184_625
<=> ! [X0,X3,X2,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X0
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_625])]) ).
fof(f2182,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X0
| ~ in(X0,X3) ),
inference(inner_rewriting,[],[f1876]) ).
fof(f1876,plain,
! [X2,X3,X0,X1] :
( sP55(X0,X1,X2,X3)
| sK171(X0,X1,X2,X3) != X0
| ~ in(sK171(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f8962,plain,
spl184_624,
inference(avatar_split_clause,[],[f1820,f8960]) ).
fof(f8960,plain,
( spl184_624
<=> ! [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,[spl184_624])]) ).
fof(f1820,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f658]) ).
fof(f658,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f657]) ).
fof(f657,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,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(f8958,plain,
spl184_623,
inference(avatar_split_clause,[],[f1796,f8956]) ).
fof(f8956,plain,
( spl184_623
<=> ! [X0,X1] :
( sP49(X0,X1)
| in(sK154(X0,X1),sK155(X0,X1))
| in(sK154(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_623])]) ).
fof(f1796,plain,
! [X0,X1] :
( sP49(X0,X1)
| in(sK154(X0,X1),sK155(X0,X1))
| in(sK154(X0,X1),X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f8954,plain,
spl184_622,
inference(avatar_split_clause,[],[f1712,f8952]) ).
fof(f8952,plain,
( spl184_622
<=> ! [X0,X1] :
( sP41(X0,X1)
| ~ in(sK144(X0,X1),sK145(X0,X1))
| ~ in(sK144(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_622])]) ).
fof(f1712,plain,
! [X0,X1] :
( sP41(X0,X1)
| ~ in(sK144(X0,X1),sK145(X0,X1))
| ~ in(sK144(X0,X1),X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f8950,plain,
spl184_621,
inference(avatar_split_clause,[],[f1655,f8948]) ).
fof(f8948,plain,
( spl184_621
<=> ! [X0,X6,X2,X1] :
( apply(X0,sK132(X0,X1,X6)) = X6
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_621])]) ).
fof(f1655,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK132(X0,X1,X6)) = X6
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f8946,plain,
spl184_620,
inference(avatar_split_clause,[],[f1539,f8944]) ).
fof(f8944,plain,
( spl184_620
<=> ! [X0,X1,X3] :
( sP17(X0,X1)
| ~ disjoint(fiber(X0,X3),sK100(X0,X1))
| ~ in(X3,sK100(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_620])]) ).
fof(f1539,plain,
! [X3,X0,X1] :
( sP17(X0,X1)
| ~ disjoint(fiber(X0,X3),sK100(X0,X1))
| ~ in(X3,sK100(X0,X1)) ),
inference(cnf_transformation,[],[f912]) ).
fof(f8785,plain,
( spl184_619
| ~ spl184_214
| ~ spl184_606 ),
inference(avatar_split_clause,[],[f8597,f8594,f3620,f8783]) ).
fof(f8783,plain,
( spl184_619
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK67(X0),sK67(X0)),unordered_pair(sK67(X0),sK68(X0))),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_619])]) ).
fof(f8594,plain,
( spl184_606
<=> ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK67(X0),sK68(X0)),unordered_pair(sK67(X0),sK67(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_606])]) ).
fof(f8597,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK67(X0),sK67(X0)),unordered_pair(sK67(X0),sK68(X0))),X0)
| sP0(X0) )
| ~ spl184_214
| ~ spl184_606 ),
inference(forward_demodulation,[],[f8595,f3621]) ).
fof(f8595,plain,
( ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK67(X0),sK68(X0)),unordered_pair(sK67(X0),sK67(X0))),X0) )
| ~ spl184_606 ),
inference(avatar_component_clause,[],[f8594]) ).
fof(f8781,plain,
( spl184_618
| ~ spl184_214
| ~ spl184_605 ),
inference(avatar_split_clause,[],[f8592,f8589,f3620,f8779]) ).
fof(f8779,plain,
( spl184_618
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK67(X0),sK68(X0)),unordered_pair(sK68(X0),sK68(X0))),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_618])]) ).
fof(f8589,plain,
( spl184_605
<=> ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK68(X0),sK67(X0)),unordered_pair(sK68(X0),sK68(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_605])]) ).
fof(f8592,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK67(X0),sK68(X0)),unordered_pair(sK68(X0),sK68(X0))),X0)
| sP0(X0) )
| ~ spl184_214
| ~ spl184_605 ),
inference(forward_demodulation,[],[f8590,f3621]) ).
fof(f8590,plain,
( ! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK68(X0),sK67(X0)),unordered_pair(sK68(X0),sK68(X0))),X0) )
| ~ spl184_605 ),
inference(avatar_component_clause,[],[f8589]) ).
fof(f8677,plain,
( spl184_617
| ~ spl184_60
| ~ spl184_598 ),
inference(avatar_split_clause,[],[f8604,f8531,f2479,f8674]) ).
fof(f8674,plain,
( spl184_617
<=> epsilon_connected(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_617])]) ).
fof(f2479,plain,
( spl184_60
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_60])]) ).
fof(f8604,plain,
( epsilon_connected(sK56)
| ~ spl184_60
| ~ spl184_598 ),
inference(resolution,[],[f8533,f2480]) ).
fof(f2480,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) )
| ~ spl184_60 ),
inference(avatar_component_clause,[],[f2479]) ).
fof(f8672,plain,
spl184_616,
inference(avatar_split_clause,[],[f2140,f8670]) ).
fof(f8670,plain,
( spl184_616
<=> ! [X5,X1,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_616])]) ).
fof(f2140,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP43(X0,X1) ),
inference(equality_resolution,[],[f2071]) ).
fof(f2071,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP43(X0,X1) ),
inference(definition_unfolding,[],[f1725,f1913]) ).
fof(f1725,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f8668,plain,
spl184_615,
inference(avatar_split_clause,[],[f2084,f8666]) ).
fof(f8666,plain,
( spl184_615
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK157(X0,X1) = X0
| in(sK157(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_615])]) ).
fof(f2084,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK157(X0,X1) = X0
| in(sK157(X0,X1),X1) ),
inference(definition_unfolding,[],[f1803,f1158]) ).
fof(f1803,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK157(X0,X1) = X0
| in(sK157(X0,X1),X1) ),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK157(X0,X1) != X0
| ~ in(sK157(X0,X1),X1) )
& ( sK157(X0,X1) = X0
| in(sK157(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f1071,f1072]) ).
fof(f1072,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK157(X0,X1) != X0
| ~ in(sK157(X0,X1),X1) )
& ( sK157(X0,X1) = X0
| in(sK157(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1071,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,[],[f1070]) ).
fof(f1070,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,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8664,plain,
spl184_614,
inference(avatar_split_clause,[],[f2073,f8662]) ).
fof(f8662,plain,
( spl184_614
<=> ! [X4,X0,X5,X1] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_614])]) ).
fof(f2073,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP43(X0,X1) ),
inference(definition_unfolding,[],[f1723,f1913]) ).
fof(f1723,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f8660,plain,
spl184_613,
inference(avatar_split_clause,[],[f2072,f8658]) ).
fof(f8658,plain,
( spl184_613
<=> ! [X4,X5,X1,X0] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP43(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_613])]) ).
fof(f2072,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP43(X0,X1) ),
inference(definition_unfolding,[],[f1724,f1913]) ).
fof(f1724,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP43(X0,X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f8656,plain,
spl184_612,
inference(avatar_split_clause,[],[f1966,f8654]) ).
fof(f8654,plain,
( spl184_612
<=> ! [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,[spl184_612])]) ).
fof(f1966,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,[],[f1345,f1913]) ).
fof(f1345,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f481]) ).
fof(f481,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f480]) ).
fof(f480,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,[],[f228]) ).
fof(f228,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(f8652,plain,
spl184_611,
inference(avatar_split_clause,[],[f1965,f8650]) ).
fof(f8650,plain,
( spl184_611
<=> ! [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,[spl184_611])]) ).
fof(f1965,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,[],[f1346,f1913]) ).
fof(f1346,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f481]) ).
fof(f8648,plain,
spl184_610,
inference(avatar_split_clause,[],[f1964,f8646]) ).
fof(f8646,plain,
( spl184_610
<=> ! [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,[spl184_610])]) ).
fof(f1964,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,[],[f1343,f1913]) ).
fof(f1343,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f479]) ).
fof(f479,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f478]) ).
fof(f478,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,[],[f249]) ).
fof(f249,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(f8644,plain,
spl184_609,
inference(avatar_split_clause,[],[f1963,f8642]) ).
fof(f8642,plain,
( spl184_609
<=> ! [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,[spl184_609])]) ).
fof(f1963,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,[],[f1344,f1913]) ).
fof(f1344,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f479]) ).
fof(f8609,plain,
( spl184_608
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_607 ),
inference(avatar_split_clause,[],[f8602,f8599,f7974,f2764,f2414,f8607]) ).
fof(f8607,plain,
( spl184_608
<=> ! [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,[spl184_608])]) ).
fof(f8599,plain,
( spl184_607
<=> ! [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,[spl184_607])]) ).
fof(f8602,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,relation_rng(relation_rng_restriction(X0,identity_relation(relation_dom(X1)))))
| ~ relation(X1) )
| ~ spl184_47
| ~ spl184_95
| ~ spl184_578
| ~ spl184_607 ),
inference(forward_demodulation,[],[f8600,f8115]) ).
fof(f8600,plain,
( ! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) )
| ~ spl184_607 ),
inference(avatar_component_clause,[],[f8599]) ).
fof(f8601,plain,
spl184_607,
inference(avatar_split_clause,[],[f1941,f8599]) ).
fof(f1941,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,[],[f1273,f1249]) ).
fof(f1273,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f206]) ).
fof(f206,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(f8596,plain,
spl184_606,
inference(avatar_split_clause,[],[f1930,f8594]) ).
fof(f1930,plain,
! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK67(X0),sK68(X0)),unordered_pair(sK67(X0),sK67(X0))),X0) ),
inference(definition_unfolding,[],[f1194,f1913]) ).
fof(f1194,plain,
! [X0] :
( sP0(X0)
| ~ in(ordered_pair(sK67(X0),sK68(X0)),X0) ),
inference(cnf_transformation,[],[f774]) ).
fof(f8591,plain,
spl184_605,
inference(avatar_split_clause,[],[f1929,f8589]) ).
fof(f1929,plain,
! [X0] :
( sP0(X0)
| ~ in(unordered_pair(unordered_pair(sK68(X0),sK67(X0)),unordered_pair(sK68(X0),sK68(X0))),X0) ),
inference(definition_unfolding,[],[f1195,f1913]) ).
fof(f1195,plain,
! [X0] :
( sP0(X0)
| ~ in(ordered_pair(sK68(X0),sK67(X0)),X0) ),
inference(cnf_transformation,[],[f774]) ).
fof(f8587,plain,
spl184_604,
inference(avatar_split_clause,[],[f1365,f8585]) ).
fof(f8585,plain,
( spl184_604
<=> ! [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,[spl184_604])]) ).
fof(f1365,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,[],[f841]) ).
fof(f841,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,[],[f840]) ).
fof(f840,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,[],[f488]) ).
fof(f488,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,[],[f319]) ).
fof(f319,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(f8583,plain,
spl184_603,
inference(avatar_split_clause,[],[f1362,f8581]) ).
fof(f8581,plain,
( spl184_603
<=> ! [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,[spl184_603])]) ).
fof(f1362,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,[],[f839]) ).
fof(f839,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,[],[f838]) ).
fof(f838,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,[],[f487]) ).
fof(f487,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,[],[f192]) ).
fof(f192,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(f8579,plain,
spl184_602,
inference(avatar_split_clause,[],[f1359,f8577]) ).
fof(f8577,plain,
( spl184_602
<=> ! [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,[spl184_602])]) ).
fof(f1359,plain,
! [X2,X0,X1] :
( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f837]) ).
fof(f837,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,[],[f836]) ).
fof(f836,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,[],[f486]) ).
fof(f486,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f216]) ).
fof(f216,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(f8575,plain,
spl184_601,
inference(avatar_split_clause,[],[f1302,f8573]) ).
fof(f8573,plain,
( spl184_601
<=> ! [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,[spl184_601])]) ).
fof(f1302,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f458]) ).
fof(f458,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f457]) ).
fof(f457,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f209]) ).
fof(f209,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(f8571,plain,
spl184_600,
inference(avatar_split_clause,[],[f1218,f8569]) ).
fof(f8569,plain,
( spl184_600
<=> ! [X2,X0,X1] :
( sP2(X1,X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_600])]) ).
fof(f1218,plain,
! [X2,X0,X1] :
( sP2(X1,X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f667]) ).
fof(f667,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP2(X1,X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f383,f666]) ).
fof(f666,plain,
! [X1,X0] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f383,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f382]) ).
fof(f382,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f291]) ).
fof(f291,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( well_founded_relation(X0)
=> well_founded_relation(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( connected(X0)
=> connected(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( reflexive(X0)
=> reflexive(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f8538,plain,
( spl184_598
| spl184_599
| ~ spl184_122
| ~ spl184_503 ),
inference(avatar_split_clause,[],[f7695,f6816,f2971,f8535,f8531]) ).
fof(f2971,plain,
( spl184_122
<=> ! [X0] :
( ordinal(X0)
| in(sK74(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_122])]) ).
fof(f7695,plain,
( in(sK74(sK56),sK57)
| ordinal(sK56)
| ~ spl184_122
| ~ spl184_503 ),
inference(resolution,[],[f6817,f2972]) ).
fof(f2972,plain,
( ! [X0] :
( in(sK74(X0),X0)
| ordinal(X0) )
| ~ spl184_122 ),
inference(avatar_component_clause,[],[f2971]) ).
fof(f8368,plain,
( spl184_597
| ~ spl184_13
| ~ spl184_109
| ~ spl184_589 ),
inference(avatar_split_clause,[],[f8336,f8333,f2823,f2246,f8366]) ).
fof(f8366,plain,
( spl184_597
<=> ! [X4,X0,X1] :
( sK173 = X4
| in(sK101(X0,X4),X4)
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_597])]) ).
fof(f8333,plain,
( spl184_589
<=> ! [X4,X0,X1] :
( in(sK101(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_589])]) ).
fof(f8336,plain,
( ! [X0,X1,X4] :
( sK173 = X4
| in(sK101(X0,X4),X4)
| ~ subset(X4,X1)
| ~ sP17(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_589 ),
inference(forward_demodulation,[],[f8334,f2880]) ).
fof(f8334,plain,
( ! [X0,X1,X4] :
( in(sK101(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) )
| ~ spl184_589 ),
inference(avatar_component_clause,[],[f8333]) ).
fof(f8364,plain,
( spl184_596
| ~ spl184_13
| ~ spl184_109
| ~ spl184_588 ),
inference(avatar_split_clause,[],[f8331,f8328,f2823,f2246,f8362]) ).
fof(f8362,plain,
( spl184_596
<=> ! [X0,X3] :
( sK173 = X3
| in(sK86(X0,X3),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_596])]) ).
fof(f8328,plain,
( spl184_588
<=> ! [X0,X3] :
( in(sK86(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_588])]) ).
fof(f8331,plain,
( ! [X3,X0] :
( sK173 = X3
| in(sK86(X0,X3),X3)
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_588 ),
inference(forward_demodulation,[],[f8329,f2880]) ).
fof(f8329,plain,
( ! [X3,X0] :
( in(sK86(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) )
| ~ spl184_588 ),
inference(avatar_component_clause,[],[f8328]) ).
fof(f8360,plain,
spl184_595,
inference(avatar_split_clause,[],[f2095,f8358]) ).
fof(f8358,plain,
( spl184_595
<=> ! [X5,X1,X0] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_595])]) ).
fof(f2095,plain,
! [X0,X1,X5] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ),
inference(equality_resolution,[],[f1230]) ).
fof(f1230,plain,
! [X0,X1,X4,X5] :
( apply(X0,X4) = X5
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f8356,plain,
spl184_594,
inference(avatar_split_clause,[],[f1808,f8354]) ).
fof(f8354,plain,
( spl184_594
<=> ! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK158(X0,X1),X0)
| ~ in(sK158(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_594])]) ).
fof(f1808,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK158(X0,X1),X0)
| ~ in(sK158(X0,X1),X1) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK158(X0,X1),X0)
| ~ in(sK158(X0,X1),X1) )
& ( subset(sK158(X0,X1),X0)
| in(sK158(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,[sK158])],[f1075,f1076]) ).
fof(f1076,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK158(X0,X1),X0)
| ~ in(sK158(X0,X1),X1) )
& ( subset(sK158(X0,X1),X0)
| in(sK158(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1075,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,[],[f1074]) ).
fof(f1074,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,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f8352,plain,
spl184_593,
inference(avatar_split_clause,[],[f1807,f8350]) ).
fof(f8350,plain,
( spl184_593
<=> ! [X0,X1] :
( powerset(X0) = X1
| subset(sK158(X0,X1),X0)
| in(sK158(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_593])]) ).
fof(f1807,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK158(X0,X1),X0)
| in(sK158(X0,X1),X1) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f8348,plain,
spl184_592,
inference(avatar_split_clause,[],[f1760,f8346]) ).
fof(f8346,plain,
( spl184_592
<=> ! [X2,X0,X1] :
( sP48(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_592])]) ).
fof(f1760,plain,
! [X2,X0,X1] :
( sP48(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f735]) ).
fof(f735,plain,
! [X0,X1] :
( ! [X2] :
( sP48(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f617,f734,f733]) ).
fof(f734,plain,
! [X2,X0,X1] :
( ( complements_of_subsets(X0,X1) = X2
<=> sP47(X1,X0,X2) )
| ~ sP48(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP48])]) ).
fof(f617,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,[],[f70]) ).
fof(f70,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(f8344,plain,
spl184_591,
inference(avatar_split_clause,[],[f1653,f8342]) ).
fof(f8342,plain,
( spl184_591
<=> ! [X0,X6,X2,X1] :
( in(sK132(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_591])]) ).
fof(f1653,plain,
! [X2,X0,X1,X6] :
( in(sK132(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f8340,plain,
spl184_590,
inference(avatar_split_clause,[],[f1634,f8338]) ).
fof(f8338,plain,
( spl184_590
<=> ! [X0,X1] :
( sP35(X0,X1)
| in(sK127(X0,X1),relation_dom(X0))
| in(sK126(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_590])]) ).
fof(f1634,plain,
! [X0,X1] :
( sP35(X0,X1)
| in(sK127(X0,X1),relation_dom(X0))
| in(sK126(X0,X1),X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f8335,plain,
spl184_589,
inference(avatar_split_clause,[],[f1535,f8333]) ).
fof(f1535,plain,
! [X0,X1,X4] :
( in(sK101(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f912]) ).
fof(f8330,plain,
spl184_588,
inference(avatar_split_clause,[],[f1469,f8328]) ).
fof(f1469,plain,
! [X3,X0] :
( in(sK86(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f865]) ).
fof(f8303,plain,
( ~ spl184_586
| spl184_587
| ~ spl184_188
| ~ spl184_348
| ~ spl184_404 ),
inference(avatar_split_clause,[],[f5583,f5393,f4543,f3484,f8301,f8297]) ).
fof(f8297,plain,
( spl184_586
<=> disjoint(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_586])]) ).
fof(f8301,plain,
( spl184_587
<=> ! [X0] : ~ in(X0,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_587])]) ).
fof(f3484,plain,
( spl184_188
<=> ! [X0] : set_difference(X0,sK173) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_188])]) ).
fof(f4543,plain,
( spl184_348
<=> sK173 = set_difference(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_348])]) ).
fof(f5393,plain,
( spl184_404
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_404])]) ).
fof(f5583,plain,
( ! [X0] :
( ~ in(X0,sK56)
| ~ disjoint(sK56,sK57) )
| ~ spl184_188
| ~ spl184_348
| ~ spl184_404 ),
inference(forward_demodulation,[],[f5576,f3485]) ).
fof(f3485,plain,
( ! [X0] : set_difference(X0,sK173) = X0
| ~ spl184_188 ),
inference(avatar_component_clause,[],[f3484]) ).
fof(f5576,plain,
( ! [X0] :
( ~ in(X0,set_difference(sK56,sK173))
| ~ disjoint(sK56,sK57) )
| ~ spl184_348
| ~ spl184_404 ),
inference(superposition,[],[f5394,f4545]) ).
fof(f4545,plain,
( sK173 = set_difference(sK56,sK57)
| ~ spl184_348 ),
inference(avatar_component_clause,[],[f4543]) ).
fof(f5394,plain,
( ! [X2,X0,X1] :
( ~ in(X2,set_difference(X0,set_difference(X0,X1)))
| ~ disjoint(X0,X1) )
| ~ spl184_404 ),
inference(avatar_component_clause,[],[f5393]) ).
fof(f8021,plain,
( spl184_585
| ~ spl184_13
| ~ spl184_109
| ~ spl184_570 ),
inference(avatar_split_clause,[],[f7943,f7939,f2823,f2246,f8019]) ).
fof(f8019,plain,
( spl184_585
<=> ! [X0,X1] :
( sK173 = X0
| relation_inverse_image(X1,X0) != sK173
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_585])]) ).
fof(f7939,plain,
( spl184_570
<=> ! [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,[spl184_570])]) ).
fof(f7943,plain,
( ! [X0,X1] :
( sK173 = X0
| relation_inverse_image(X1,X0) != sK173
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_570 ),
inference(forward_demodulation,[],[f7942,f2880]) ).
fof(f7942,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,X0) != sK173
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_570 ),
inference(forward_demodulation,[],[f7940,f2880]) ).
fof(f7940,plain,
( ! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) )
| ~ spl184_570 ),
inference(avatar_component_clause,[],[f7939]) ).
fof(f8017,plain,
( spl184_584
| ~ spl184_257
| ~ spl184_281 ),
inference(avatar_split_clause,[],[f4335,f4233,f3952,f8014]) ).
fof(f8014,plain,
( spl184_584
<=> sK56 = set_union2(relation_rng(sK59),sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_584])]) ).
fof(f3952,plain,
( spl184_257
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_257])]) ).
fof(f4233,plain,
( spl184_281
<=> subset(relation_rng(sK59),sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_281])]) ).
fof(f4335,plain,
( sK56 = set_union2(relation_rng(sK59),sK56)
| ~ spl184_257
| ~ spl184_281 ),
inference(resolution,[],[f4235,f3953]) ).
fof(f3953,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl184_257 ),
inference(avatar_component_clause,[],[f3952]) ).
fof(f4235,plain,
( subset(relation_rng(sK59),sK56)
| ~ spl184_281 ),
inference(avatar_component_clause,[],[f4233]) ).
fof(f7996,plain,
spl184_583,
inference(avatar_split_clause,[],[f2093,f7994]) ).
fof(f7994,plain,
( spl184_583
<=> ! [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,[spl184_583])]) ).
fof(f2093,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,[],[f1917]) ).
fof(f1917,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| set_union2(X1,unordered_pair(X1,X1)) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1164,f1912]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| succ(X1) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f753]) ).
fof(f753,plain,
! [X0] :
( ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( succ(X1) != X0
| ~ ordinal(X1) ) )
& ( ( succ(sK60(X0)) = X0
& ordinal(sK60(X0)) )
| being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f349,f752]) ).
fof(f752,plain,
! [X0] :
( ? [X2] :
( succ(X2) = X0
& ordinal(X2) )
=> ( succ(sK60(X0)) = X0
& ordinal(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,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,[],[f333]) ).
fof(f333,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,[],[f274]) ).
fof(f274,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(f7992,plain,
spl184_582,
inference(avatar_split_clause,[],[f1986,f7990]) ).
fof(f7990,plain,
( spl184_582
<=> ! [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,[spl184_582])]) ).
fof(f1986,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,[],[f1399,f1913]) ).
fof(f1399,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f851]) ).
fof(f7988,plain,
spl184_581,
inference(avatar_split_clause,[],[f1985,f7986]) ).
fof(f7986,plain,
( spl184_581
<=> ! [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,[spl184_581])]) ).
fof(f1985,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,[],[f1400,f1913]) ).
fof(f1400,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f851]) ).
fof(f7984,plain,
spl184_580,
inference(avatar_split_clause,[],[f1971,f7982]) ).
fof(f7982,plain,
( spl184_580
<=> ! [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,[spl184_580])]) ).
fof(f1971,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,[],[f1366,f1249,f1249]) ).
fof(f1366,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f489]) ).
fof(f489,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f243]) ).
fof(f243,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(f7980,plain,
spl184_579,
inference(avatar_split_clause,[],[f1940,f7978]) ).
fof(f7978,plain,
( spl184_579
<=> ! [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,[spl184_579])]) ).
fof(f1940,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,[],[f1272,f1249]) ).
fof(f1272,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f326]) ).
fof(f326,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(f7976,plain,
spl184_578,
inference(avatar_split_clause,[],[f1939,f7974]) ).
fof(f1939,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,[],[f1271,f1249]) ).
fof(f1271,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f415]) ).
fof(f415,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f197]) ).
fof(f197,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(f7972,plain,
spl184_577,
inference(avatar_split_clause,[],[f1922,f7970]) ).
fof(f7970,plain,
( spl184_577
<=> ! [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,[spl184_577])]) ).
fof(f1922,plain,
! [X0,X1] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1169,f1912]) ).
fof(f1169,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f758]) ).
fof(f758,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,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ! [X1] :
( ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f254]) ).
fof(f254,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(f7968,plain,
spl184_576,
inference(avatar_split_clause,[],[f1921,f7966]) ).
fof(f7966,plain,
( spl184_576
<=> ! [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,[spl184_576])]) ).
fof(f1921,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1170,f1912]) ).
fof(f1170,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f758]) ).
fof(f7964,plain,
spl184_575,
inference(avatar_split_clause,[],[f1919,f7962]) ).
fof(f7962,plain,
( spl184_575
<=> ! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK61(X0),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_575])]) ).
fof(f1919,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK61(X0),unordered_pair(sK61(X0),sK61(X0))),X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1168,f1912]) ).
fof(f1168,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(succ(sK61(X0)),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f757]) ).
fof(f7960,plain,
( spl184_574
| ~ spl184_279
| ~ spl184_281 ),
inference(avatar_split_clause,[],[f4334,f4233,f4166,f7957]) ).
fof(f7957,plain,
( spl184_574
<=> sK173 = set_difference(relation_rng(sK59),sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_574])]) ).
fof(f4166,plain,
( spl184_279
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK173
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_279])]) ).
fof(f4334,plain,
( sK173 = set_difference(relation_rng(sK59),sK56)
| ~ spl184_279
| ~ spl184_281 ),
inference(resolution,[],[f4235,f4167]) ).
fof(f4167,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK173 )
| ~ spl184_279 ),
inference(avatar_component_clause,[],[f4166]) ).
fof(f7955,plain,
spl184_573,
inference(avatar_split_clause,[],[f1918,f7953]) ).
fof(f7953,plain,
( spl184_573
<=> ! [X0] :
( set_union2(sK60(X0),unordered_pair(sK60(X0),sK60(X0))) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_573])]) ).
fof(f1918,plain,
! [X0] :
( set_union2(sK60(X0),unordered_pair(sK60(X0),sK60(X0))) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1163,f1912]) ).
fof(f1163,plain,
! [X0] :
( succ(sK60(X0)) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f753]) ).
fof(f7951,plain,
spl184_572,
inference(avatar_split_clause,[],[f1353,f7949]) ).
fof(f7949,plain,
( spl184_572
<=> ! [X2,X0,X1] :
( in(sK83(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_572])]) ).
fof(f1353,plain,
! [X2,X0,X1] :
( in(sK83(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f835]) ).
fof(f7947,plain,
spl184_571,
inference(avatar_split_clause,[],[f1349,f7945]) ).
fof(f7945,plain,
( spl184_571
<=> ! [X2,X0,X1] :
( in(sK82(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_571])]) ).
fof(f1349,plain,
! [X2,X0,X1] :
( in(sK82(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f831]) ).
fof(f7941,plain,
spl184_570,
inference(avatar_split_clause,[],[f1284,f7939]) ).
fof(f1284,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f436]) ).
fof(f436,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(flattening,[],[f435]) ).
fof(f435,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,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(f7937,plain,
spl184_569,
inference(avatar_split_clause,[],[f1283,f7935]) ).
fof(f7935,plain,
( spl184_569
<=> ! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_569])]) ).
fof(f1283,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f434]) ).
fof(f434,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(flattening,[],[f433]) ).
fof(f433,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f264]) ).
fof(f264,axiom,
! [X0,X1] :
( relation(X1)
=> ( ( subset(X0,relation_field(X1))
& well_ordering(X1) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
fof(f7911,plain,
( spl184_568
| ~ spl184_13
| ~ spl184_109
| ~ spl184_562 ),
inference(avatar_split_clause,[],[f7681,f7678,f2823,f2246,f7909]) ).
fof(f7909,plain,
( spl184_568
<=> ! [X0,X1] :
( apply(X0,X1) = sK173
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_568])]) ).
fof(f7678,plain,
( spl184_562
<=> ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_562])]) ).
fof(f7681,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK173
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_562 ),
inference(forward_demodulation,[],[f7679,f2880]) ).
fof(f7679,plain,
( ! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl184_562 ),
inference(avatar_component_clause,[],[f7678]) ).
fof(f7907,plain,
( spl184_567
| ~ spl184_257
| ~ spl184_280 ),
inference(avatar_split_clause,[],[f4291,f4174,f3952,f7904]) ).
fof(f7904,plain,
( spl184_567
<=> sK58 = set_union2(relation_dom(sK59),sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_567])]) ).
fof(f4174,plain,
( spl184_280
<=> subset(relation_dom(sK59),sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_280])]) ).
fof(f4291,plain,
( sK58 = set_union2(relation_dom(sK59),sK58)
| ~ spl184_257
| ~ spl184_280 ),
inference(resolution,[],[f4176,f3953]) ).
fof(f4176,plain,
( subset(relation_dom(sK59),sK58)
| ~ spl184_280 ),
inference(avatar_component_clause,[],[f4174]) ).
fof(f7735,plain,
( spl184_566
| ~ spl184_279
| ~ spl184_280 ),
inference(avatar_split_clause,[],[f4290,f4174,f4166,f7732]) ).
fof(f7732,plain,
( spl184_566
<=> sK173 = set_difference(relation_dom(sK59),sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_566])]) ).
fof(f4290,plain,
( sK173 = set_difference(relation_dom(sK59),sK58)
| ~ spl184_279
| ~ spl184_280 ),
inference(resolution,[],[f4176,f4167]) ).
fof(f7718,plain,
spl184_565,
inference(avatar_split_clause,[],[f2179,f7716]) ).
fof(f7716,plain,
( spl184_565
<=> ! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_565])]) ).
fof(f2179,plain,
! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f1830]) ).
fof(f1830,plain,
! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X1
| ~ in(sK162(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f7689,plain,
spl184_564,
inference(avatar_split_clause,[],[f2178,f7687]) ).
fof(f7687,plain,
( spl184_564
<=> ! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_564])]) ).
fof(f2178,plain,
! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f1831]) ).
fof(f1831,plain,
! [X2,X0,X1] :
( sP50(X0,X1,X2)
| sK162(X0,X1,X2) != X0
| ~ in(sK162(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f7685,plain,
spl184_563,
inference(avatar_split_clause,[],[f2167,f7683]) ).
fof(f7683,plain,
( spl184_563
<=> ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| sK117(X0,X1,X2) != X1
| in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_563])]) ).
fof(f2167,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| sK117(X0,X1,X2) != X1
| in(X1,X2) ),
inference(inner_rewriting,[],[f1591]) ).
fof(f1591,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| sK117(X0,X1,X2) != X1
| in(sK117(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f7680,plain,
spl184_562,
inference(avatar_split_clause,[],[f2127,f7678]) ).
fof(f2127,plain,
! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1641]) ).
fof(f1641,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| empty_set != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f979]) ).
fof(f979,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,[],[f581]) ).
fof(f581,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,[],[f580]) ).
fof(f580,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,[],[f47]) ).
fof(f47,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(f7676,plain,
spl184_561,
inference(avatar_split_clause,[],[f2096,f7674]) ).
fof(f7674,plain,
( spl184_561
<=> ! [X5,X1,X0] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_561])]) ).
fof(f2096,plain,
! [X0,X1,X5] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ),
inference(equality_resolution,[],[f1229]) ).
fof(f1229,plain,
! [X0,X1,X4,X5] :
( in(X4,relation_rng(X1))
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f7672,plain,
spl184_560,
inference(avatar_split_clause,[],[f1862,f7670]) ).
fof(f7670,plain,
( spl184_560
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_560])]) ).
fof(f1862,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f7668,plain,
spl184_559,
inference(avatar_split_clause,[],[f1854,f7666]) ).
fof(f7666,plain,
( spl184_559
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_559])]) ).
fof(f1854,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f7664,plain,
spl184_558,
inference(avatar_split_clause,[],[f1844,f7662]) ).
fof(f7662,plain,
( spl184_558
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_558])]) ).
fof(f1844,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f7660,plain,
spl184_557,
inference(avatar_split_clause,[],[f1835,f7658]) ).
fof(f7658,plain,
( spl184_557
<=> ! [X0,X8,X2,X1] :
( in(sK167(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_557])]) ).
fof(f1835,plain,
! [X2,X0,X1,X8] :
( in(sK167(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f7656,plain,
spl184_556,
inference(avatar_split_clause,[],[f1834,f7654]) ).
fof(f7654,plain,
( spl184_556
<=> ! [X0,X8,X2,X1] :
( in(sK166(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_556])]) ).
fof(f1834,plain,
! [X2,X0,X1,X8] :
( in(sK166(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1098]) ).
fof(f7652,plain,
spl184_555,
inference(avatar_split_clause,[],[f1826,f7650]) ).
fof(f7650,plain,
( spl184_555
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_555])]) ).
fof(f1826,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f7642,plain,
spl184_554,
inference(avatar_split_clause,[],[f1797,f7640]) ).
fof(f7640,plain,
( spl184_554
<=> ! [X0,X1] :
( sP49(X0,X1)
| in(sK155(X0,X1),X0)
| in(sK154(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_554])]) ).
fof(f1797,plain,
! [X0,X1] :
( sP49(X0,X1)
| in(sK155(X0,X1),X0)
| in(sK154(X0,X1),X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f7638,plain,
spl184_553,
inference(avatar_split_clause,[],[f1783,f7636]) ).
fof(f7636,plain,
( spl184_553
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK152(X0,X1),X1)
| ~ in(sK152(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_553])]) ).
fof(f1783,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK152(X0,X1),X1)
| ~ in(sK152(X0,X1),X0) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK152(X0,X1),X1)
| ~ in(sK152(X0,X1),X0) )
& ( in(sK152(X0,X1),X1)
| in(sK152(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f1053,f1054]) ).
fof(f1054,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK152(X0,X1),X1)
| ~ in(sK152(X0,X1),X0) )
& ( in(sK152(X0,X1),X1)
| in(sK152(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1053,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f646]) ).
fof(f646,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f247]) ).
fof(f247,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f7634,plain,
spl184_552,
inference(avatar_split_clause,[],[f1782,f7632]) ).
fof(f7632,plain,
( spl184_552
<=> ! [X0,X1] :
( X0 = X1
| in(sK152(X0,X1),X1)
| in(sK152(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_552])]) ).
fof(f1782,plain,
! [X0,X1] :
( X0 = X1
| in(sK152(X0,X1),X1)
| in(sK152(X0,X1),X0) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f7630,plain,
spl184_551,
inference(avatar_split_clause,[],[f1754,f7628]) ).
fof(f7628,plain,
( spl184_551
<=> ! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP47(X2,X1,X0)
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_551])]) ).
fof(f1754,plain,
! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP47(X2,X1,X0)
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,plain,
! [X0,X1,X2] :
( ( ( complements_of_subsets(X1,X2) = X0
| ~ sP47(X2,X1,X0) )
& ( sP47(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0 ) )
| ~ sP48(X0,X1,X2) ),
inference(rectify,[],[f1045]) ).
fof(f1045,plain,
! [X2,X0,X1] :
( ( ( complements_of_subsets(X0,X1) = X2
| ~ sP47(X1,X0,X2) )
& ( sP47(X1,X0,X2)
| complements_of_subsets(X0,X1) != X2 ) )
| ~ sP48(X2,X0,X1) ),
inference(nnf_transformation,[],[f734]) ).
fof(f7626,plain,
spl184_550,
inference(avatar_split_clause,[],[f1731,f7624]) ).
fof(f7624,plain,
( spl184_550
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP45(X2,X1,X0)
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_550])]) ).
fof(f1731,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X1,X2) = X0
| ~ sP45(X2,X1,X0)
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP45(X2,X1,X0) )
& ( sP45(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP46(X0,X1,X2) ),
inference(rectify,[],[f1038]) ).
fof(f1038,plain,
! [X2,X0,X1] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP45(X1,X0,X2) )
& ( sP45(X1,X0,X2)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP46(X2,X0,X1) ),
inference(nnf_transformation,[],[f731]) ).
fof(f731,plain,
! [X2,X0,X1] :
( ( relation_rng_restriction(X0,X1) = X2
<=> sP45(X1,X0,X2) )
| ~ sP46(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP46])]) ).
fof(f7622,plain,
spl184_549,
inference(avatar_split_clause,[],[f1711,f7620]) ).
fof(f7620,plain,
( spl184_549
<=> ! [X0,X1] :
( sP41(X0,X1)
| in(sK145(X0,X1),X0)
| ~ in(sK144(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_549])]) ).
fof(f1711,plain,
! [X0,X1] :
( sP41(X0,X1)
| in(sK145(X0,X1),X0)
| ~ in(sK144(X0,X1),X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f7618,plain,
spl184_548,
inference(avatar_split_clause,[],[f1654,f7616]) ).
fof(f7616,plain,
( spl184_548
<=> ! [X0,X6,X2,X1] :
( in(sK132(X0,X1,X6),X1)
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_548])]) ).
fof(f1654,plain,
! [X2,X0,X1,X6] :
( in(sK132(X0,X1,X6),X1)
| ~ in(X6,X2)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f992]) ).
fof(f7614,plain,
spl184_547,
inference(avatar_split_clause,[],[f1632,f7612]) ).
fof(f7612,plain,
( spl184_547
<=> ! [X5,X0,X1] :
( apply(X0,sK128(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_547])]) ).
fof(f1632,plain,
! [X0,X1,X5] :
( apply(X0,sK128(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f7610,plain,
spl184_546,
inference(avatar_split_clause,[],[f1607,f7608]) ).
fof(f7608,plain,
( spl184_546
<=> ! [X0,X6,X2,X1] :
( in(sK123(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_546])]) ).
fof(f1607,plain,
! [X2,X0,X1,X6] :
( in(sK123(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f966]) ).
fof(f7606,plain,
spl184_545,
inference(avatar_split_clause,[],[f1598,f7604]) ).
fof(f7604,plain,
( spl184_545
<=> ! [X0,X6,X2,X1] :
( in(sK120(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_545])]) ).
fof(f1598,plain,
! [X2,X0,X1,X6] :
( in(sK120(X0,X1,X6),X0)
| ~ in(X6,X2)
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f959]) ).
fof(f7602,plain,
( spl184_544
| ~ spl184_123
| ~ spl184_538 ),
inference(avatar_split_clause,[],[f7465,f7247,f2975,f7600]) ).
fof(f7600,plain,
( spl184_544
<=> ! [X0] : ~ proper_subset(sK57,set_difference(sK56,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_544])]) ).
fof(f2975,plain,
( spl184_123
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_123])]) ).
fof(f7247,plain,
( spl184_538
<=> ! [X0] : subset(set_difference(sK56,X0),sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_538])]) ).
fof(f7465,plain,
( ! [X0] : ~ proper_subset(sK57,set_difference(sK56,X0))
| ~ spl184_123
| ~ spl184_538 ),
inference(resolution,[],[f7248,f2976]) ).
fof(f2976,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl184_123 ),
inference(avatar_component_clause,[],[f2975]) ).
fof(f7248,plain,
( ! [X0] : subset(set_difference(sK56,X0),sK57)
| ~ spl184_538 ),
inference(avatar_component_clause,[],[f7247]) ).
fof(f7598,plain,
spl184_543,
inference(avatar_split_clause,[],[f1578,f7596]) ).
fof(f7596,plain,
( spl184_543
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP25(X2,X1,X0)
| ~ sP26(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_543])]) ).
fof(f1578,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP25(X2,X1,X0)
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f941]) ).
fof(f941,plain,
! [X0,X1,X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| ~ sP25(X2,X1,X0) )
& ( sP25(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ sP26(X0,X1,X2) ),
inference(rectify,[],[f940]) ).
fof(f940,plain,
! [X2,X1,X0] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ~ sP25(X0,X1,X2) )
& ( sP25(X0,X1,X2)
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ sP26(X2,X1,X0) ),
inference(nnf_transformation,[],[f701]) ).
fof(f701,plain,
! [X2,X1,X0] :
( ( relation_dom_restriction(X0,X1) = X2
<=> sP25(X0,X1,X2) )
| ~ sP26(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f7594,plain,
spl184_542,
inference(avatar_split_clause,[],[f1497,f7592]) ).
fof(f7592,plain,
( spl184_542
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP10(X2,X1,X0)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_542])]) ).
fof(f1497,plain,
! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP10(X2,X1,X0)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f882]) ).
fof(f882,plain,
! [X0,X1,X2] :
( ( ( relation_composition(X1,X2) = X0
| ~ sP10(X2,X1,X0) )
& ( sP10(X2,X1,X0)
| relation_composition(X1,X2) != X0 ) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f881]) ).
fof(f881,plain,
! [X2,X0,X1] :
( ( ( relation_composition(X0,X1) = X2
| ~ sP10(X1,X0,X2) )
& ( sP10(X1,X0,X2)
| relation_composition(X0,X1) != X2 ) )
| ~ sP11(X2,X0,X1) ),
inference(nnf_transformation,[],[f679]) ).
fof(f679,plain,
! [X2,X0,X1] :
( ( relation_composition(X0,X1) = X2
<=> sP10(X1,X0,X2) )
| ~ sP11(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f7494,plain,
( spl184_541
| ~ spl184_13
| ~ spl184_109
| ~ spl184_534 ),
inference(avatar_split_clause,[],[f7233,f7230,f2823,f2246,f7492]) ).
fof(f7492,plain,
( spl184_541
<=> ! [X0,X1] :
( sK173 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_541])]) ).
fof(f7230,plain,
( spl184_534
<=> ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_534])]) ).
fof(f7233,plain,
( ! [X0,X1] :
( sK173 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_534 ),
inference(forward_demodulation,[],[f7231,f2880]) ).
fof(f7231,plain,
( ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl184_534 ),
inference(avatar_component_clause,[],[f7230]) ).
fof(f7370,plain,
( spl184_540
| ~ spl184_13
| ~ spl184_109
| ~ spl184_528 ),
inference(avatar_split_clause,[],[f7208,f7204,f2823,f2246,f7368]) ).
fof(f7368,plain,
( spl184_540
<=> ! [X0,X1] :
( sK173 = X1
| complements_of_subsets(X0,X1) != sK173
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_540])]) ).
fof(f7204,plain,
( spl184_528
<=> ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_528])]) ).
fof(f7208,plain,
( ! [X0,X1] :
( sK173 = X1
| complements_of_subsets(X0,X1) != sK173
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_528 ),
inference(forward_demodulation,[],[f7207,f2880]) ).
fof(f7207,plain,
( ! [X0,X1] :
( complements_of_subsets(X0,X1) != sK173
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_528 ),
inference(forward_demodulation,[],[f7205,f2880]) ).
fof(f7205,plain,
( ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl184_528 ),
inference(avatar_component_clause,[],[f7204]) ).
fof(f7253,plain,
spl184_539,
inference(avatar_split_clause,[],[f2177,f7251]) ).
fof(f7251,plain,
( spl184_539
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK157(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_539])]) ).
fof(f2177,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK157(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f2083]) ).
fof(f2083,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK157(X0,X1) != X0
| ~ in(sK157(X0,X1),X1) ),
inference(definition_unfolding,[],[f1804,f1158]) ).
fof(f1804,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK157(X0,X1) != X0
| ~ in(sK157(X0,X1),X1) ),
inference(cnf_transformation,[],[f1073]) ).
fof(f7249,plain,
( spl184_538
| ~ spl184_97
| ~ spl184_432 ),
inference(avatar_split_clause,[],[f7019,f5842,f2772,f7247]) ).
fof(f2772,plain,
( spl184_97
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_97])]) ).
fof(f5842,plain,
( spl184_432
<=> ! [X0] :
( subset(X0,sK57)
| ~ subset(X0,sK56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_432])]) ).
fof(f7019,plain,
( ! [X0] : subset(set_difference(sK56,X0),sK57)
| ~ spl184_97
| ~ spl184_432 ),
inference(resolution,[],[f5843,f2773]) ).
fof(f2773,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl184_97 ),
inference(avatar_component_clause,[],[f2772]) ).
fof(f5843,plain,
( ! [X0] :
( ~ subset(X0,sK56)
| subset(X0,sK57) )
| ~ spl184_432 ),
inference(avatar_component_clause,[],[f5842]) ).
fof(f7245,plain,
spl184_537,
inference(avatar_split_clause,[],[f1997,f7243]) ).
fof(f7243,plain,
( spl184_537
<=> ! [X0,X1] :
( relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_537])]) ).
fof(f1997,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1)))
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1484,f1249]) ).
fof(f1484,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f543]) ).
fof(f543,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,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(f7241,plain,
spl184_536,
inference(avatar_split_clause,[],[f1978,f7239]) ).
fof(f7239,plain,
( spl184_536
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_536])]) ).
fof(f1978,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1386,f1249]) ).
fof(f1386,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f512,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f511]) ).
fof(f511,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f223]) ).
fof(f223,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(f7237,plain,
spl184_535,
inference(avatar_split_clause,[],[f1972,f7235]) ).
fof(f7235,plain,
( spl184_535
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_535])]) ).
fof(f1972,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1370,f1158]) ).
fof(f1370,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f493]) ).
fof(f493,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f492]) ).
fof(f492,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f160]) ).
fof(f160,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(f7232,plain,
spl184_534,
inference(avatar_split_clause,[],[f1952,f7230]) ).
fof(f1952,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f1322,f1158,f1158]) ).
fof(f1322,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f820]) ).
fof(f820,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,[],[f819]) ).
fof(f819,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,[],[f162]) ).
fof(f162,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f7228,plain,
spl184_533,
inference(avatar_split_clause,[],[f1405,f7226]) ).
fof(f7226,plain,
( spl184_533
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_533])]) ).
fof(f1405,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f522]) ).
fof(f522,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,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(f7224,plain,
spl184_532,
inference(avatar_split_clause,[],[f1398,f7222]) ).
fof(f7222,plain,
( spl184_532
<=> ! [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,[spl184_532])]) ).
fof(f1398,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f521]) ).
fof(f521,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f520]) ).
fof(f520,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f198]) ).
fof(f198,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(f7220,plain,
spl184_531,
inference(avatar_split_clause,[],[f1355,f7218]) ).
fof(f7218,plain,
( spl184_531
<=> ! [X2,X0,X1] :
( in(sK83(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_531])]) ).
fof(f1355,plain,
! [X2,X0,X1] :
( in(sK83(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f835]) ).
fof(f7216,plain,
spl184_530,
inference(avatar_split_clause,[],[f1351,f7214]) ).
fof(f7214,plain,
( spl184_530
<=> ! [X2,X0,X1] :
( in(sK82(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_530])]) ).
fof(f1351,plain,
! [X2,X0,X1] :
( in(sK82(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f831]) ).
fof(f7212,plain,
spl184_529,
inference(avatar_split_clause,[],[f1341,f7210]) ).
fof(f7210,plain,
( spl184_529
<=> ! [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,[spl184_529])]) ).
fof(f1341,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,[],[f475]) ).
fof(f475,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,[],[f202]) ).
fof(f202,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(f7206,plain,
spl184_528,
inference(avatar_split_clause,[],[f1299,f7204]) ).
fof(f1299,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f453]) ).
fof(f453,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f452]) ).
fof(f452,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f280]) ).
fof(f280,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(f7202,plain,
spl184_527,
inference(avatar_split_clause,[],[f1282,f7200]) ).
fof(f7200,plain,
( spl184_527
<=> ! [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,[spl184_527])]) ).
fof(f1282,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f432]) ).
fof(f432,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(flattening,[],[f431]) ).
fof(f431,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f207]) ).
fof(f207,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(f7198,plain,
spl184_526,
inference(avatar_split_clause,[],[f1239,f7196]) ).
fof(f7196,plain,
( spl184_526
<=> ! [X0,X1] :
( sP5(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_526])]) ).
fof(f1239,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f671]) ).
fof(f671,plain,
! [X0] :
( ! [X1] :
( sP5(X0,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f394,f670,f669,f668]) ).
fof(f670,plain,
! [X0,X1] :
( ( function_inverse(X0) = X1
<=> sP4(X1,X0) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f394,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,[],[f393]) ).
fof(f393,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,[],[f292]) ).
fof(f292,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(f7194,plain,
spl184_525,
inference(avatar_split_clause,[],[f1207,f7192]) ).
fof(f7192,plain,
( spl184_525
<=> ! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_525])]) ).
fof(f1207,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f211]) ).
fof(f211,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(f7190,plain,
spl184_524,
inference(avatar_split_clause,[],[f1171,f7188]) ).
fof(f7188,plain,
( spl184_524
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_524])]) ).
fof(f1171,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f239]) ).
fof(f239,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(f7155,plain,
( ~ spl184_523
| ~ spl184_123
| ~ spl184_514 ),
inference(avatar_split_clause,[],[f7101,f7064,f2975,f7152]) ).
fof(f7152,plain,
( spl184_523
<=> proper_subset(sK57,relation_rng(sK59)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_523])]) ).
fof(f7101,plain,
( ~ proper_subset(sK57,relation_rng(sK59))
| ~ spl184_123
| ~ spl184_514 ),
inference(resolution,[],[f7066,f2976]) ).
fof(f7099,plain,
spl184_522,
inference(avatar_split_clause,[],[f2142,f7097]) ).
fof(f7097,plain,
( spl184_522
<=> ! [X2,X1] :
( sP47(X2,X1,complements_of_subsets(X1,X2))
| ~ sP48(complements_of_subsets(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_522])]) ).
fof(f2142,plain,
! [X2,X1] :
( sP47(X2,X1,complements_of_subsets(X1,X2))
| ~ sP48(complements_of_subsets(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1753]) ).
fof(f1753,plain,
! [X2,X0,X1] :
( sP47(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1046]) ).
fof(f7095,plain,
spl184_521,
inference(avatar_split_clause,[],[f2141,f7093]) ).
fof(f7093,plain,
( spl184_521
<=> ! [X2,X1] :
( sP45(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP46(relation_rng_restriction(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_521])]) ).
fof(f2141,plain,
! [X2,X1] :
( sP45(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP46(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1730]) ).
fof(f1730,plain,
! [X2,X0,X1] :
( sP45(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1039]) ).
fof(f7091,plain,
spl184_520,
inference(avatar_split_clause,[],[f2126,f7089]) ).
fof(f7089,plain,
( spl184_520
<=> ! [X6,X0,X1] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_520])]) ).
fof(f2126,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP35(X0,X1) ),
inference(equality_resolution,[],[f1633]) ).
fof(f1633,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f7087,plain,
spl184_519,
inference(avatar_split_clause,[],[f2120,f7085]) ).
fof(f7085,plain,
( spl184_519
<=> ! [X2,X1] :
( sP25(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP26(relation_dom_restriction(X2,X1),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_519])]) ).
fof(f2120,plain,
! [X2,X1] :
( sP25(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP26(relation_dom_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f1577]) ).
fof(f1577,plain,
! [X2,X0,X1] :
( sP25(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f941]) ).
fof(f7083,plain,
spl184_518,
inference(avatar_split_clause,[],[f2115,f7081]) ).
fof(f7081,plain,
( spl184_518
<=> ! [X2,X1] :
( sP10(X2,X1,relation_composition(X1,X2))
| ~ sP11(relation_composition(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_518])]) ).
fof(f2115,plain,
! [X2,X1] :
( sP10(X2,X1,relation_composition(X1,X2))
| ~ sP11(relation_composition(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f1496]) ).
fof(f1496,plain,
! [X2,X0,X1] :
( sP10(X2,X1,X0)
| relation_composition(X1,X2) != X0
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f882]) ).
fof(f7079,plain,
spl184_517,
inference(avatar_split_clause,[],[f1795,f7077]) ).
fof(f7077,plain,
( spl184_517
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP49(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_517])]) ).
fof(f1795,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP49(X0,X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f7075,plain,
spl184_516,
inference(avatar_split_clause,[],[f1773,f7073]) ).
fof(f7073,plain,
( spl184_516
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_516])]) ).
fof(f1773,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f633]) ).
fof(f633,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f632]) ).
fof(f632,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,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(f7071,plain,
spl184_515,
inference(avatar_split_clause,[],[f1752,f7069]) ).
fof(f7069,plain,
( spl184_515
<=> ! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_515])]) ).
fof(f1752,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f616]) ).
fof(f616,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,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(f7067,plain,
( spl184_514
| ~ spl184_281
| ~ spl184_432 ),
inference(avatar_split_clause,[],[f7020,f5842,f4233,f7064]) ).
fof(f7020,plain,
( subset(relation_rng(sK59),sK57)
| ~ spl184_281
| ~ spl184_432 ),
inference(resolution,[],[f5843,f4235]) ).
fof(f7062,plain,
spl184_513,
inference(avatar_split_clause,[],[f1751,f7060]) ).
fof(f7060,plain,
( spl184_513
<=> ! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_513])]) ).
fof(f1751,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f615]) ).
fof(f615,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f147]) ).
fof(f147,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(f7058,plain,
spl184_512,
inference(avatar_split_clause,[],[f1707,f7056]) ).
fof(f7056,plain,
( spl184_512
<=> ! [X0,X5,X1,X7] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP41(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_512])]) ).
fof(f1707,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP41(X0,X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f7054,plain,
spl184_511,
inference(avatar_split_clause,[],[f1688,f7052]) ).
fof(f7052,plain,
( spl184_511
<=> ! [X2,X0,X4] :
( in(X4,sK142(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK141(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_511])]) ).
fof(f1688,plain,
! [X2,X0,X4] :
( in(X4,sK142(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK141(X0)) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,plain,
! [X0] :
( ! [X2] :
( ( ! [X4] :
( in(X4,sK142(X0,X2))
| ~ subset(X4,X2) )
& in(sK142(X0,X2),sK141(X0)) )
| ~ in(X2,sK141(X0)) )
& ! [X5,X6] :
( in(X6,sK141(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK141(X0)) )
& in(X0,sK141(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142])],[f1015,f1017,f1016]) ).
fof(f1016,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,sK141(X0)) )
| ~ in(X2,sK141(X0)) )
& ! [X6,X5] :
( in(X6,sK141(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK141(X0)) )
& in(X0,sK141(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1017,plain,
! [X0,X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK141(X0)) )
=> ( ! [X4] :
( in(X4,sK142(X0,X2))
| ~ subset(X4,X2) )
& in(sK142(X0,X2),sK141(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1015,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,[],[f592]) ).
fof(f592,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,[],[f591]) ).
fof(f591,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,[],[f343]) ).
fof(f343,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,[],[f337]) ).
fof(f337,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,[],[f331]) ).
fof(f331,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(f7050,plain,
spl184_510,
inference(avatar_split_clause,[],[f1645,f7048]) ).
fof(f7048,plain,
( spl184_510
<=> ! [X2,X4,X0,X1] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_510])]) ).
fof(f1645,plain,
! [X2,X0,X1,X4] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f7046,plain,
spl184_509,
inference(avatar_split_clause,[],[f1631,f7044]) ).
fof(f7044,plain,
( spl184_509
<=> ! [X5,X0,X1] :
( in(sK128(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP35(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_509])]) ).
fof(f1631,plain,
! [X0,X1,X5] :
( in(sK128(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f978]) ).
fof(f7042,plain,
spl184_508,
inference(avatar_split_clause,[],[f1520,f7040]) ).
fof(f7040,plain,
( spl184_508
<=> ! [X2,X0,X1] :
( sP14(X1,X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_508])]) ).
fof(f1520,plain,
! [X2,X0,X1] :
( sP14(X1,X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f684]) ).
fof(f684,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP14(X1,X2,X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f549,f683,f682,f681]) ).
fof(f683,plain,
! [X1,X2,X0] :
( ( relation_isomorphism(X0,X1,X2)
<=> sP13(X0,X2,X1) )
| ~ sP14(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f549,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f548]) ).
fof(f548,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_field(X0) = relation_dom(X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
fof(f7038,plain,
spl184_507,
inference(avatar_split_clause,[],[f1506,f7036]) ).
fof(f7036,plain,
( spl184_507
<=> ! [X2,X0,X1] :
( relation_isomorphism(X2,X0,X1)
| ~ sP13(X2,X1,X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_507])]) ).
fof(f1506,plain,
! [X2,X0,X1] :
( relation_isomorphism(X2,X0,X1)
| ~ sP13(X2,X1,X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f890]) ).
fof(f890,plain,
! [X0,X1,X2] :
( ( ( relation_isomorphism(X2,X0,X1)
| ~ sP13(X2,X1,X0) )
& ( sP13(X2,X1,X0)
| ~ relation_isomorphism(X2,X0,X1) ) )
| ~ sP14(X0,X1,X2) ),
inference(rectify,[],[f889]) ).
fof(f889,plain,
! [X1,X2,X0] :
( ( ( relation_isomorphism(X0,X1,X2)
| ~ sP13(X0,X2,X1) )
& ( sP13(X0,X2,X1)
| ~ relation_isomorphism(X0,X1,X2) ) )
| ~ sP14(X1,X2,X0) ),
inference(nnf_transformation,[],[f683]) ).
fof(f7034,plain,
spl184_506,
inference(avatar_split_clause,[],[f1505,f7032]) ).
fof(f7032,plain,
( spl184_506
<=> ! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ relation_isomorphism(X2,X0,X1)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_506])]) ).
fof(f1505,plain,
! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ relation_isomorphism(X2,X0,X1)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f890]) ).
fof(f7030,plain,
spl184_505,
inference(avatar_split_clause,[],[f1482,f7028]) ).
fof(f7028,plain,
( spl184_505
<=> ! [X0] :
( sP8(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_505])]) ).
fof(f1482,plain,
! [X0] :
( sP8(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f868,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(flattening,[],[f867]) ).
fof(f867,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f675]) ).
fof(f675,plain,
! [X0] :
( sP8(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f7026,plain,
spl184_504,
inference(avatar_split_clause,[],[f1473,f7024]) ).
fof(f7024,plain,
( spl184_504
<=> ! [X2,X0] :
( sP6(X0)
| ~ disjoint(fiber(X0,X2),sK85(X0))
| ~ in(X2,sK85(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_504])]) ).
fof(f1473,plain,
! [X2,X0] :
( sP6(X0)
| ~ disjoint(fiber(X0,X2),sK85(X0))
| ~ in(X2,sK85(X0)) ),
inference(cnf_transformation,[],[f865]) ).
fof(f6818,plain,
( spl184_503
| ~ spl184_1
| ~ spl184_386 ),
inference(avatar_split_clause,[],[f5313,f5208,f2186,f6816]) ).
fof(f5208,plain,
( spl184_386
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_386])]) ).
fof(f5313,plain,
( ! [X0] :
( ~ in(X0,sK56)
| in(X0,sK57) )
| ~ spl184_1
| ~ spl184_386 ),
inference(resolution,[],[f5209,f2188]) ).
fof(f5209,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl184_386 ),
inference(avatar_component_clause,[],[f5208]) ).
fof(f6814,plain,
( spl184_502
| ~ spl184_13
| ~ spl184_109
| ~ spl184_492 ),
inference(avatar_split_clause,[],[f6718,f6715,f2823,f2246,f6812]) ).
fof(f6812,plain,
( spl184_502
<=> ! [X0,X1] :
( sK173 = X0
| in(sK78(X0),X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_502])]) ).
fof(f6715,plain,
( spl184_492
<=> ! [X0,X1] :
( in(sK78(X0),X0)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_492])]) ).
fof(f6718,plain,
( ! [X0,X1] :
( sK173 = X0
| in(sK78(X0),X0)
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_492 ),
inference(forward_demodulation,[],[f6716,f2880]) ).
fof(f6716,plain,
( ! [X0,X1] :
( in(sK78(X0),X0)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_492 ),
inference(avatar_component_clause,[],[f6715]) ).
fof(f6756,plain,
spl184_501,
inference(avatar_split_clause,[],[f2063,f6754]) ).
fof(f6754,plain,
( spl184_501
<=> ! [X2,X0,X3] :
( relation(X0)
| sK136(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_501])]) ).
fof(f2063,plain,
! [X2,X3,X0] :
( relation(X0)
| sK136(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1681,f1913]) ).
fof(f1681,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK136(X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f6752,plain,
spl184_500,
inference(avatar_split_clause,[],[f1938,f6750]) ).
fof(f6750,plain,
( spl184_500
<=> ! [X0,X1] :
( in(sK76(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_500])]) ).
fof(f1938,plain,
! [X0,X1] :
( in(sK76(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1251,f1249]) ).
fof(f1251,plain,
! [X0,X1] :
( in(sK76(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f798]) ).
fof(f798,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK76(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f398,f797]) ).
fof(f797,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK76(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f398,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,[],[f335]) ).
fof(f335,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,[],[f289]) ).
fof(f289,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(f6748,plain,
spl184_499,
inference(avatar_split_clause,[],[f1395,f6746]) ).
fof(f1395,plain,
! [X2,X3,X0,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(cnf_transformation,[],[f518]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f517]) ).
fof(f517,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f210]) ).
fof(f210,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f6744,plain,
spl184_498,
inference(avatar_split_clause,[],[f1371,f6742]) ).
fof(f6742,plain,
( spl184_498
<=> ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_498])]) ).
fof(f1371,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f494]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f293]) ).
fof(f293,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(f6740,plain,
spl184_497,
inference(avatar_split_clause,[],[f1364,f6738]) ).
fof(f6738,plain,
( spl184_497
<=> ! [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,[spl184_497])]) ).
fof(f1364,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f841]) ).
fof(f6734,plain,
spl184_496,
inference(avatar_split_clause,[],[f1361,f6732]) ).
fof(f6732,plain,
( spl184_496
<=> ! [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,[spl184_496])]) ).
fof(f1361,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f839]) ).
fof(f6730,plain,
spl184_495,
inference(avatar_split_clause,[],[f1358,f6728]) ).
fof(f6728,plain,
( spl184_495
<=> ! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_495])]) ).
fof(f1358,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f837]) ).
fof(f6726,plain,
spl184_494,
inference(avatar_split_clause,[],[f1347,f6724]) ).
fof(f6724,plain,
( spl184_494
<=> ! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_494])]) ).
fof(f1347,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f483]) ).
fof(f483,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f482]) ).
fof(f482,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f222]) ).
fof(f222,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f6722,plain,
spl184_493,
inference(avatar_split_clause,[],[f1342,f6720]) ).
fof(f6720,plain,
( spl184_493
<=> ! [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,[spl184_493])]) ).
fof(f1342,plain,
! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f477]) ).
fof(f477,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f476]) ).
fof(f476,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f218]) ).
fof(f218,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(f6717,plain,
spl184_492,
inference(avatar_split_clause,[],[f1258,f6715]) ).
fof(f1258,plain,
! [X0,X1] :
( in(sK78(X0),X0)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f802]) ).
fof(f6713,plain,
spl184_491,
inference(avatar_split_clause,[],[f1224,f6711]) ).
fof(f6711,plain,
( spl184_491
<=> ! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_491])]) ).
fof(f1224,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f392]) ).
fof(f392,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,[],[f391]) ).
fof(f391,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,[],[f295]) ).
fof(f295,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(f6709,plain,
spl184_490,
inference(avatar_split_clause,[],[f1223,f6707]) ).
fof(f6707,plain,
( spl184_490
<=> ! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_490])]) ).
fof(f1223,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f392]) ).
fof(f6705,plain,
spl184_489,
inference(avatar_split_clause,[],[f1209,f6703]) ).
fof(f6703,plain,
( spl184_489
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_489])]) ).
fof(f1209,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,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,[],[f374]) ).
fof(f374,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,[],[f241]) ).
fof(f241,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(f6701,plain,
spl184_488,
inference(avatar_split_clause,[],[f1208,f6699]) ).
fof(f6699,plain,
( spl184_488
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_488])]) ).
fof(f1208,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f6576,plain,
( ~ spl184_2
| spl184_3
| ~ spl184_444 ),
inference(avatar_split_clause,[],[f6121,f5890,f2196,f2191]) ).
fof(f5890,plain,
( spl184_444
<=> sK56 = sK57 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_444])]) ).
fof(f6121,plain,
( ~ relation_of2_as_subset(sK59,sK58,sK56)
| spl184_3
| ~ spl184_444 ),
inference(superposition,[],[f2198,f5892]) ).
fof(f5892,plain,
( sK56 = sK57
| ~ spl184_444 ),
inference(avatar_component_clause,[],[f5890]) ).
fof(f2198,plain,
( ~ relation_of2_as_subset(sK59,sK58,sK57)
| spl184_3 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f6573,plain,
spl184_487,
inference(avatar_split_clause,[],[f2097,f6571]) ).
fof(f6571,plain,
( spl184_487
<=> ! [X2,X1,X3] :
( sP3(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_487])]) ).
fof(f2097,plain,
! [X2,X3,X1] :
( sP3(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ),
inference(equality_resolution,[],[f1238]) ).
fof(f1238,plain,
! [X2,X3,X0,X1] :
( sP3(X0,X1,X2,X3)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f791]) ).
fof(f6569,plain,
spl184_486,
inference(avatar_split_clause,[],[f1878,f6567]) ).
fof(f6567,plain,
( spl184_486
<=> ! [X0,X3,X2,X1] :
( unordered_triple(X0,X1,X2) = X3
| ~ sP55(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_486])]) ).
fof(f1878,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| ~ sP55(X2,X1,X0,X3) ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ~ sP55(X2,X1,X0,X3) )
& ( sP55(X2,X1,X0,X3)
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(nnf_transformation,[],[f749]) ).
fof(f749,plain,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> sP55(X2,X1,X0,X3) ),
inference(definition_folding,[],[f662,f748]) ).
fof(f662,plain,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,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(f6565,plain,
spl184_485,
inference(avatar_split_clause,[],[f1794,f6563]) ).
fof(f6563,plain,
( spl184_485
<=> ! [X5,X0,X1] :
( in(sK156(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP49(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_485])]) ).
fof(f1794,plain,
! [X0,X1,X5] :
( in(sK156(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP49(X0,X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f6561,plain,
spl184_484,
inference(avatar_split_clause,[],[f1793,f6559]) ).
fof(f6559,plain,
( spl184_484
<=> ! [X5,X0,X1] :
( in(X5,sK156(X0,X5))
| ~ in(X5,X1)
| ~ sP49(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_484])]) ).
fof(f1793,plain,
! [X0,X1,X5] :
( in(X5,sK156(X0,X5))
| ~ in(X5,X1)
| ~ sP49(X0,X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f6557,plain,
spl184_483,
inference(avatar_split_clause,[],[f1757,f6555]) ).
fof(f6555,plain,
( spl184_483
<=> ! [X2,X0,X1] :
( sP47(X0,X1,X2)
| element(sK151(X0,X1,X2),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_483])]) ).
fof(f1757,plain,
! [X2,X0,X1] :
( sP47(X0,X1,X2)
| element(sK151(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f6553,plain,
spl184_482,
inference(avatar_split_clause,[],[f1750,f6551]) ).
fof(f6551,plain,
( spl184_482
<=> ! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_482])]) ).
fof(f1750,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f614]) ).
fof(f614,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,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(f6549,plain,
spl184_481,
inference(avatar_split_clause,[],[f1749,f6547]) ).
fof(f6547,plain,
( spl184_481
<=> ! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_481])]) ).
fof(f1749,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,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(f6545,plain,
spl184_480,
inference(avatar_split_clause,[],[f1748,f6543]) ).
fof(f6543,plain,
( spl184_480
<=> ! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_480])]) ).
fof(f1748,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f181]) ).
fof(f181,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(f6541,plain,
spl184_479,
inference(avatar_split_clause,[],[f1747,f6539]) ).
fof(f6539,plain,
( spl184_479
<=> ! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_479])]) ).
fof(f1747,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f611]) ).
fof(f611,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,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(f6536,plain,
( ~ spl184_51
| spl184_468 ),
inference(avatar_contradiction_clause,[],[f6535]) ).
fof(f6535,plain,
( $false
| ~ spl184_51
| spl184_468 ),
inference(resolution,[],[f6493,f2431]) ).
fof(f2431,plain,
( ! [X0] : subset(X0,X0)
| ~ spl184_51 ),
inference(avatar_component_clause,[],[f2430]) ).
fof(f2430,plain,
( spl184_51
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_51])]) ).
fof(f6493,plain,
( ~ subset(sK56,sK56)
| spl184_468 ),
inference(avatar_component_clause,[],[f6491]) ).
fof(f6491,plain,
( spl184_468
<=> subset(sK56,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_468])]) ).
fof(f6534,plain,
spl184_478,
inference(avatar_split_clause,[],[f1746,f6532]) ).
fof(f6532,plain,
( spl184_478
<=> ! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_478])]) ).
fof(f1746,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f610]) ).
fof(f610,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,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(f6530,plain,
spl184_477,
inference(avatar_split_clause,[],[f1745,f6528]) ).
fof(f6528,plain,
( spl184_477
<=> ! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_477])]) ).
fof(f1745,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f609]) ).
fof(f609,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,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(f6526,plain,
spl184_476,
inference(avatar_split_clause,[],[f1709,f6524]) ).
fof(f6524,plain,
( spl184_476
<=> ! [X5,X1,X0] :
( in(X5,X1)
| ~ in(X5,sK146(X0,X5))
| ~ sP41(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_476])]) ).
fof(f1709,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK146(X0,X5))
| ~ sP41(X0,X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f6522,plain,
spl184_475,
inference(avatar_split_clause,[],[f1708,f6520]) ).
fof(f6520,plain,
( spl184_475
<=> ! [X5,X1,X0] :
( in(X5,X1)
| in(sK146(X0,X5),X0)
| ~ sP41(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_475])]) ).
fof(f1708,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK146(X0,X5),X0)
| ~ sP41(X0,X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f6518,plain,
spl184_474,
inference(avatar_split_clause,[],[f1686,f6516]) ).
fof(f6516,plain,
( spl184_474
<=> ! [X6,X0,X5] :
( in(X6,sK141(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK141(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_474])]) ).
fof(f1686,plain,
! [X0,X6,X5] :
( in(X6,sK141(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK141(X0)) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f6514,plain,
spl184_473,
inference(avatar_split_clause,[],[f1652,f6512]) ).
fof(f6512,plain,
( spl184_473
<=> ! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP39(X0,X1,X2)
| ~ sP40(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_473])]) ).
fof(f1652,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP39(X0,X1,X2)
| ~ sP40(X0) ),
inference(cnf_transformation,[],[f986]) ).
fof(f986,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP39(X0,X1,X2) )
& ( sP39(X0,X1,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP40(X0) ),
inference(nnf_transformation,[],[f722]) ).
fof(f722,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP39(X0,X1,X2) )
| ~ sP40(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
fof(f6510,plain,
spl184_472,
inference(avatar_split_clause,[],[f1644,f6508]) ).
fof(f6508,plain,
( spl184_472
<=> ! [X4,X0,X1,X2] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_472])]) ).
fof(f1644,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f985]) ).
fof(f6506,plain,
spl184_471,
inference(avatar_split_clause,[],[f1643,f6504]) ).
fof(f6504,plain,
( spl184_471
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP37(X1,X0,X2)
| ~ sP38(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_471])]) ).
fof(f1643,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP37(X1,X0,X2)
| ~ sP38(X0) ),
inference(cnf_transformation,[],[f980]) ).
fof(f980,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP37(X1,X0,X2) )
& ( sP37(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP38(X0) ),
inference(nnf_transformation,[],[f719]) ).
fof(f719,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP37(X1,X0,X2) )
| ~ sP38(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f6502,plain,
spl184_470,
inference(avatar_split_clause,[],[f1626,f6500]) ).
fof(f6500,plain,
( spl184_470
<=> ! [X0] :
( sP33(X0)
| apply(X0,sK124(X0)) = apply(X0,sK125(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_470])]) ).
fof(f1626,plain,
! [X0] :
( sP33(X0)
| apply(X0,sK124(X0)) = apply(X0,sK125(X0)) ),
inference(cnf_transformation,[],[f971]) ).
fof(f6498,plain,
spl184_469,
inference(avatar_split_clause,[],[f1620,f6496]) ).
fof(f6496,plain,
( spl184_469
<=> ! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_469])]) ).
fof(f1620,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f575]) ).
fof(f575,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f574]) ).
fof(f574,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,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(f6494,plain,
( ~ spl184_468
| spl184_443
| ~ spl184_444 ),
inference(avatar_split_clause,[],[f6131,f5890,f5886,f6491]) ).
fof(f5886,plain,
( spl184_443
<=> subset(sK57,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_443])]) ).
fof(f6131,plain,
( ~ subset(sK56,sK56)
| spl184_443
| ~ spl184_444 ),
inference(superposition,[],[f5888,f5892]) ).
fof(f5888,plain,
( ~ subset(sK57,sK56)
| spl184_443 ),
inference(avatar_component_clause,[],[f5886]) ).
fof(f6489,plain,
spl184_467,
inference(avatar_split_clause,[],[f1605,f6487]) ).
fof(f6487,plain,
( spl184_467
<=> ! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP31(X1,X0,X2)
| ~ sP32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_467])]) ).
fof(f1605,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| ~ sP31(X1,X0,X2)
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f960,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP31(X1,X0,X2) )
& ( sP31(X1,X0,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP32(X0) ),
inference(nnf_transformation,[],[f710]) ).
fof(f710,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP31(X1,X0,X2) )
| ~ sP32(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f6485,plain,
spl184_466,
inference(avatar_split_clause,[],[f1596,f6483]) ).
fof(f6483,plain,
( spl184_466
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP29(X1,X0,X2)
| ~ sP30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_466])]) ).
fof(f1596,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP29(X1,X0,X2)
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f953]) ).
fof(f953,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP29(X1,X0,X2) )
& ( sP29(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP30(X0) ),
inference(nnf_transformation,[],[f707]) ).
fof(f707,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP29(X1,X0,X2) )
| ~ sP30(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f6481,plain,
spl184_465,
inference(avatar_split_clause,[],[f1587,f6479]) ).
fof(f6479,plain,
( spl184_465
<=> ! [X2,X0,X1] :
( fiber(X0,X1) = X2
| ~ sP27(X0,X1,X2)
| ~ sP28(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_465])]) ).
fof(f1587,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| ~ sP27(X0,X1,X2)
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f947]) ).
fof(f947,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ~ sP27(X0,X1,X2) )
& ( sP27(X0,X1,X2)
| fiber(X0,X1) != X2 ) )
| ~ sP28(X0) ),
inference(nnf_transformation,[],[f704]) ).
fof(f704,plain,
! [X0] :
( ! [X1,X2] :
( fiber(X0,X1) = X2
<=> sP27(X0,X1,X2) )
| ~ sP28(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f6191,plain,
( spl184_464
| ~ spl184_13
| ~ spl184_109
| ~ spl184_451 ),
inference(avatar_split_clause,[],[f6074,f6071,f2823,f2246,f6189]) ).
fof(f6189,plain,
( spl184_464
<=> ! [X0,X1] :
( sK173 = X0
| ordinal(sK78(X0))
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_464])]) ).
fof(f6071,plain,
( spl184_451
<=> ! [X0,X1] :
( ordinal(sK78(X0))
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_451])]) ).
fof(f6074,plain,
( ! [X0,X1] :
( sK173 = X0
| ordinal(sK78(X0))
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_451 ),
inference(forward_demodulation,[],[f6072,f2880]) ).
fof(f6072,plain,
( ! [X0,X1] :
( ordinal(sK78(X0))
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) )
| ~ spl184_451 ),
inference(avatar_component_clause,[],[f6071]) ).
fof(f6135,plain,
spl184_463,
inference(avatar_split_clause,[],[f2091,f6133]) ).
fof(f6133,plain,
( spl184_463
<=> ! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP54(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_463])]) ).
fof(f2091,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP54(X1,X0,X2) ),
inference(definition_unfolding,[],[f1867,f1249]) ).
fof(f1867,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP54(X1,X0,X2) ),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP54(X1,X0,X2) )
& ( sP54(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f747]) ).
fof(f747,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP54(X1,X0,X2) ),
inference(definition_folding,[],[f46,f746]) ).
fof(f46,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(f6119,plain,
spl184_462,
inference(avatar_split_clause,[],[f2067,f6117]) ).
fof(f6117,plain,
( spl184_462
<=> ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_462])]) ).
fof(f2067,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f1699,f1249,f1249]) ).
fof(f1699,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6115,plain,
spl184_461,
inference(avatar_split_clause,[],[f1390,f6113]) ).
fof(f6113,plain,
( spl184_461
<=> ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_461])]) ).
fof(f1390,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f847]) ).
fof(f847,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,[],[f846]) ).
fof(f846,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,[],[f263]) ).
fof(f263,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(f6111,plain,
spl184_460,
inference(avatar_split_clause,[],[f1387,f6109]) ).
fof(f6109,plain,
( spl184_460
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_460])]) ).
fof(f1387,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f514]) ).
fof(f514,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f513]) ).
fof(f513,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f324]) ).
fof(f324,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(f6107,plain,
spl184_459,
inference(avatar_split_clause,[],[f1363,f6105]) ).
fof(f6105,plain,
( spl184_459
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_459])]) ).
fof(f1363,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f841]) ).
fof(f6103,plain,
spl184_458,
inference(avatar_split_clause,[],[f1360,f6101]) ).
fof(f6101,plain,
( spl184_458
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_458])]) ).
fof(f1360,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f839]) ).
fof(f6099,plain,
spl184_457,
inference(avatar_split_clause,[],[f1348,f6097]) ).
fof(f6097,plain,
( spl184_457
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_457])]) ).
fof(f1348,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f483]) ).
fof(f6095,plain,
spl184_456,
inference(avatar_split_clause,[],[f1340,f6093]) ).
fof(f6093,plain,
( spl184_456
<=> ! [X2,X0,X1] :
( subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_456])]) ).
fof(f1340,plain,
! [X2,X0,X1] :
( subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f474]) ).
fof(f474,plain,
! [X0,X1,X2] :
( subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f233]) ).
fof(f233,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f6091,plain,
spl184_455,
inference(avatar_split_clause,[],[f1301,f6089]) ).
fof(f6089,plain,
( spl184_455
<=> ! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_455])]) ).
fof(f1301,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f455]) ).
fof(f455,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f205,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(f6087,plain,
spl184_454,
inference(avatar_split_clause,[],[f1270,f6085]) ).
fof(f6085,plain,
( spl184_454
<=> ! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_454])]) ).
fof(f1270,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f414]) ).
fof(f414,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f219,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(f6083,plain,
spl184_453,
inference(avatar_split_clause,[],[f1269,f6081]) ).
fof(f6081,plain,
( spl184_453
<=> ! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_453])]) ).
fof(f1269,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f413]) ).
fof(f413,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f221]) ).
fof(f221,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(f6079,plain,
( spl184_452
| spl184_444
| ~ spl184_1
| ~ spl184_385 ),
inference(avatar_split_clause,[],[f5289,f5204,f2186,f5890,f6076]) ).
fof(f6076,plain,
( spl184_452
<=> proper_subset(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_452])]) ).
fof(f5204,plain,
( spl184_385
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_385])]) ).
fof(f5289,plain,
( sK56 = sK57
| proper_subset(sK56,sK57)
| ~ spl184_1
| ~ spl184_385 ),
inference(resolution,[],[f5205,f2188]) ).
fof(f5205,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) )
| ~ spl184_385 ),
inference(avatar_component_clause,[],[f5204]) ).
fof(f6073,plain,
spl184_451,
inference(avatar_split_clause,[],[f1257,f6071]) ).
fof(f1257,plain,
! [X0,X1] :
( ordinal(sK78(X0))
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f802]) ).
fof(f6069,plain,
spl184_450,
inference(avatar_split_clause,[],[f1243,f6067]) ).
fof(f6067,plain,
( spl184_450
<=> ! [X4,X0,X3] :
( in(X4,sK75(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK75(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_450])]) ).
fof(f1243,plain,
! [X3,X0,X4] :
( in(X4,sK75(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK75(X0)) ),
inference(cnf_transformation,[],[f796]) ).
fof(f796,plain,
! [X0] :
( ! [X2] :
( in(powerset(X2),sK75(X0))
| ~ in(X2,sK75(X0)) )
& ! [X3,X4] :
( in(X4,sK75(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK75(X0)) )
& in(X0,sK75(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f794,f795]) ).
fof(f795,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),sK75(X0))
| ~ in(X2,sK75(X0)) )
& ! [X4,X3] :
( in(X4,sK75(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK75(X0)) )
& in(X0,sK75(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f794,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,[],[f397]) ).
fof(f397,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,[],[f396]) ).
fof(f396,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,[],[f344]) ).
fof(f344,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,[],[f334]) ).
fof(f334,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,[],[f201]) ).
fof(f201,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(f6065,plain,
spl184_449,
inference(avatar_split_clause,[],[f1206,f6063]) ).
fof(f6063,plain,
( spl184_449
<=> ! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_449])]) ).
fof(f1206,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f276]) ).
fof(f276,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(f6061,plain,
spl184_448,
inference(avatar_split_clause,[],[f1205,f6059]) ).
fof(f6059,plain,
( spl184_448
<=> ! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_448])]) ).
fof(f1205,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f277]) ).
fof(f277,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(f5905,plain,
( spl184_447
| ~ spl184_215
| ~ spl184_423 ),
inference(avatar_split_clause,[],[f5808,f5805,f3624,f5903]) ).
fof(f5903,plain,
( spl184_447
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_447])]) ).
fof(f3624,plain,
( spl184_215
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_215])]) ).
fof(f5805,plain,
( spl184_423
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_423])]) ).
fof(f5808,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) )
| ~ spl184_215
| ~ spl184_423 ),
inference(forward_demodulation,[],[f5806,f3625]) ).
fof(f3625,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl184_215 ),
inference(avatar_component_clause,[],[f3624]) ).
fof(f5806,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) )
| ~ spl184_423 ),
inference(avatar_component_clause,[],[f5805]) ).
fof(f5901,plain,
spl184_446,
inference(avatar_split_clause,[],[f1861,f5899]) ).
fof(f5899,plain,
( spl184_446
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_446])]) ).
fof(f1861,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f5897,plain,
spl184_445,
inference(avatar_split_clause,[],[f1860,f5895]) ).
fof(f5895,plain,
( spl184_445
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_445])]) ).
fof(f1860,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f5893,plain,
( ~ spl184_443
| spl184_444
| ~ spl184_1
| ~ spl184_384 ),
inference(avatar_split_clause,[],[f5265,f5200,f2186,f5890,f5886]) ).
fof(f5200,plain,
( spl184_384
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_384])]) ).
fof(f5265,plain,
( sK56 = sK57
| ~ subset(sK57,sK56)
| ~ spl184_1
| ~ spl184_384 ),
inference(resolution,[],[f5201,f2188]) ).
fof(f5201,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl184_384 ),
inference(avatar_component_clause,[],[f5200]) ).
fof(f5884,plain,
spl184_442,
inference(avatar_split_clause,[],[f1853,f5882]) ).
fof(f5882,plain,
( spl184_442
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_442])]) ).
fof(f1853,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f5880,plain,
spl184_441,
inference(avatar_split_clause,[],[f1852,f5878]) ).
fof(f5878,plain,
( spl184_441
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_441])]) ).
fof(f1852,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f5876,plain,
spl184_440,
inference(avatar_split_clause,[],[f1846,f5874]) ).
fof(f5874,plain,
( spl184_440
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_440])]) ).
fof(f1846,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f5872,plain,
spl184_439,
inference(avatar_split_clause,[],[f1845,f5870]) ).
fof(f5870,plain,
( spl184_439
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_439])]) ).
fof(f1845,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1104]) ).
fof(f5868,plain,
spl184_438,
inference(avatar_split_clause,[],[f1819,f5866]) ).
fof(f5866,plain,
( spl184_438
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_438])]) ).
fof(f1819,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f656]) ).
fof(f656,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f655]) ).
fof(f655,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f288]) ).
fof(f288,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f5864,plain,
spl184_437,
inference(avatar_split_clause,[],[f1817,f5862]) ).
fof(f5862,plain,
( spl184_437
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_437])]) ).
fof(f1817,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f653]) ).
fof(f653,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f5860,plain,
spl184_436,
inference(avatar_split_clause,[],[f1814,f5858]) ).
fof(f5858,plain,
( spl184_436
<=> ! [X0,X1,X3] :
( ~ in(X3,sK159(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_436])]) ).
fof(f1814,plain,
! [X3,X0,X1] :
( ~ in(X3,sK159(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK159(X1))
| ~ in(X3,X1) )
& in(sK159(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f652,f1079]) ).
fof(f1079,plain,
! [X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
=> ( ! [X3] :
( ~ in(X3,sK159(X1))
| ~ in(X3,X1) )
& in(sK159(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f652,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f316]) ).
fof(f316,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(f5856,plain,
spl184_435,
inference(avatar_split_clause,[],[f1765,f5854]) ).
fof(f1765,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f624]) ).
fof(f624,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,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(f5852,plain,
spl184_434,
inference(avatar_split_clause,[],[f1764,f5850]) ).
fof(f5850,plain,
( spl184_434
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_434])]) ).
fof(f1764,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1052]) ).
fof(f5848,plain,
spl184_433,
inference(avatar_split_clause,[],[f1763,f5846]) ).
fof(f5846,plain,
( spl184_433
<=> ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_433])]) ).
fof(f1763,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f622]) ).
fof(f622,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,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(f5844,plain,
( spl184_432
| ~ spl184_1
| ~ spl184_374 ),
inference(avatar_split_clause,[],[f5138,f4938,f2186,f5842]) ).
fof(f4938,plain,
( spl184_374
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_374])]) ).
fof(f5138,plain,
( ! [X0] :
( subset(X0,sK57)
| ~ subset(X0,sK56) )
| ~ spl184_1
| ~ spl184_374 ),
inference(resolution,[],[f4939,f2188]) ).
fof(f4939,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl184_374 ),
inference(avatar_component_clause,[],[f4938]) ).
fof(f5840,plain,
spl184_431,
inference(avatar_split_clause,[],[f1744,f5838]) ).
fof(f5838,plain,
( spl184_431
<=> ! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_431])]) ).
fof(f1744,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f608]) ).
fof(f608,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,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(f5836,plain,
spl184_430,
inference(avatar_split_clause,[],[f1722,f5834]) ).
fof(f5834,plain,
( spl184_430
<=> ! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP43(X1,X0)
| ~ sP44(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_430])]) ).
fof(f1722,plain,
! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP43(X1,X0)
| ~ sP44(X0,X1) ),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,plain,
! [X0,X1] :
( ( ( identity_relation(X1) = X0
| ~ sP43(X1,X0) )
& ( sP43(X1,X0)
| identity_relation(X1) != X0 ) )
| ~ sP44(X0,X1) ),
inference(rectify,[],[f1031]) ).
fof(f1031,plain,
! [X1,X0] :
( ( ( identity_relation(X0) = X1
| ~ sP43(X0,X1) )
& ( sP43(X0,X1)
| identity_relation(X0) != X1 ) )
| ~ sP44(X1,X0) ),
inference(nnf_transformation,[],[f728]) ).
fof(f728,plain,
! [X1,X0] :
( ( identity_relation(X0) = X1
<=> sP43(X0,X1) )
| ~ sP44(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP44])]) ).
fof(f5832,plain,
spl184_429,
inference(avatar_split_clause,[],[f1706,f5830]) ).
fof(f5830,plain,
( spl184_429
<=> ! [X0,X1] :
( set_meet(X1) = X0
| ~ sP41(X1,X0)
| ~ sP42(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_429])]) ).
fof(f1706,plain,
! [X0,X1] :
( set_meet(X1) = X0
| ~ sP41(X1,X0)
| ~ sP42(X0,X1) ),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP41(X1,X0) )
& ( sP41(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP42(X0,X1) ),
inference(rectify,[],[f1022]) ).
fof(f1022,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP41(X0,X1) )
& ( sP41(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP42(X1,X0) ),
inference(nnf_transformation,[],[f725]) ).
fof(f725,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP41(X0,X1) )
| ~ sP42(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
fof(f5828,plain,
spl184_428,
inference(avatar_split_clause,[],[f1687,f5826]) ).
fof(f5826,plain,
( spl184_428
<=> ! [X2,X0] :
( in(sK142(X0,X2),sK141(X0))
| ~ in(X2,sK141(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_428])]) ).
fof(f1687,plain,
! [X2,X0] :
( in(sK142(X0,X2),sK141(X0))
| ~ in(X2,sK141(X0)) ),
inference(cnf_transformation,[],[f1018]) ).
fof(f5824,plain,
spl184_427,
inference(avatar_split_clause,[],[f1555,f5822]) ).
fof(f5822,plain,
( spl184_427
<=> ! [X0,X1] :
( sP21(X0,X1)
| sK104(X0,X1) != sK105(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_427])]) ).
fof(f1555,plain,
! [X0,X1] :
( sP21(X0,X1)
| sK104(X0,X1) != sK105(X0,X1) ),
inference(cnf_transformation,[],[f922]) ).
fof(f5820,plain,
spl184_426,
inference(avatar_split_clause,[],[f1548,f5818]) ).
fof(f5818,plain,
( spl184_426
<=> ! [X0,X1] :
( sP19(X0,X1)
| sK102(X0,X1) != sK103(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_426])]) ).
fof(f1548,plain,
! [X0,X1] :
( sP19(X0,X1)
| sK102(X0,X1) != sK103(X0,X1) ),
inference(cnf_transformation,[],[f917]) ).
fof(f5816,plain,
spl184_425,
inference(avatar_split_clause,[],[f1531,f5814]) ).
fof(f5814,plain,
( spl184_425
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_425])]) ).
fof(f1531,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f5812,plain,
spl184_424,
inference(avatar_split_clause,[],[f1504,f5810]) ).
fof(f5810,plain,
( spl184_424
<=> ! [X2,X0,X1] :
( sP11(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_424])]) ).
fof(f1504,plain,
! [X2,X0,X1] :
( sP11(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f680]) ).
fof(f680,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP11(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f547,f679,f678]) ).
fof(f547,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,[],[f68]) ).
fof(f68,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(f5807,plain,
spl184_423,
inference(avatar_split_clause,[],[f1458,f5805]) ).
fof(f1458,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f536]) ).
fof(f536,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,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(f5803,plain,
spl184_422,
inference(avatar_split_clause,[],[f1237,f5801]) ).
fof(f5801,plain,
( spl184_422
<=> ! [X0,X3,X2,X1] :
( sP3(X0,X1,X2,X3)
| apply(X3,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_422])]) ).
fof(f1237,plain,
! [X2,X3,X0,X1] :
( sP3(X0,X1,X2,X3)
| apply(X3,X0) = X1 ),
inference(cnf_transformation,[],[f791]) ).
fof(f5798,plain,
spl184_421,
inference(avatar_split_clause,[],[f1226,f5796]) ).
fof(f5796,plain,
( spl184_421
<=> ! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_421])]) ).
fof(f1226,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f783]) ).
fof(f783,plain,
! [X0,X1] :
( ( ( function_inverse(X0) = X1
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| function_inverse(X0) != X1 ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f670]) ).
fof(f5761,plain,
( spl184_420
| ~ spl184_13
| ~ spl184_109
| ~ spl184_415 ),
inference(avatar_split_clause,[],[f5442,f5439,f2823,f2246,f5759]) ).
fof(f5759,plain,
( spl184_420
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK173
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_420])]) ).
fof(f5439,plain,
( spl184_415
<=> ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_415])]) ).
fof(f5442,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK173
| ~ disjoint(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_415 ),
inference(forward_demodulation,[],[f5440,f2880]) ).
fof(f5440,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl184_415 ),
inference(avatar_component_clause,[],[f5439]) ).
fof(f5757,plain,
( spl184_419
| ~ spl184_13
| ~ spl184_109
| ~ spl184_414 ),
inference(avatar_split_clause,[],[f5437,f5434,f2823,f2246,f5755]) ).
fof(f5755,plain,
( spl184_419
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK173
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_419])]) ).
fof(f5434,plain,
( spl184_414
<=> ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_414])]) ).
fof(f5437,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK173
| disjoint(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_414 ),
inference(forward_demodulation,[],[f5435,f2880]) ).
fof(f5435,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) )
| ~ spl184_414 ),
inference(avatar_component_clause,[],[f5434]) ).
fof(f5709,plain,
( spl184_418
| ~ spl184_171
| ~ spl184_410 ),
inference(avatar_split_clause,[],[f5490,f5417,f3189,f5706]) ).
fof(f5706,plain,
( spl184_418
<=> sP52(sK56,sK57,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_418])]) ).
fof(f3189,plain,
( spl184_171
<=> ! [X0,X1] : sP52(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_171])]) ).
fof(f5417,plain,
( spl184_410
<=> sK57 = set_union2(sK57,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_410])]) ).
fof(f5490,plain,
( sP52(sK56,sK57,sK57)
| ~ spl184_171
| ~ spl184_410 ),
inference(superposition,[],[f3190,f5419]) ).
fof(f5419,plain,
( sK57 = set_union2(sK57,sK56)
| ~ spl184_410 ),
inference(avatar_component_clause,[],[f5417]) ).
fof(f3190,plain,
( ! [X0,X1] : sP52(X1,X0,set_union2(X0,X1))
| ~ spl184_171 ),
inference(avatar_component_clause,[],[f3189]) ).
fof(f5450,plain,
( spl184_417
| ~ spl184_13
| ~ spl184_109
| ~ spl184_397 ),
inference(avatar_split_clause,[],[f5367,f5363,f2823,f2246,f5448]) ).
fof(f5448,plain,
( spl184_417
<=> ! [X0] :
( relation_rng(X0) != sK173
| relation_dom(X0) = sK173
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_417])]) ).
fof(f5363,plain,
( spl184_397
<=> ! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_397])]) ).
fof(f5367,plain,
( ! [X0] :
( relation_rng(X0) != sK173
| relation_dom(X0) = sK173
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_397 ),
inference(forward_demodulation,[],[f5366,f2880]) ).
fof(f5366,plain,
( ! [X0] :
( relation_dom(X0) = sK173
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_397 ),
inference(forward_demodulation,[],[f5364,f2880]) ).
fof(f5364,plain,
( ! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl184_397 ),
inference(avatar_component_clause,[],[f5363]) ).
fof(f5446,plain,
( spl184_416
| ~ spl184_13
| ~ spl184_109
| ~ spl184_396 ),
inference(avatar_split_clause,[],[f5361,f5357,f2823,f2246,f5444]) ).
fof(f5444,plain,
( spl184_416
<=> ! [X0] :
( relation_dom(X0) != sK173
| relation_rng(X0) = sK173
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_416])]) ).
fof(f5357,plain,
( spl184_396
<=> ! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_396])]) ).
fof(f5361,plain,
( ! [X0] :
( relation_dom(X0) != sK173
| relation_rng(X0) = sK173
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_396 ),
inference(forward_demodulation,[],[f5360,f2880]) ).
fof(f5360,plain,
( ! [X0] :
( relation_rng(X0) = sK173
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_396 ),
inference(forward_demodulation,[],[f5358,f2880]) ).
fof(f5358,plain,
( ! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl184_396 ),
inference(avatar_component_clause,[],[f5357]) ).
fof(f5441,plain,
spl184_415,
inference(avatar_split_clause,[],[f2082,f5439]) ).
fof(f2082,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1788,f1249]) ).
fof(f1788,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f5436,plain,
spl184_414,
inference(avatar_split_clause,[],[f2081,f5434]) ).
fof(f2081,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f1789,f1249]) ).
fof(f1789,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f1058]) ).
fof(f5432,plain,
spl184_413,
inference(avatar_split_clause,[],[f2080,f5430]) ).
fof(f5430,plain,
( spl184_413
<=> ! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_413])]) ).
fof(f2080,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1781,f1249]) ).
fof(f1781,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f645]) ).
fof(f645,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f644]) ).
fof(f644,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f5428,plain,
spl184_412,
inference(avatar_split_clause,[],[f1974,f5426]) ).
fof(f5426,plain,
( spl184_412
<=> ! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_412])]) ).
fof(f1974,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f1375,f1158]) ).
fof(f1375,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f498]) ).
fof(f498,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f332]) ).
fof(f332,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f5424,plain,
spl184_411,
inference(avatar_split_clause,[],[f1973,f5422]) ).
fof(f5422,plain,
( spl184_411
<=> ! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_411])]) ).
fof(f1973,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f1374,f1158]) ).
fof(f1374,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f497]) ).
fof(f497,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f325]) ).
fof(f325,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f5420,plain,
( spl184_410
| ~ spl184_13
| ~ spl184_102
| ~ spl184_109
| ~ spl184_215
| ~ spl184_348
| ~ spl184_362 ),
inference(avatar_split_clause,[],[f5117,f4889,f4543,f3624,f2823,f2794,f2246,f5417]) ).
fof(f2794,plain,
( spl184_102
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_102])]) ).
fof(f4889,plain,
( spl184_362
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_362])]) ).
fof(f5117,plain,
( sK57 = set_union2(sK57,sK56)
| ~ spl184_13
| ~ spl184_102
| ~ spl184_109
| ~ spl184_215
| ~ spl184_348
| ~ spl184_362 ),
inference(forward_demodulation,[],[f5116,f3792]) ).
fof(f3792,plain,
( ! [X0] : set_union2(sK173,X0) = X0
| ~ spl184_13
| ~ spl184_102
| ~ spl184_109
| ~ spl184_215 ),
inference(forward_demodulation,[],[f3780,f2880]) ).
fof(f3780,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl184_102
| ~ spl184_215 ),
inference(superposition,[],[f3625,f2795]) ).
fof(f2795,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl184_102 ),
inference(avatar_component_clause,[],[f2794]) ).
fof(f5116,plain,
( set_union2(sK57,sK56) = set_union2(sK173,sK57)
| ~ spl184_215
| ~ spl184_348
| ~ spl184_362 ),
inference(forward_demodulation,[],[f5112,f3625]) ).
fof(f5112,plain,
( set_union2(sK57,sK56) = set_union2(sK57,sK173)
| ~ spl184_348
| ~ spl184_362 ),
inference(superposition,[],[f4890,f4545]) ).
fof(f4890,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))
| ~ spl184_362 ),
inference(avatar_component_clause,[],[f4889]) ).
fof(f5415,plain,
spl184_409,
inference(avatar_split_clause,[],[f1961,f5413]) ).
fof(f5413,plain,
( spl184_409
<=> ! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_409])]) ).
fof(f1961,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f1336,f1158]) ).
fof(f1336,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f306]) ).
fof(f306,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f5411,plain,
spl184_408,
inference(avatar_split_clause,[],[f1960,f5409]) ).
fof(f5409,plain,
( spl184_408
<=> ! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_408])]) ).
fof(f1960,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f1337,f1158]) ).
fof(f1337,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f827]) ).
fof(f5407,plain,
spl184_407,
inference(avatar_split_clause,[],[f1946,f5405]) ).
fof(f5405,plain,
( spl184_407
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_407])]) ).
fof(f1946,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f1300,f1158,f1158]) ).
fof(f1300,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f454]) ).
fof(f454,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f310]) ).
fof(f310,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f5403,plain,
spl184_406,
inference(avatar_split_clause,[],[f1945,f5401]) ).
fof(f5401,plain,
( spl184_406
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_406])]) ).
fof(f1945,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1292,f1249]) ).
fof(f1292,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f444]) ).
fof(f444,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f244]) ).
fof(f244,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f5399,plain,
spl184_405,
inference(avatar_split_clause,[],[f1943,f5397]) ).
fof(f5397,plain,
( spl184_405
<=> ! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_405])]) ).
fof(f1943,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f1288,f1158]) ).
fof(f1288,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
fof(f440,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f5395,plain,
spl184_404,
inference(avatar_split_clause,[],[f1937,f5393]) ).
fof(f1937,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f1252,f1249]) ).
fof(f1252,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f798]) ).
fof(f5391,plain,
spl184_403,
inference(avatar_split_clause,[],[f1369,f5389]) ).
fof(f5389,plain,
( spl184_403
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_403])]) ).
fof(f1369,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f491]) ).
fof(f491,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,[],[f196]) ).
fof(f196,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(f5387,plain,
spl184_402,
inference(avatar_split_clause,[],[f1368,f5385]) ).
fof(f5385,plain,
( spl184_402
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_402])]) ).
fof(f1368,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f491]) ).
fof(f5383,plain,
spl184_401,
inference(avatar_split_clause,[],[f1367,f5381]) ).
fof(f5381,plain,
( spl184_401
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_401])]) ).
fof(f1367,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f255]) ).
fof(f255,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(f5379,plain,
spl184_400,
inference(avatar_split_clause,[],[f1357,f5377]) ).
fof(f5377,plain,
( spl184_400
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_400])]) ).
fof(f1357,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f837]) ).
fof(f5375,plain,
spl184_399,
inference(avatar_split_clause,[],[f1294,f5373]) ).
fof(f5373,plain,
( spl184_399
<=> ! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_399])]) ).
fof(f1294,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f446]) ).
fof(f446,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,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(f5371,plain,
spl184_398,
inference(avatar_split_clause,[],[f1268,f5369]) ).
fof(f5369,plain,
( spl184_398
<=> ! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_398])]) ).
fof(f1268,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f328]) ).
fof(f328,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(f5365,plain,
spl184_397,
inference(avatar_split_clause,[],[f1202,f5363]) ).
fof(f1202,plain,
! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f779]) ).
fof(f779,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,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ( relation_dom(X0) = empty_set
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f305]) ).
fof(f305,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(f5359,plain,
spl184_396,
inference(avatar_split_clause,[],[f1201,f5357]) ).
fof(f1201,plain,
! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f779]) ).
fof(f5355,plain,
spl184_395,
inference(avatar_split_clause,[],[f1161,f5353]) ).
fof(f5353,plain,
( spl184_395
<=> ! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_395])]) ).
fof(f1161,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f231]) ).
fof(f231,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(f5243,plain,
( spl184_394
| ~ spl184_188
| ~ spl184_275
| ~ spl184_348 ),
inference(avatar_split_clause,[],[f5115,f4543,f4029,f3484,f5240]) ).
fof(f5240,plain,
( spl184_394
<=> sP54(sK57,sK56,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_394])]) ).
fof(f4029,plain,
( spl184_275
<=> ! [X0,X1] : sP54(X1,X0,set_difference(X0,set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_275])]) ).
fof(f5115,plain,
( sP54(sK57,sK56,sK56)
| ~ spl184_188
| ~ spl184_275
| ~ spl184_348 ),
inference(forward_demodulation,[],[f5109,f3485]) ).
fof(f5109,plain,
( sP54(sK57,sK56,set_difference(sK56,sK173))
| ~ spl184_275
| ~ spl184_348 ),
inference(superposition,[],[f4030,f4545]) ).
fof(f4030,plain,
( ! [X0,X1] : sP54(X1,X0,set_difference(X0,set_difference(X0,X1)))
| ~ spl184_275 ),
inference(avatar_component_clause,[],[f4029]) ).
fof(f5238,plain,
spl184_393,
inference(avatar_split_clause,[],[f1868,f5236]) ).
fof(f5236,plain,
( spl184_393
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_393])]) ).
fof(f1868,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f661]) ).
fof(f661,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f298]) ).
fof(f298,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f5234,plain,
spl184_392,
inference(avatar_split_clause,[],[f1859,f5232]) ).
fof(f5232,plain,
( spl184_392
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP53(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_392])]) ).
fof(f1859,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP53(X1,X0,X2) ),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP53(X1,X0,X2) )
& ( sP53(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f745]) ).
fof(f745,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP53(X1,X0,X2) ),
inference(definition_folding,[],[f54,f744]) ).
fof(f54,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(f5230,plain,
spl184_391,
inference(avatar_split_clause,[],[f1851,f5228]) ).
fof(f5228,plain,
( spl184_391
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP52(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_391])]) ).
fof(f1851,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP52(X1,X0,X2) ),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP52(X1,X0,X2) )
& ( sP52(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f743]) ).
fof(f743,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP52(X1,X0,X2) ),
inference(definition_folding,[],[f40,f742]) ).
fof(f40,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(f5226,plain,
spl184_390,
inference(avatar_split_clause,[],[f1843,f5224]) ).
fof(f5224,plain,
( spl184_390
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP51(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_390])]) ).
fof(f1843,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP51(X1,X0,X2) ),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP51(X1,X0,X2) )
& ( sP51(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f741]) ).
fof(f741,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP51(X1,X0,X2) ),
inference(definition_folding,[],[f41,f740]) ).
fof(f41,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(f5222,plain,
spl184_389,
inference(avatar_split_clause,[],[f1833,f5220]) ).
fof(f5220,plain,
( spl184_389
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP50(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_389])]) ).
fof(f1833,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP50(X1,X0,X2) ),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP50(X1,X0,X2) )
& ( sP50(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f739]) ).
fof(f739,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP50(X1,X0,X2) ),
inference(definition_folding,[],[f38,f738]) ).
fof(f38,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(f5218,plain,
spl184_388,
inference(avatar_split_clause,[],[f1823,f5216]) ).
fof(f5216,plain,
( spl184_388
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_388])]) ).
fof(f1823,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,plain,
! [X0,X1,X2] :
( ( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) )
& ( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f5214,plain,
spl184_387,
inference(avatar_split_clause,[],[f1822,f5212]) ).
fof(f5212,plain,
( spl184_387
<=> ! [X2,X0,X1] :
( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_387])]) ).
fof(f1822,plain,
! [X2,X0,X1] :
( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1085]) ).
fof(f5210,plain,
spl184_386,
inference(avatar_split_clause,[],[f1790,f5208]) ).
fof(f1790,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK153(X0,X1),X1)
& in(sK153(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f1060,f1061]) ).
fof(f1061,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK153(X0,X1),X1)
& in(sK153(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1060,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,[],[f1059]) ).
fof(f1059,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,[],[f649]) ).
fof(f649,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5206,plain,
spl184_385,
inference(avatar_split_clause,[],[f1787,f5204]) ).
fof(f1787,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f648]) ).
fof(f648,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f647]) ).
fof(f647,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f5202,plain,
spl184_384,
inference(avatar_split_clause,[],[f1786,f5200]) ).
fof(f1786,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f1056]) ).
fof(f1056,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f5198,plain,
( spl184_383
| ~ spl184_172
| ~ spl184_348 ),
inference(avatar_split_clause,[],[f5107,f4543,f3193,f5195]) ).
fof(f5195,plain,
( spl184_383
<=> sP53(sK57,sK56,sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_383])]) ).
fof(f3193,plain,
( spl184_172
<=> ! [X0,X1] : sP53(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_172])]) ).
fof(f5107,plain,
( sP53(sK57,sK56,sK173)
| ~ spl184_172
| ~ spl184_348 ),
inference(superposition,[],[f3194,f4545]) ).
fof(f3194,plain,
( ! [X0,X1] : sP53(X1,X0,set_difference(X0,X1))
| ~ spl184_172 ),
inference(avatar_component_clause,[],[f3193]) ).
fof(f5193,plain,
spl184_382,
inference(avatar_split_clause,[],[f1630,f5191]) ).
fof(f5191,plain,
( spl184_382
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP35(X0,X1)
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_382])]) ).
fof(f1630,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP35(X0,X1)
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f972]) ).
fof(f972,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP35(X0,X1) )
& ( sP35(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP36(X0) ),
inference(nnf_transformation,[],[f716]) ).
fof(f716,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP35(X0,X1) )
| ~ sP36(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f5189,plain,
spl184_381,
inference(avatar_split_clause,[],[f1617,f5187]) ).
fof(f5187,plain,
( spl184_381
<=> ! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_381])]) ).
fof(f1617,plain,
! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f571]) ).
fof(f571,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f570]) ).
fof(f570,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,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(f5185,plain,
spl184_380,
inference(avatar_split_clause,[],[f1508,f5183]) ).
fof(f5183,plain,
( spl184_380
<=> ! [X2,X0,X1] :
( relation_rng(X1) = relation_field(X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_380])]) ).
fof(f1508,plain,
! [X2,X0,X1] :
( relation_rng(X1) = relation_field(X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f893]) ).
fof(f5181,plain,
spl184_379,
inference(avatar_split_clause,[],[f1507,f5179]) ).
fof(f5179,plain,
( spl184_379
<=> ! [X2,X0,X1] :
( relation_field(X0) = relation_dom(X1)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_379])]) ).
fof(f1507,plain,
! [X2,X0,X1] :
( relation_field(X0) = relation_dom(X1)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f893]) ).
fof(f5177,plain,
spl184_378,
inference(avatar_split_clause,[],[f1236,f5175]) ).
fof(f5175,plain,
( spl184_378
<=> ! [X0,X3,X2,X1] :
( sP3(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_378])]) ).
fof(f1236,plain,
! [X2,X3,X0,X1] :
( sP3(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f791]) ).
fof(f4994,plain,
( spl184_377
| ~ spl184_13
| ~ spl184_109
| ~ spl184_356 ),
inference(avatar_split_clause,[],[f4867,f4863,f2823,f2246,f4992]) ).
fof(f4992,plain,
( spl184_377
<=> ! [X0] :
( relation_rng(X0) != sK173
| sK173 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_377])]) ).
fof(f4863,plain,
( spl184_356
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_356])]) ).
fof(f4867,plain,
( ! [X0] :
( relation_rng(X0) != sK173
| sK173 = X0
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_356 ),
inference(forward_demodulation,[],[f4866,f2880]) ).
fof(f4866,plain,
( ! [X0] :
( sK173 = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_356 ),
inference(forward_demodulation,[],[f4864,f2880]) ).
fof(f4864,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl184_356 ),
inference(avatar_component_clause,[],[f4863]) ).
fof(f4990,plain,
( spl184_376
| ~ spl184_13
| ~ spl184_109
| ~ spl184_355 ),
inference(avatar_split_clause,[],[f4861,f4857,f2823,f2246,f4988]) ).
fof(f4988,plain,
( spl184_376
<=> ! [X0] :
( relation_dom(X0) != sK173
| sK173 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_376])]) ).
fof(f4857,plain,
( spl184_355
<=> ! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_355])]) ).
fof(f4861,plain,
( ! [X0] :
( relation_dom(X0) != sK173
| sK173 = X0
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_355 ),
inference(forward_demodulation,[],[f4860,f2880]) ).
fof(f4860,plain,
( ! [X0] :
( sK173 = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_355 ),
inference(forward_demodulation,[],[f4858,f2880]) ).
fof(f4858,plain,
( ! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) )
| ~ spl184_355 ),
inference(avatar_component_clause,[],[f4857]) ).
fof(f4945,plain,
spl184_375,
inference(avatar_split_clause,[],[f1391,f4943]) ).
fof(f4943,plain,
( spl184_375
<=> ! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_375])]) ).
fof(f1391,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f515]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f268]) ).
fof(f268,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f4940,plain,
spl184_374,
inference(avatar_split_clause,[],[f1385,f4938]) ).
fof(f1385,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f510]) ).
fof(f510,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f509]) ).
fof(f509,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f226]) ).
fof(f226,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f4936,plain,
spl184_373,
inference(avatar_split_clause,[],[f1384,f4934]) ).
fof(f4934,plain,
( spl184_373
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_373])]) ).
fof(f1384,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f508]) ).
fof(f508,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f507]) ).
fof(f507,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f303]) ).
fof(f303,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f4932,plain,
spl184_372,
inference(avatar_split_clause,[],[f1319,f4930]) ).
fof(f4930,plain,
( spl184_372
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK81(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_372])]) ).
fof(f1319,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK81(X0,X1),X1) ),
inference(cnf_transformation,[],[f817]) ).
fof(f817,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK81(X0,X1),X1)
& in(sK81(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f471,f816]) ).
fof(f816,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK81(X0,X1),X1)
& in(sK81(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f471,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f165]) ).
fof(f165,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(f4928,plain,
spl184_371,
inference(avatar_split_clause,[],[f1318,f4926]) ).
fof(f4926,plain,
( spl184_371
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| in(sK81(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_371])]) ).
fof(f1318,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK81(X0,X1),X0) ),
inference(cnf_transformation,[],[f817]) ).
fof(f4924,plain,
spl184_370,
inference(avatar_split_clause,[],[f1290,f4922]) ).
fof(f4922,plain,
( spl184_370
<=> ! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_370])]) ).
fof(f1290,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f442]) ).
fof(f442,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f258]) ).
fof(f258,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f4920,plain,
spl184_369,
inference(avatar_split_clause,[],[f1274,f4918]) ).
fof(f4918,plain,
( spl184_369
<=> ! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_369])]) ).
fof(f1274,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1] :
( ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f229]) ).
fof(f229,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f4916,plain,
spl184_368,
inference(avatar_split_clause,[],[f1267,f4914]) ).
fof(f4914,plain,
( spl184_368
<=> ! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_368])]) ).
fof(f1267,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f411]) ).
fof(f411,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f154]) ).
fof(f154,axiom,
! [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(f4912,plain,
spl184_367,
inference(avatar_split_clause,[],[f1266,f4910]) ).
fof(f4910,plain,
( spl184_367
<=> ! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_367])]) ).
fof(f1266,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f329]) ).
fof(f329,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(f4908,plain,
spl184_366,
inference(avatar_split_clause,[],[f1265,f4906]) ).
fof(f4906,plain,
( spl184_366
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_366])]) ).
fof(f1265,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f195]) ).
fof(f195,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(f4904,plain,
spl184_365,
inference(avatar_split_clause,[],[f1255,f4902]) ).
fof(f4902,plain,
( spl184_365
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_365])]) ).
fof(f1255,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f800]) ).
fof(f800,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK77(X0,X1),X1)
& in(sK77(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f399,f799]) ).
fof(f799,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK77(X0,X1),X1)
& in(sK77(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f399,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,[],[f336]) ).
fof(f336,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,[],[f270]) ).
fof(f270,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(f4900,plain,
( spl184_364
| ~ spl184_2
| ~ spl184_333 ),
inference(avatar_split_clause,[],[f4836,f4472,f2191,f4897]) ).
fof(f4897,plain,
( spl184_364
<=> relation_of2(sK59,sK58,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_364])]) ).
fof(f4472,plain,
( spl184_333
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_333])]) ).
fof(f4836,plain,
( relation_of2(sK59,sK58,sK56)
| ~ spl184_2
| ~ spl184_333 ),
inference(resolution,[],[f4473,f2193]) ).
fof(f4473,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl184_333 ),
inference(avatar_component_clause,[],[f4472]) ).
fof(f4895,plain,
spl184_363,
inference(avatar_split_clause,[],[f1250,f4893]) ).
fof(f4893,plain,
( spl184_363
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_363])]) ).
fof(f1250,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f272]) ).
fof(f272,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(f4891,plain,
spl184_362,
inference(avatar_split_clause,[],[f1248,f4889]) ).
fof(f1248,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f265]) ).
fof(f265,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(f4887,plain,
spl184_361,
inference(avatar_split_clause,[],[f1244,f4885]) ).
fof(f4885,plain,
( spl184_361
<=> ! [X2,X0] :
( in(powerset(X2),sK75(X0))
| ~ in(X2,sK75(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_361])]) ).
fof(f1244,plain,
! [X2,X0] :
( in(powerset(X2),sK75(X0))
| ~ in(X2,sK75(X0)) ),
inference(cnf_transformation,[],[f796]) ).
fof(f4883,plain,
spl184_360,
inference(avatar_split_clause,[],[f1241,f4881]) ).
fof(f4881,plain,
( spl184_360
<=> ! [X0] :
( ordinal(X0)
| ~ subset(sK74(X0),X0)
| ~ ordinal(sK74(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_360])]) ).
fof(f1241,plain,
! [X0] :
( ordinal(X0)
| ~ subset(sK74(X0),X0)
| ~ ordinal(sK74(X0)) ),
inference(cnf_transformation,[],[f793]) ).
fof(f793,plain,
! [X0] :
( ordinal(X0)
| ( ( ~ subset(sK74(X0),X0)
| ~ ordinal(sK74(X0)) )
& in(sK74(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f395,f792]) ).
fof(f792,plain,
! [X0] :
( ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) )
=> ( ( ~ subset(sK74(X0),X0)
| ~ ordinal(sK74(X0)) )
& in(sK74(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f395,plain,
! [X0] :
( ordinal(X0)
| ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f250]) ).
fof(f250,axiom,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f4879,plain,
spl184_359,
inference(avatar_split_clause,[],[f1222,f4877]) ).
fof(f4877,plain,
( spl184_359
<=> ! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_359])]) ).
fof(f1222,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f390,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f389]) ).
fof(f389,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f302]) ).
fof(f302,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(f4875,plain,
spl184_358,
inference(avatar_split_clause,[],[f1187,f4873]) ).
fof(f4873,plain,
( spl184_358
<=> ! [X0] :
( antisymmetric(X0)
| sK65(X0) != sK66(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_358])]) ).
fof(f1187,plain,
! [X0] :
( antisymmetric(X0)
| sK65(X0) != sK66(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f769]) ).
fof(f4871,plain,
spl184_357,
inference(avatar_split_clause,[],[f1182,f4869]) ).
fof(f4869,plain,
( spl184_357
<=> ! [X0] :
( reflexive(X0)
| in(sK64(X0),relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_357])]) ).
fof(f1182,plain,
! [X0] :
( reflexive(X0)
| in(sK64(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f765]) ).
fof(f4865,plain,
spl184_356,
inference(avatar_split_clause,[],[f1177,f4863]) ).
fof(f1177,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(flattening,[],[f358]) ).
fof(f358,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f304]) ).
fof(f304,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(f4859,plain,
spl184_355,
inference(avatar_split_clause,[],[f1176,f4857]) ).
fof(f1176,plain,
! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f4855,plain,
spl184_354,
inference(avatar_split_clause,[],[f1173,f4853]) ).
fof(f4853,plain,
( spl184_354
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_354])]) ).
fof(f1173,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f232]) ).
fof(f232,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(f4851,plain,
spl184_353,
inference(avatar_split_clause,[],[f1172,f4849]) ).
fof(f4849,plain,
( spl184_353
<=> ! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_353])]) ).
fof(f1172,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f208]) ).
fof(f208,axiom,
! [X0] :
( relation(X0)
=> relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f4798,plain,
( spl184_351
| ~ spl184_352
| ~ spl184_157
| ~ spl184_347 ),
inference(avatar_split_clause,[],[f4596,f4530,f3133,f4795,f4791]) ).
fof(f4791,plain,
( spl184_351
<=> empty(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_351])]) ).
fof(f4795,plain,
( spl184_352
<=> empty(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_352])]) ).
fof(f3133,plain,
( spl184_157
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_157])]) ).
fof(f4530,plain,
( spl184_347
<=> sK57 = set_union2(sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_347])]) ).
fof(f4596,plain,
( ~ empty(sK57)
| empty(sK56)
| ~ spl184_157
| ~ spl184_347 ),
inference(superposition,[],[f3134,f4532]) ).
fof(f4532,plain,
( sK57 = set_union2(sK56,sK57)
| ~ spl184_347 ),
inference(avatar_component_clause,[],[f4530]) ).
fof(f3134,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl184_157 ),
inference(avatar_component_clause,[],[f3133]) ).
fof(f4686,plain,
( spl184_350
| ~ spl184_171
| ~ spl184_347 ),
inference(avatar_split_clause,[],[f4594,f4530,f3189,f4683]) ).
fof(f4683,plain,
( spl184_350
<=> sP52(sK57,sK56,sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_350])]) ).
fof(f4594,plain,
( sP52(sK57,sK56,sK57)
| ~ spl184_171
| ~ spl184_347 ),
inference(superposition,[],[f3190,f4532]) ).
fof(f4555,plain,
( spl184_349
| ~ spl184_13
| ~ spl184_109
| ~ spl184_298 ),
inference(avatar_split_clause,[],[f4329,f4326,f2823,f2246,f4553]) ).
fof(f4553,plain,
( spl184_349
<=> ! [X0,X1] :
( sK100(X0,X1) != sK173
| sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_349])]) ).
fof(f4326,plain,
( spl184_298
<=> ! [X0,X1] :
( sP17(X0,X1)
| empty_set != sK100(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_298])]) ).
fof(f4329,plain,
( ! [X0,X1] :
( sK100(X0,X1) != sK173
| sP17(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_298 ),
inference(forward_demodulation,[],[f4327,f2880]) ).
fof(f4327,plain,
( ! [X0,X1] :
( sP17(X0,X1)
| empty_set != sK100(X0,X1) )
| ~ spl184_298 ),
inference(avatar_component_clause,[],[f4326]) ).
fof(f4546,plain,
( spl184_348
| ~ spl184_1
| ~ spl184_279 ),
inference(avatar_split_clause,[],[f4255,f4166,f2186,f4543]) ).
fof(f4255,plain,
( sK173 = set_difference(sK56,sK57)
| ~ spl184_1
| ~ spl184_279 ),
inference(resolution,[],[f4167,f2188]) ).
fof(f4533,plain,
( spl184_347
| ~ spl184_1
| ~ spl184_257 ),
inference(avatar_split_clause,[],[f4143,f3952,f2186,f4530]) ).
fof(f4143,plain,
( sK57 = set_union2(sK56,sK57)
| ~ spl184_1
| ~ spl184_257 ),
inference(resolution,[],[f3953,f2188]) ).
fof(f4526,plain,
spl184_346,
inference(avatar_split_clause,[],[f2162,f4524]) ).
fof(f4524,plain,
( spl184_346
<=> ! [X2,X0,X1] : sP55(X2,X1,X0,unordered_triple(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_346])]) ).
fof(f2162,plain,
! [X2,X0,X1] : sP55(X2,X1,X0,unordered_triple(X0,X1,X2)),
inference(equality_resolution,[],[f1877]) ).
fof(f1877,plain,
! [X2,X3,X0,X1] :
( sP55(X2,X1,X0,X3)
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f4522,plain,
spl184_345,
inference(avatar_split_clause,[],[f2161,f4520]) ).
fof(f4520,plain,
( spl184_345
<=> ! [X5,X1,X0,X3] :
( in(X5,X3)
| ~ sP55(X0,X1,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_345])]) ).
fof(f2161,plain,
! [X3,X0,X1,X5] :
( in(X5,X3)
| ~ sP55(X0,X1,X5,X3) ),
inference(equality_resolution,[],[f1870]) ).
fof(f1870,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X2 != X5
| ~ sP55(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f4518,plain,
spl184_344,
inference(avatar_split_clause,[],[f2160,f4516]) ).
fof(f4516,plain,
( spl184_344
<=> ! [X2,X5,X0,X3] :
( in(X5,X3)
| ~ sP55(X0,X5,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_344])]) ).
fof(f2160,plain,
! [X2,X3,X0,X5] :
( in(X5,X3)
| ~ sP55(X0,X5,X2,X3) ),
inference(equality_resolution,[],[f1871]) ).
fof(f1871,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X1 != X5
| ~ sP55(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f4514,plain,
spl184_343,
inference(avatar_split_clause,[],[f2159,f4512]) ).
fof(f4512,plain,
( spl184_343
<=> ! [X3,X5,X2,X1] :
( in(X5,X3)
| ~ sP55(X5,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_343])]) ).
fof(f2159,plain,
! [X2,X3,X1,X5] :
( in(X5,X3)
| ~ sP55(X5,X1,X2,X3) ),
inference(equality_resolution,[],[f1872]) ).
fof(f1872,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X0 != X5
| ~ sP55(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1122]) ).
fof(f4510,plain,
spl184_342,
inference(avatar_split_clause,[],[f2139,f4508]) ).
fof(f4508,plain,
( spl184_342
<=> ! [X1] :
( sP43(X1,identity_relation(X1))
| ~ sP44(identity_relation(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_342])]) ).
fof(f2139,plain,
! [X1] :
( sP43(X1,identity_relation(X1))
| ~ sP44(identity_relation(X1),X1) ),
inference(equality_resolution,[],[f1721]) ).
fof(f1721,plain,
! [X0,X1] :
( sP43(X1,X0)
| identity_relation(X1) != X0
| ~ sP44(X0,X1) ),
inference(cnf_transformation,[],[f1032]) ).
fof(f4506,plain,
spl184_341,
inference(avatar_split_clause,[],[f2134,f4504]) ).
fof(f4504,plain,
( spl184_341
<=> ! [X1] :
( sP41(X1,set_meet(X1))
| ~ sP42(set_meet(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_341])]) ).
fof(f2134,plain,
! [X1] :
( sP41(X1,set_meet(X1))
| ~ sP42(set_meet(X1),X1) ),
inference(equality_resolution,[],[f1705]) ).
fof(f1705,plain,
! [X0,X1] :
( sP41(X1,X0)
| set_meet(X1) != X0
| ~ sP42(X0,X1) ),
inference(cnf_transformation,[],[f1023]) ).
fof(f4502,plain,
spl184_340,
inference(avatar_split_clause,[],[f2131,f4500]) ).
fof(f4500,plain,
( spl184_340
<=> ! [X0,X1] :
( sP39(X0,X1,relation_image(X0,X1))
| ~ sP40(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_340])]) ).
fof(f2131,plain,
! [X0,X1] :
( sP39(X0,X1,relation_image(X0,X1))
| ~ sP40(X0) ),
inference(equality_resolution,[],[f1651]) ).
fof(f1651,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| relation_image(X0,X1) != X2
| ~ sP40(X0) ),
inference(cnf_transformation,[],[f986]) ).
fof(f4498,plain,
spl184_339,
inference(avatar_split_clause,[],[f2130,f4496]) ).
fof(f4496,plain,
( spl184_339
<=> ! [X0,X1] :
( sP37(X1,X0,relation_inverse_image(X0,X1))
| ~ sP38(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_339])]) ).
fof(f2130,plain,
! [X0,X1] :
( sP37(X1,X0,relation_inverse_image(X0,X1))
| ~ sP38(X0) ),
inference(equality_resolution,[],[f1642]) ).
fof(f1642,plain,
! [X2,X0,X1] :
( sP37(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP38(X0) ),
inference(cnf_transformation,[],[f980]) ).
fof(f4494,plain,
spl184_338,
inference(avatar_split_clause,[],[f2124,f4492]) ).
fof(f4492,plain,
( spl184_338
<=> ! [X0,X1] :
( sP31(X1,X0,relation_image(X0,X1))
| ~ sP32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_338])]) ).
fof(f2124,plain,
! [X0,X1] :
( sP31(X1,X0,relation_image(X0,X1))
| ~ sP32(X0) ),
inference(equality_resolution,[],[f1604]) ).
fof(f1604,plain,
! [X2,X0,X1] :
( sP31(X1,X0,X2)
| relation_image(X0,X1) != X2
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f4490,plain,
spl184_337,
inference(avatar_split_clause,[],[f2123,f4488]) ).
fof(f4488,plain,
( spl184_337
<=> ! [X0,X1] :
( sP29(X1,X0,relation_inverse_image(X0,X1))
| ~ sP30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_337])]) ).
fof(f2123,plain,
! [X0,X1] :
( sP29(X1,X0,relation_inverse_image(X0,X1))
| ~ sP30(X0) ),
inference(equality_resolution,[],[f1595]) ).
fof(f1595,plain,
! [X2,X0,X1] :
( sP29(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f953]) ).
fof(f4486,plain,
spl184_336,
inference(avatar_split_clause,[],[f2121,f4484]) ).
fof(f4484,plain,
( spl184_336
<=> ! [X0,X1] :
( sP27(X0,X1,fiber(X0,X1))
| ~ sP28(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_336])]) ).
fof(f2121,plain,
! [X0,X1] :
( sP27(X0,X1,fiber(X0,X1))
| ~ sP28(X0) ),
inference(equality_resolution,[],[f1586]) ).
fof(f1586,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| fiber(X0,X1) != X2
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f947]) ).
fof(f4482,plain,
spl184_335,
inference(avatar_split_clause,[],[f2094,f4480]) ).
fof(f4480,plain,
( spl184_335
<=> ! [X0] :
( sP4(function_inverse(X0),X0)
| ~ sP5(X0,function_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_335])]) ).
fof(f2094,plain,
! [X0] :
( sP4(function_inverse(X0),X0)
| ~ sP5(X0,function_inverse(X0)) ),
inference(equality_resolution,[],[f1225]) ).
fof(f1225,plain,
! [X0,X1] :
( sP4(X1,X0)
| function_inverse(X0) != X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f783]) ).
fof(f4478,plain,
spl184_334,
inference(avatar_split_clause,[],[f1825,f4476]) ).
fof(f4476,plain,
( spl184_334
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_334])]) ).
fof(f1825,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f184]) ).
fof(f184,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f4474,plain,
spl184_333,
inference(avatar_split_clause,[],[f1824,f4472]) ).
fof(f1824,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1086]) ).
fof(f4470,plain,
spl184_332,
inference(avatar_split_clause,[],[f1818,f4468]) ).
fof(f4468,plain,
( spl184_332
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_332])]) ).
fof(f1818,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f654]) ).
fof(f654,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f4466,plain,
spl184_331,
inference(avatar_split_clause,[],[f1792,f4464]) ).
fof(f4464,plain,
( spl184_331
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK153(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_331])]) ).
fof(f1792,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK153(X0,X1),X1) ),
inference(cnf_transformation,[],[f1062]) ).
fof(f4462,plain,
spl184_330,
inference(avatar_split_clause,[],[f1791,f4460]) ).
fof(f4460,plain,
( spl184_330
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK153(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_330])]) ).
fof(f1791,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK153(X0,X1),X0) ),
inference(cnf_transformation,[],[f1062]) ).
fof(f4458,plain,
spl184_329,
inference(avatar_split_clause,[],[f1780,f4456]) ).
fof(f4456,plain,
( spl184_329
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_329])]) ).
fof(f1780,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f643]) ).
fof(f643,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f642]) ).
fof(f642,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f4454,plain,
spl184_328,
inference(avatar_split_clause,[],[f1779,f4452]) ).
fof(f4452,plain,
( spl184_328
<=> ! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_328])]) ).
fof(f1779,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f641]) ).
fof(f641,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f640]) ).
fof(f640,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f4450,plain,
spl184_327,
inference(avatar_split_clause,[],[f1778,f4448]) ).
fof(f4448,plain,
( spl184_327
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_327])]) ).
fof(f1778,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f639]) ).
fof(f639,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f638]) ).
fof(f638,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f4446,plain,
spl184_326,
inference(avatar_split_clause,[],[f1777,f4444]) ).
fof(f4444,plain,
( spl184_326
<=> ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_326])]) ).
fof(f1777,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f637]) ).
fof(f637,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f636]) ).
fof(f636,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,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(f4442,plain,
spl184_325,
inference(avatar_split_clause,[],[f1775,f4440]) ).
fof(f4440,plain,
( spl184_325
<=> ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_325])]) ).
fof(f1775,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f635]) ).
fof(f635,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f634]) ).
fof(f634,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,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(f4438,plain,
spl184_324,
inference(avatar_split_clause,[],[f1771,f4436]) ).
fof(f4436,plain,
( spl184_324
<=> ! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_324])]) ).
fof(f1771,plain,
! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f631]) ).
fof(f631,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,[],[f630]) ).
fof(f630,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,[],[f116]) ).
fof(f116,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(f4434,plain,
spl184_323,
inference(avatar_split_clause,[],[f1769,f4432]) ).
fof(f4432,plain,
( spl184_323
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_323])]) ).
fof(f1769,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f629]) ).
fof(f629,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f628]) ).
fof(f628,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,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(f4430,plain,
spl184_322,
inference(avatar_split_clause,[],[f1768,f4428]) ).
fof(f4428,plain,
( spl184_322
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_322])]) ).
fof(f1768,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f629]) ).
fof(f4426,plain,
( ~ spl184_321
| ~ spl184_123
| ~ spl184_281 ),
inference(avatar_split_clause,[],[f4336,f4233,f2975,f4423]) ).
fof(f4423,plain,
( spl184_321
<=> proper_subset(sK56,relation_rng(sK59)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_321])]) ).
fof(f4336,plain,
( ~ proper_subset(sK56,relation_rng(sK59))
| ~ spl184_123
| ~ spl184_281 ),
inference(resolution,[],[f4235,f2976]) ).
fof(f4421,plain,
spl184_320,
inference(avatar_split_clause,[],[f1767,f4419]) ).
fof(f4419,plain,
( spl184_320
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_320])]) ).
fof(f1767,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f627]) ).
fof(f627,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f626]) ).
fof(f626,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,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(f4417,plain,
spl184_319,
inference(avatar_split_clause,[],[f1766,f4415]) ).
fof(f4415,plain,
( spl184_319
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_319])]) ).
fof(f1766,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f627]) ).
fof(f4413,plain,
spl184_318,
inference(avatar_split_clause,[],[f1761,f4411]) ).
fof(f4411,plain,
( spl184_318
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_318])]) ).
fof(f1761,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f619]) ).
fof(f619,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f618]) ).
fof(f618,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f4409,plain,
spl184_317,
inference(avatar_split_clause,[],[f1738,f4407]) ).
fof(f4407,plain,
( spl184_317
<=> ! [X2,X0,X1] :
( sP46(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_317])]) ).
fof(f1738,plain,
! [X2,X0,X1] :
( sP46(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f732]) ).
fof(f732,plain,
! [X0,X1] :
( ! [X2] :
( sP46(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f601,f731,f730]) ).
fof(f601,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,[],[f18]) ).
fof(f18,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(f4405,plain,
spl184_316,
inference(avatar_split_clause,[],[f1701,f4403]) ).
fof(f4403,plain,
( spl184_316
<=> ! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_316])]) ).
fof(f1701,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,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,[],[f593]) ).
fof(f593,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,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(f4401,plain,
spl184_315,
inference(avatar_split_clause,[],[f1673,f4399]) ).
fof(f4399,plain,
( spl184_315
<=> ! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_315])]) ).
fof(f1673,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1001]) ).
fof(f1001,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK135(X0),X0)
& in(sK135(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f999,f1000]) ).
fof(f1000,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK135(X0),X0)
& in(sK135(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f999,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f998]) ).
fof(f998,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,[],[f589]) ).
fof(f589,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f4397,plain,
spl184_314,
inference(avatar_split_clause,[],[f1664,f4395]) ).
fof(f4395,plain,
( spl184_314
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_314])]) ).
fof(f1664,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f587]) ).
fof(f587,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f586]) ).
fof(f586,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,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(f4393,plain,
spl184_313,
inference(avatar_split_clause,[],[f1585,f4391]) ).
fof(f4391,plain,
( spl184_313
<=> ! [X2,X0,X1] :
( sP26(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_313])]) ).
fof(f1585,plain,
! [X2,X0,X1] :
( sP26(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f702,plain,
! [X0] :
( ! [X1,X2] :
( sP26(X2,X1,X0)
| ~ relation(X2) )
| ~ relation(X0) ),
inference(definition_folding,[],[f560,f701,f700]) ).
fof(f560,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,[],[f16]) ).
fof(f16,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(f4389,plain,
spl184_312,
inference(avatar_split_clause,[],[f1564,f4387]) ).
fof(f4387,plain,
( spl184_312
<=> ! [X0,X1] :
( sP23(X0,X1)
| in(sK108(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_312])]) ).
fof(f1564,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(sK108(X0,X1),X1) ),
inference(cnf_transformation,[],[f927]) ).
fof(f4385,plain,
spl184_311,
inference(avatar_split_clause,[],[f1563,f4383]) ).
fof(f4383,plain,
( spl184_311
<=> ! [X0,X1] :
( sP23(X0,X1)
| in(sK107(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_311])]) ).
fof(f1563,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(sK107(X0,X1),X1) ),
inference(cnf_transformation,[],[f927]) ).
fof(f4381,plain,
( ~ spl184_310
| ~ spl184_123
| ~ spl184_280 ),
inference(avatar_split_clause,[],[f4292,f4174,f2975,f4378]) ).
fof(f4378,plain,
( spl184_310
<=> proper_subset(sK58,relation_dom(sK59)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_310])]) ).
fof(f4292,plain,
( ~ proper_subset(sK58,relation_dom(sK59))
| ~ spl184_123
| ~ spl184_280 ),
inference(resolution,[],[f4176,f2976]) ).
fof(f4376,plain,
spl184_309,
inference(avatar_split_clause,[],[f1562,f4374]) ).
fof(f4374,plain,
( spl184_309
<=> ! [X0,X1] :
( sP23(X0,X1)
| in(sK106(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_309])]) ).
fof(f1562,plain,
! [X0,X1] :
( sP23(X0,X1)
| in(sK106(X0,X1),X1) ),
inference(cnf_transformation,[],[f927]) ).
fof(f4372,plain,
spl184_308,
inference(avatar_split_clause,[],[f1560,f4370]) ).
fof(f4370,plain,
( spl184_308
<=> ! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP23(X0,X1)
| ~ sP24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_308])]) ).
fof(f1560,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP23(X0,X1)
| ~ sP24(X0) ),
inference(cnf_transformation,[],[f923]) ).
fof(f923,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ~ sP23(X0,X1) )
& ( sP23(X0,X1)
| ~ is_transitive_in(X0,X1) ) )
| ~ sP24(X0) ),
inference(nnf_transformation,[],[f698]) ).
fof(f698,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> sP23(X0,X1) )
| ~ sP24(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f4368,plain,
spl184_307,
inference(avatar_split_clause,[],[f1559,f4366]) ).
fof(f4366,plain,
( spl184_307
<=> ! [X0,X1] :
( sP23(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_307])]) ).
fof(f1559,plain,
! [X0,X1] :
( sP23(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP24(X0) ),
inference(cnf_transformation,[],[f923]) ).
fof(f4364,plain,
spl184_306,
inference(avatar_split_clause,[],[f1554,f4362]) ).
fof(f4362,plain,
( spl184_306
<=> ! [X0,X1] :
( sP21(X0,X1)
| in(sK105(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_306])]) ).
fof(f1554,plain,
! [X0,X1] :
( sP21(X0,X1)
| in(sK105(X0,X1),X1) ),
inference(cnf_transformation,[],[f922]) ).
fof(f4360,plain,
spl184_305,
inference(avatar_split_clause,[],[f1553,f4358]) ).
fof(f4358,plain,
( spl184_305
<=> ! [X0,X1] :
( sP21(X0,X1)
| in(sK104(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_305])]) ).
fof(f1553,plain,
! [X0,X1] :
( sP21(X0,X1)
| in(sK104(X0,X1),X1) ),
inference(cnf_transformation,[],[f922]) ).
fof(f4356,plain,
spl184_304,
inference(avatar_split_clause,[],[f1551,f4354]) ).
fof(f4354,plain,
( spl184_304
<=> ! [X0,X1] :
( is_connected_in(X0,X1)
| ~ sP21(X0,X1)
| ~ sP22(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_304])]) ).
fof(f1551,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ sP21(X0,X1)
| ~ sP22(X0) ),
inference(cnf_transformation,[],[f918]) ).
fof(f918,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ~ sP21(X0,X1) )
& ( sP21(X0,X1)
| ~ is_connected_in(X0,X1) ) )
| ~ sP22(X0) ),
inference(nnf_transformation,[],[f695]) ).
fof(f695,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> sP21(X0,X1) )
| ~ sP22(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f4352,plain,
spl184_303,
inference(avatar_split_clause,[],[f1550,f4350]) ).
fof(f4350,plain,
( spl184_303
<=> ! [X0,X1] :
( sP21(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ sP22(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_303])]) ).
fof(f1550,plain,
! [X0,X1] :
( sP21(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ sP22(X0) ),
inference(cnf_transformation,[],[f918]) ).
fof(f4348,plain,
spl184_302,
inference(avatar_split_clause,[],[f1545,f4346]) ).
fof(f4346,plain,
( spl184_302
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK103(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_302])]) ).
fof(f1545,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK103(X0,X1),X1) ),
inference(cnf_transformation,[],[f917]) ).
fof(f4344,plain,
spl184_301,
inference(avatar_split_clause,[],[f1544,f4342]) ).
fof(f4342,plain,
( spl184_301
<=> ! [X0,X1] :
( sP19(X0,X1)
| in(sK102(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_301])]) ).
fof(f1544,plain,
! [X0,X1] :
( sP19(X0,X1)
| in(sK102(X0,X1),X1) ),
inference(cnf_transformation,[],[f917]) ).
fof(f4340,plain,
spl184_300,
inference(avatar_split_clause,[],[f1542,f4338]) ).
fof(f4338,plain,
( spl184_300
<=> ! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ sP19(X0,X1)
| ~ sP20(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_300])]) ).
fof(f1542,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ sP19(X0,X1)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f913]) ).
fof(f913,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ~ sP19(X0,X1) )
& ( sP19(X0,X1)
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ sP20(X0) ),
inference(nnf_transformation,[],[f692]) ).
fof(f692,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> sP19(X0,X1) )
| ~ sP20(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f4333,plain,
spl184_299,
inference(avatar_split_clause,[],[f1541,f4331]) ).
fof(f4331,plain,
( spl184_299
<=> ! [X0,X1] :
( sP19(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ sP20(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_299])]) ).
fof(f1541,plain,
! [X0,X1] :
( sP19(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f913]) ).
fof(f4328,plain,
spl184_298,
inference(avatar_split_clause,[],[f1538,f4326]) ).
fof(f1538,plain,
! [X0,X1] :
( sP17(X0,X1)
| empty_set != sK100(X0,X1) ),
inference(cnf_transformation,[],[f912]) ).
fof(f4324,plain,
spl184_297,
inference(avatar_split_clause,[],[f1537,f4322]) ).
fof(f4322,plain,
( spl184_297
<=> ! [X0,X1] :
( sP17(X0,X1)
| subset(sK100(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_297])]) ).
fof(f1537,plain,
! [X0,X1] :
( sP17(X0,X1)
| subset(sK100(X0,X1),X1) ),
inference(cnf_transformation,[],[f912]) ).
fof(f4320,plain,
spl184_296,
inference(avatar_split_clause,[],[f1534,f4318]) ).
fof(f4318,plain,
( spl184_296
<=> ! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ sP17(X0,X1)
| ~ sP18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_296])]) ).
fof(f1534,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ sP17(X0,X1)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f907]) ).
fof(f907,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ~ sP17(X0,X1) )
& ( sP17(X0,X1)
| ~ is_well_founded_in(X0,X1) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f689]) ).
fof(f689,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> sP17(X0,X1) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f4316,plain,
spl184_295,
inference(avatar_split_clause,[],[f1533,f4314]) ).
fof(f4314,plain,
( spl184_295
<=> ! [X0,X1] :
( sP17(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ sP18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_295])]) ).
fof(f1533,plain,
! [X0,X1] :
( sP17(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f907]) ).
fof(f4312,plain,
spl184_294,
inference(avatar_split_clause,[],[f1522,f4310]) ).
fof(f4310,plain,
( spl184_294
<=> ! [X0,X1] :
( well_orders(X0,X1)
| ~ sP15(X1,X0)
| ~ sP16(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_294])]) ).
fof(f1522,plain,
! [X0,X1] :
( well_orders(X0,X1)
| ~ sP15(X1,X0)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f899]) ).
fof(f899,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ sP15(X1,X0) )
& ( sP15(X1,X0)
| ~ well_orders(X0,X1) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f686]) ).
fof(f686,plain,
! [X0] :
( ! [X1] :
( well_orders(X0,X1)
<=> sP15(X1,X0) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f4308,plain,
spl184_293,
inference(avatar_split_clause,[],[f1521,f4306]) ).
fof(f4306,plain,
( spl184_293
<=> ! [X0,X1] :
( sP15(X1,X0)
| ~ well_orders(X0,X1)
| ~ sP16(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_293])]) ).
fof(f1521,plain,
! [X0,X1] :
( sP15(X1,X0)
| ~ well_orders(X0,X1)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f899]) ).
fof(f4304,plain,
spl184_292,
inference(avatar_split_clause,[],[f1510,f4302]) ).
fof(f4302,plain,
( spl184_292
<=> ! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_292])]) ).
fof(f1510,plain,
! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f893]) ).
fof(f4300,plain,
spl184_291,
inference(avatar_split_clause,[],[f1466,f4298]) ).
fof(f4298,plain,
( spl184_291
<=> ! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_291])]) ).
fof(f1466,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f859]) ).
fof(f859,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,[],[f540]) ).
fof(f540,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f4296,plain,
spl184_290,
inference(avatar_split_clause,[],[f1465,f4294]) ).
fof(f4294,plain,
( spl184_290
<=> ! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_290])]) ).
fof(f1465,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f859]) ).
fof(f4289,plain,
spl184_289,
inference(avatar_split_clause,[],[f1464,f4287]) ).
fof(f4287,plain,
( spl184_289
<=> ! [X0] :
( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_289])]) ).
fof(f1464,plain,
! [X0] :
( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f858]) ).
fof(f858,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,[],[f539]) ).
fof(f539,plain,
! [X0] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f4285,plain,
spl184_288,
inference(avatar_split_clause,[],[f1463,f4283]) ).
fof(f4283,plain,
( spl184_288
<=> ! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_288])]) ).
fof(f1463,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f858]) ).
fof(f4281,plain,
spl184_287,
inference(avatar_split_clause,[],[f1462,f4279]) ).
fof(f4279,plain,
( spl184_287
<=> ! [X0] :
( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_287])]) ).
fof(f1462,plain,
! [X0] :
( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f857]) ).
fof(f857,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,[],[f538]) ).
fof(f538,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f4277,plain,
spl184_286,
inference(avatar_split_clause,[],[f1461,f4275]) ).
fof(f4275,plain,
( spl184_286
<=> ! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_286])]) ).
fof(f1461,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f857]) ).
fof(f4273,plain,
spl184_285,
inference(avatar_split_clause,[],[f1460,f4271]) ).
fof(f4271,plain,
( spl184_285
<=> ! [X0] :
( connected(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_285])]) ).
fof(f1460,plain,
! [X0] :
( connected(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f856]) ).
fof(f856,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,[],[f537]) ).
fof(f537,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f4269,plain,
spl184_284,
inference(avatar_split_clause,[],[f1459,f4267]) ).
fof(f4267,plain,
( spl184_284
<=> ! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_284])]) ).
fof(f1459,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f856]) ).
fof(f4265,plain,
spl184_283,
inference(avatar_split_clause,[],[f1228,f4263]) ).
fof(f4263,plain,
( spl184_283
<=> ! [X4,X0,X5,X1] :
( sP3(X4,X5,X1,X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_283])]) ).
fof(f1228,plain,
! [X0,X1,X4,X5] :
( sP3(X4,X5,X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f4261,plain,
spl184_282,
inference(avatar_split_clause,[],[f1227,f4259]) ).
fof(f4259,plain,
( spl184_282
<=> ! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_282])]) ).
fof(f1227,plain,
! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f788]) ).
fof(f4236,plain,
( spl184_281
| ~ spl184_2
| ~ spl184_264 ),
inference(avatar_split_clause,[],[f4171,f3983,f2191,f4233]) ).
fof(f3983,plain,
( spl184_264
<=> ! [X2,X0,X1] :
( subset(relation_rng(X2),X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_264])]) ).
fof(f4171,plain,
( subset(relation_rng(sK59),sK56)
| ~ spl184_2
| ~ spl184_264 ),
inference(resolution,[],[f3984,f2193]) ).
fof(f3984,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_rng(X2),X1) )
| ~ spl184_264 ),
inference(avatar_component_clause,[],[f3983]) ).
fof(f4177,plain,
( spl184_280
| ~ spl184_2
| ~ spl184_263 ),
inference(avatar_split_clause,[],[f4169,f3979,f2191,f4174]) ).
fof(f3979,plain,
( spl184_263
<=> ! [X2,X0,X1] :
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_263])]) ).
fof(f4169,plain,
( subset(relation_dom(sK59),sK58)
| ~ spl184_2
| ~ spl184_263 ),
inference(resolution,[],[f3980,f2193]) ).
fof(f3980,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) )
| ~ spl184_263 ),
inference(avatar_component_clause,[],[f3979]) ).
fof(f4168,plain,
( spl184_279
| ~ spl184_13
| ~ spl184_109
| ~ spl184_262 ),
inference(avatar_split_clause,[],[f3977,f3974,f2823,f2246,f4166]) ).
fof(f3974,plain,
( spl184_262
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_262])]) ).
fof(f3977,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK173
| ~ subset(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_262 ),
inference(forward_demodulation,[],[f3975,f2880]) ).
fof(f3975,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl184_262 ),
inference(avatar_component_clause,[],[f3974]) ).
fof(f4164,plain,
( spl184_278
| ~ spl184_13
| ~ spl184_109
| ~ spl184_261 ),
inference(avatar_split_clause,[],[f3972,f3969,f2823,f2246,f4162]) ).
fof(f4162,plain,
( spl184_278
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK173
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_278])]) ).
fof(f3969,plain,
( spl184_261
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_261])]) ).
fof(f3972,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK173
| subset(X0,X1) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_261 ),
inference(forward_demodulation,[],[f3970,f2880]) ).
fof(f3970,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl184_261 ),
inference(avatar_component_clause,[],[f3969]) ).
fof(f4131,plain,
( spl184_277
| ~ spl184_27
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2645,f2503,f2316,f4128]) ).
fof(f4128,plain,
( spl184_277
<=> sP7(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_277])]) ).
fof(f2645,plain,
( sP7(sK179)
| ~ spl184_27
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2318]) ).
fof(f4094,plain,
( spl184_276
| ~ spl184_25
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2644,f2503,f2306,f4091]) ).
fof(f4091,plain,
( spl184_276
<=> sP7(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_276])]) ).
fof(f2644,plain,
( sP7(sK178)
| ~ spl184_25
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2308]) ).
fof(f4031,plain,
spl184_275,
inference(avatar_split_clause,[],[f2158,f4029]) ).
fof(f2158,plain,
! [X0,X1] : sP54(X1,X0,set_difference(X0,set_difference(X0,X1))),
inference(equality_resolution,[],[f2092]) ).
fof(f2092,plain,
! [X2,X0,X1] :
( sP54(X1,X0,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f1866,f1249]) ).
fof(f1866,plain,
! [X2,X0,X1] :
( sP54(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1117]) ).
fof(f4027,plain,
spl184_274,
inference(avatar_split_clause,[],[f2148,f4025]) ).
fof(f4025,plain,
( spl184_274
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_274])]) ).
fof(f2148,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f2086]) ).
fof(f2086,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1801,f1158]) ).
fof(f1801,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f1073]) ).
fof(f4023,plain,
spl184_273,
inference(avatar_split_clause,[],[f1995,f4021]) ).
fof(f4021,plain,
( spl184_273
<=> ! [X0] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_273])]) ).
fof(f1995,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1438,f1912]) ).
fof(f1438,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f525]) ).
fof(f525,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,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(f4019,plain,
spl184_272,
inference(avatar_split_clause,[],[f1994,f4017]) ).
fof(f4017,plain,
( spl184_272
<=> ! [X0] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_272])]) ).
fof(f1994,plain,
! [X0] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1439,f1912]) ).
fof(f1439,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f525]) ).
fof(f4014,plain,
( spl184_271
| ~ spl184_24
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2643,f2503,f2301,f4011]) ).
fof(f4011,plain,
( spl184_271
<=> sP7(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_271])]) ).
fof(f2643,plain,
( sP7(sK177)
| ~ spl184_24
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2303]) ).
fof(f4009,plain,
spl184_270,
inference(avatar_split_clause,[],[f1993,f4007]) ).
fof(f4007,plain,
( spl184_270
<=> ! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_270])]) ).
fof(f1993,plain,
! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1440,f1912]) ).
fof(f1440,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f525]) ).
fof(f4005,plain,
spl184_269,
inference(avatar_split_clause,[],[f1962,f4003]) ).
fof(f4003,plain,
( spl184_269
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_269])]) ).
fof(f1962,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1339,f1158]) ).
fof(f1339,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f473]) ).
fof(f473,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f152]) ).
fof(f152,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f4001,plain,
spl184_268,
inference(avatar_split_clause,[],[f1956,f3999]) ).
fof(f3999,plain,
( spl184_268
<=> ! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_268])]) ).
fof(f1956,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f1329,f1158]) ).
fof(f1329,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f823]) ).
fof(f823,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f262]) ).
fof(f262,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f3997,plain,
spl184_267,
inference(avatar_split_clause,[],[f1942,f3995]) ).
fof(f3995,plain,
( spl184_267
<=> ! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_267])]) ).
fof(f1942,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f1285,f1158]) ).
fof(f1285,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f437]) ).
fof(f437,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f3993,plain,
spl184_266,
inference(avatar_split_clause,[],[f1389,f3991]) ).
fof(f3991,plain,
( spl184_266
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_266])]) ).
fof(f1389,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f847]) ).
fof(f3989,plain,
spl184_265,
inference(avatar_split_clause,[],[f1388,f3987]) ).
fof(f3987,plain,
( spl184_265
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_265])]) ).
fof(f1388,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f847]) ).
fof(f3985,plain,
spl184_264,
inference(avatar_split_clause,[],[f1373,f3983]) ).
fof(f1373,plain,
! [X2,X0,X1] :
( subset(relation_rng(X2),X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f496]) ).
fof(f496,plain,
! [X0,X1,X2] :
( ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f199]) ).
fof(f199,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f3981,plain,
spl184_263,
inference(avatar_split_clause,[],[f1372,f3979]) ).
fof(f1372,plain,
! [X2,X0,X1] :
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f496]) ).
fof(f3976,plain,
spl184_262,
inference(avatar_split_clause,[],[f1333,f3974]) ).
fof(f1333,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f825]) ).
fof(f825,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f261]) ).
fof(f261,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f3971,plain,
spl184_261,
inference(avatar_split_clause,[],[f1332,f3969]) ).
fof(f1332,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f825]) ).
fof(f3967,plain,
( spl184_260
| ~ spl184_19
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2642,f2503,f2276,f3964]) ).
fof(f3964,plain,
( spl184_260
<=> sP7(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_260])]) ).
fof(f2642,plain,
( sP7(sK175)
| ~ spl184_19
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2278]) ).
fof(f3962,plain,
spl184_259,
inference(avatar_split_clause,[],[f1321,f3960]) ).
fof(f3960,plain,
( spl184_259
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_259])]) ).
fof(f1321,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f818]) ).
fof(f818,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f318]) ).
fof(f318,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f3958,plain,
spl184_258,
inference(avatar_split_clause,[],[f1320,f3956]) ).
fof(f3956,plain,
( spl184_258
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_258])]) ).
fof(f1320,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f818]) ).
fof(f3954,plain,
spl184_257,
inference(avatar_split_clause,[],[f1291,f3952]) ).
fof(f1291,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f443]) ).
fof(f443,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f3950,plain,
spl184_256,
inference(avatar_split_clause,[],[f1281,f3948]) ).
fof(f3948,plain,
( spl184_256
<=> ! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_256])]) ).
fof(f1281,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(flattening,[],[f429]) ).
fof(f429,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f253]) ).
fof(f253,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f3946,plain,
spl184_255,
inference(avatar_split_clause,[],[f1280,f3944]) ).
fof(f3944,plain,
( spl184_255
<=> ! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_255])]) ).
fof(f1280,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f428]) ).
fof(f428,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f427]) ).
fof(f427,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f240]) ).
fof(f240,axiom,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f3942,plain,
spl184_254,
inference(avatar_split_clause,[],[f1279,f3940]) ).
fof(f3940,plain,
( spl184_254
<=> ! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_254])]) ).
fof(f1279,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(flattening,[],[f425]) ).
fof(f425,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f242]) ).
fof(f242,axiom,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f3938,plain,
spl184_253,
inference(avatar_split_clause,[],[f1278,f3936]) ).
fof(f3936,plain,
( spl184_253
<=> ! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_253])]) ).
fof(f1278,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f424]) ).
fof(f424,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(flattening,[],[f423]) ).
fof(f423,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f251]) ).
fof(f251,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f3934,plain,
spl184_252,
inference(avatar_split_clause,[],[f1277,f3932]) ).
fof(f3932,plain,
( spl184_252
<=> ! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_252])]) ).
fof(f1277,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f422]) ).
fof(f422,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f421]) ).
fof(f421,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f235]) ).
fof(f235,axiom,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f3930,plain,
spl184_251,
inference(avatar_split_clause,[],[f1276,f3928]) ).
fof(f3928,plain,
( spl184_251
<=> ! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_251])]) ).
fof(f1276,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f420]) ).
fof(f420,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(flattening,[],[f419]) ).
fof(f419,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f238]) ).
fof(f238,axiom,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f3926,plain,
spl184_250,
inference(avatar_split_clause,[],[f1275,f3924]) ).
fof(f3924,plain,
( spl184_250
<=> ! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_250])]) ).
fof(f1275,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f418]) ).
fof(f3921,plain,
( spl184_249
| ~ spl184_5
| ~ spl184_66 ),
inference(avatar_split_clause,[],[f2641,f2503,f2206,f3918]) ).
fof(f3918,plain,
( spl184_249
<=> sP7(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_249])]) ).
fof(f2641,plain,
( sP7(empty_set)
| ~ spl184_5
| ~ spl184_66 ),
inference(resolution,[],[f2504,f2208]) ).
fof(f3916,plain,
spl184_248,
inference(avatar_split_clause,[],[f1264,f3914]) ).
fof(f3914,plain,
( spl184_248
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_248])]) ).
fof(f1264,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f193]) ).
fof(f193,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(f3912,plain,
spl184_247,
inference(avatar_split_clause,[],[f1263,f3910]) ).
fof(f3910,plain,
( spl184_247
<=> ! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_247])]) ).
fof(f1263,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f407]) ).
fof(f407,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f3908,plain,
spl184_246,
inference(avatar_split_clause,[],[f1262,f3906]) ).
fof(f3906,plain,
( spl184_246
<=> ! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_246])]) ).
fof(f1262,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f406]) ).
fof(f406,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f213]) ).
fof(f213,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(f3904,plain,
spl184_245,
inference(avatar_split_clause,[],[f1254,f3902]) ).
fof(f3902,plain,
( spl184_245
<=> ! [X0,X1] :
( in(sK77(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_245])]) ).
fof(f1254,plain,
! [X0,X1] :
( in(sK77(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f800]) ).
fof(f3900,plain,
spl184_244,
inference(avatar_split_clause,[],[f1253,f3898]) ).
fof(f3898,plain,
( spl184_244
<=> ! [X0,X1] :
( in(sK77(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_244])]) ).
fof(f1253,plain,
! [X0,X1] :
( in(sK77(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f800]) ).
fof(f3896,plain,
spl184_243,
inference(avatar_split_clause,[],[f1204,f3894]) ).
fof(f3894,plain,
( spl184_243
<=> ! [X0] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_243])]) ).
fof(f1204,plain,
! [X0] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f780]) ).
fof(f780,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,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f323]) ).
fof(f323,axiom,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f3892,plain,
spl184_242,
inference(avatar_split_clause,[],[f1203,f3890]) ).
fof(f3890,plain,
( spl184_242
<=> ! [X0] :
( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_242])]) ).
fof(f1203,plain,
! [X0] :
( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f780]) ).
fof(f3888,plain,
spl184_241,
inference(avatar_split_clause,[],[f1180,f3886]) ).
fof(f3886,plain,
( spl184_241
<=> ! [X0] :
( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_241])]) ).
fof(f1180,plain,
! [X0] :
( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f761]) ).
fof(f761,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,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f299]) ).
fof(f299,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(f3884,plain,
spl184_240,
inference(avatar_split_clause,[],[f1179,f3882]) ).
fof(f3882,plain,
( spl184_240
<=> ! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_240])]) ).
fof(f1179,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f761]) ).
fof(f3880,plain,
spl184_239,
inference(avatar_split_clause,[],[f1175,f3878]) ).
fof(f3878,plain,
( spl184_239
<=> ! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_239])]) ).
fof(f1175,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f260]) ).
fof(f260,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(f3875,plain,
( spl184_238
| ~ spl184_43
| ~ spl184_65 ),
inference(avatar_split_clause,[],[f2639,f2499,f2396,f3872]) ).
fof(f3872,plain,
( spl184_238
<=> ordinal(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_238])]) ).
fof(f2396,plain,
( spl184_43
<=> empty(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_43])]) ).
fof(f2499,plain,
( spl184_65
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_65])]) ).
fof(f2639,plain,
( ordinal(sK183)
| ~ spl184_43
| ~ spl184_65 ),
inference(resolution,[],[f2500,f2398]) ).
fof(f2398,plain,
( empty(sK183)
| ~ spl184_43 ),
inference(avatar_component_clause,[],[f2396]) ).
fof(f2500,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl184_65 ),
inference(avatar_component_clause,[],[f2499]) ).
fof(f3870,plain,
spl184_237,
inference(avatar_split_clause,[],[f1174,f3868]) ).
fof(f3868,plain,
( spl184_237
<=> ! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_237])]) ).
fof(f1174,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f3866,plain,
spl184_236,
inference(avatar_split_clause,[],[f1167,f3864]) ).
fof(f3864,plain,
( spl184_236
<=> ! [X0] :
( being_limit_ordinal(X0)
| in(sK61(X0),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_236])]) ).
fof(f1167,plain,
! [X0] :
( being_limit_ordinal(X0)
| in(sK61(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f757]) ).
fof(f3815,plain,
( spl184_235
| ~ spl184_23
| ~ spl184_65 ),
inference(avatar_split_clause,[],[f2637,f2499,f2296,f3812]) ).
fof(f3812,plain,
( spl184_235
<=> ordinal(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_235])]) ).
fof(f2296,plain,
( spl184_23
<=> empty(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_23])]) ).
fof(f2637,plain,
( ordinal(sK177)
| ~ spl184_23
| ~ spl184_65 ),
inference(resolution,[],[f2500,f2298]) ).
fof(f2298,plain,
( empty(sK177)
| ~ spl184_23 ),
inference(avatar_component_clause,[],[f2296]) ).
fof(f3775,plain,
( spl184_234
| ~ spl184_13
| ~ spl184_109
| ~ spl184_213 ),
inference(avatar_split_clause,[],[f3618,f3615,f2823,f2246,f3773]) ).
fof(f3773,plain,
( spl184_234
<=> ! [X0] :
( sK173 = X0
| in(sK139(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_234])]) ).
fof(f3615,plain,
( spl184_213
<=> ! [X0] :
( empty_set = X0
| in(sK139(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_213])]) ).
fof(f3618,plain,
( ! [X0] :
( sK173 = X0
| in(sK139(X0),X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_213 ),
inference(forward_demodulation,[],[f3616,f2880]) ).
fof(f3616,plain,
( ! [X0] :
( empty_set = X0
| in(sK139(X0),X0) )
| ~ spl184_213 ),
inference(avatar_component_clause,[],[f3615]) ).
fof(f3771,plain,
( spl184_233
| ~ spl184_13
| ~ spl184_65 ),
inference(avatar_split_clause,[],[f2636,f2499,f2246,f3768]) ).
fof(f3768,plain,
( spl184_233
<=> ordinal(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_233])]) ).
fof(f2636,plain,
( ordinal(sK173)
| ~ spl184_13
| ~ spl184_65 ),
inference(resolution,[],[f2500,f2248]) ).
fof(f3705,plain,
( spl184_232
| ~ spl184_43
| ~ spl184_64 ),
inference(avatar_split_clause,[],[f2633,f2495,f2396,f3702]) ).
fof(f3702,plain,
( spl184_232
<=> epsilon_connected(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_232])]) ).
fof(f2495,plain,
( spl184_64
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_64])]) ).
fof(f2633,plain,
( epsilon_connected(sK183)
| ~ spl184_43
| ~ spl184_64 ),
inference(resolution,[],[f2496,f2398]) ).
fof(f2496,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl184_64 ),
inference(avatar_component_clause,[],[f2495]) ).
fof(f3692,plain,
spl184_231,
inference(avatar_split_clause,[],[f2152,f3690]) ).
fof(f3690,plain,
( spl184_231
<=> ! [X2,X0,X4] :
( in(X4,X2)
| ~ sP50(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_231])]) ).
fof(f2152,plain,
! [X2,X0,X4] :
( in(X4,X2)
| ~ sP50(X0,X4,X2) ),
inference(equality_resolution,[],[f1827]) ).
fof(f1827,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f3687,plain,
( spl184_230
| ~ spl184_23
| ~ spl184_64 ),
inference(avatar_split_clause,[],[f2631,f2495,f2296,f3684]) ).
fof(f3684,plain,
( spl184_230
<=> epsilon_connected(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_230])]) ).
fof(f2631,plain,
( epsilon_connected(sK177)
| ~ spl184_23
| ~ spl184_64 ),
inference(resolution,[],[f2496,f2298]) ).
fof(f3682,plain,
spl184_229,
inference(avatar_split_clause,[],[f2151,f3680]) ).
fof(f3680,plain,
( spl184_229
<=> ! [X2,X1,X4] :
( in(X4,X2)
| ~ sP50(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_229])]) ).
fof(f2151,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ sP50(X4,X1,X2) ),
inference(equality_resolution,[],[f1828]) ).
fof(f1828,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1091]) ).
fof(f3678,plain,
spl184_228,
inference(avatar_split_clause,[],[f2150,f3676]) ).
fof(f3676,plain,
( spl184_228
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_228])]) ).
fof(f2150,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f1805]) ).
fof(f1805,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f1077]) ).
fof(f3674,plain,
spl184_227,
inference(avatar_split_clause,[],[f2149,f3672]) ).
fof(f3672,plain,
( spl184_227
<=> ! [X0,X3] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_227])]) ).
fof(f2149,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f1806]) ).
fof(f1806,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f1077]) ).
fof(f3670,plain,
spl184_226,
inference(avatar_split_clause,[],[f2122,f3668]) ).
fof(f3668,plain,
( spl184_226
<=> ! [X2,X0,X4] :
( ~ in(X4,X2)
| ~ sP27(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_226])]) ).
fof(f2122,plain,
! [X2,X0,X4] :
( ~ in(X4,X2)
| ~ sP27(X0,X4,X2) ),
inference(equality_resolution,[],[f1588]) ).
fof(f1588,plain,
! [X2,X0,X1,X4] :
( X1 != X4
| ~ in(X4,X2)
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f952]) ).
fof(f3666,plain,
spl184_225,
inference(avatar_split_clause,[],[f1813,f3664]) ).
fof(f1813,plain,
! [X0,X1] :
( in(sK159(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f3662,plain,
spl184_224,
inference(avatar_split_clause,[],[f1811,f3660]) ).
fof(f3660,plain,
( spl184_224
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_224])]) ).
fof(f1811,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f650]) ).
fof(f650,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f321]) ).
fof(f321,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f3658,plain,
spl184_223,
inference(avatar_split_clause,[],[f1810,f3656]) ).
fof(f3656,plain,
( spl184_223
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_223])]) ).
fof(f1810,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f269]) ).
fof(f269,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f3654,plain,
spl184_222,
inference(avatar_split_clause,[],[f1809,f3652]) ).
fof(f3652,plain,
( spl184_222
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_222])]) ).
fof(f1809,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1078]) ).
fof(f3650,plain,
spl184_221,
inference(avatar_split_clause,[],[f1800,f3648]) ).
fof(f3648,plain,
( spl184_221
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP49(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_221])]) ).
fof(f1800,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP49(X0,X1) ),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP49(X0,X1) )
& ( sP49(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f737]) ).
fof(f737,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP49(X0,X1) ),
inference(definition_folding,[],[f52,f736]) ).
fof(f52,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(f3646,plain,
( spl184_220
| ~ spl184_13
| ~ spl184_64 ),
inference(avatar_split_clause,[],[f2630,f2495,f2246,f3643]) ).
fof(f3643,plain,
( spl184_220
<=> epsilon_connected(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_220])]) ).
fof(f2630,plain,
( epsilon_connected(sK173)
| ~ spl184_13
| ~ spl184_64 ),
inference(resolution,[],[f2496,f2248]) ).
fof(f3641,plain,
( spl184_218
| spl184_219 ),
inference(avatar_split_clause,[],[f1762,f3639,f3636]) ).
fof(f3636,plain,
( spl184_218
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_218])]) ).
fof(f3639,plain,
( spl184_219
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_219])]) ).
fof(f1762,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f621]) ).
fof(f621,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f620]) ).
fof(f620,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f3634,plain,
spl184_217,
inference(avatar_split_clause,[],[f1704,f3632]) ).
fof(f3632,plain,
( spl184_217
<=> ! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_217])]) ).
fof(f1704,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1021]) ).
fof(f3630,plain,
spl184_216,
inference(avatar_split_clause,[],[f1703,f3628]) ).
fof(f3628,plain,
( spl184_216
<=> ! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_216])]) ).
fof(f1703,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1021]) ).
fof(f3626,plain,
spl184_215,
inference(avatar_split_clause,[],[f1698,f3624]) ).
fof(f1698,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3622,plain,
spl184_214,
inference(avatar_split_clause,[],[f1697,f3620]) ).
fof(f3617,plain,
spl184_213,
inference(avatar_split_clause,[],[f1683,f3615]) ).
fof(f1683,plain,
! [X0] :
( empty_set = X0
| in(sK139(X0),X0) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,plain,
! [X0] :
( ( empty_set = X0
| in(sK139(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139])],[f1010,f1011]) ).
fof(f1011,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK139(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f1010,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f1009]) ).
fof(f1009,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3613,plain,
spl184_212,
inference(avatar_split_clause,[],[f1672,f3611]) ).
fof(f3611,plain,
( spl184_212
<=> ! [X0] :
( epsilon_connected(X0)
| ~ in(sK134(X0),sK133(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_212])]) ).
fof(f1672,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK134(X0),sK133(X0)) ),
inference(cnf_transformation,[],[f997]) ).
fof(f3609,plain,
spl184_211,
inference(avatar_split_clause,[],[f1671,f3607]) ).
fof(f3607,plain,
( spl184_211
<=> ! [X0] :
( epsilon_connected(X0)
| sK133(X0) != sK134(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_211])]) ).
fof(f1671,plain,
! [X0] :
( epsilon_connected(X0)
| sK133(X0) != sK134(X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f3605,plain,
spl184_210,
inference(avatar_split_clause,[],[f1670,f3603]) ).
fof(f3603,plain,
( spl184_210
<=> ! [X0] :
( epsilon_connected(X0)
| ~ in(sK133(X0),sK134(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_210])]) ).
fof(f1670,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK133(X0),sK134(X0)) ),
inference(cnf_transformation,[],[f997]) ).
fof(f3601,plain,
spl184_209,
inference(avatar_split_clause,[],[f1627,f3599]) ).
fof(f3599,plain,
( spl184_209
<=> ! [X0] :
( sP33(X0)
| sK124(X0) != sK125(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_209])]) ).
fof(f1627,plain,
! [X0] :
( sP33(X0)
| sK124(X0) != sK125(X0) ),
inference(cnf_transformation,[],[f971]) ).
fof(f3596,plain,
( spl184_208
| ~ spl184_43
| ~ spl184_63 ),
inference(avatar_split_clause,[],[f2627,f2491,f2396,f3593]) ).
fof(f3593,plain,
( spl184_208
<=> epsilon_transitive(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_208])]) ).
fof(f2491,plain,
( spl184_63
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_63])]) ).
fof(f2627,plain,
( epsilon_transitive(sK183)
| ~ spl184_43
| ~ spl184_63 ),
inference(resolution,[],[f2492,f2398]) ).
fof(f2492,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl184_63 ),
inference(avatar_component_clause,[],[f2491]) ).
fof(f3591,plain,
spl184_207,
inference(avatar_split_clause,[],[f1625,f3589]) ).
fof(f3589,plain,
( spl184_207
<=> ! [X0] :
( sP33(X0)
| in(sK125(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_207])]) ).
fof(f1625,plain,
! [X0] :
( sP33(X0)
| in(sK125(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f971]) ).
fof(f3587,plain,
spl184_206,
inference(avatar_split_clause,[],[f1624,f3585]) ).
fof(f3585,plain,
( spl184_206
<=> ! [X0] :
( sP33(X0)
| in(sK124(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_206])]) ).
fof(f1624,plain,
! [X0] :
( sP33(X0)
| in(sK124(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f971]) ).
fof(f3583,plain,
spl184_205,
inference(avatar_split_clause,[],[f1619,f3581]) ).
fof(f3581,plain,
( spl184_205
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_205])]) ).
fof(f1619,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f573]) ).
fof(f573,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f572]) ).
fof(f572,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,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(f3579,plain,
spl184_204,
inference(avatar_split_clause,[],[f1618,f3577]) ).
fof(f3577,plain,
( spl184_204
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_204])]) ).
fof(f1618,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f573]) ).
fof(f3575,plain,
spl184_203,
inference(avatar_split_clause,[],[f1614,f3573]) ).
fof(f3573,plain,
( spl184_203
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_203])]) ).
fof(f1614,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f567]) ).
fof(f567,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f566]) ).
fof(f566,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f3571,plain,
spl184_202,
inference(avatar_split_clause,[],[f1613,f3569]) ).
fof(f3569,plain,
( spl184_202
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_202])]) ).
fof(f1613,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f565]) ).
fof(f565,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f564]) ).
fof(f564,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f139]) ).
fof(f139,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f3567,plain,
spl184_201,
inference(avatar_split_clause,[],[f1471,f3565]) ).
fof(f3565,plain,
( spl184_201
<=> ! [X0] :
( sP6(X0)
| subset(sK85(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_201])]) ).
fof(f1471,plain,
! [X0] :
( sP6(X0)
| subset(sK85(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f865]) ).
fof(f3563,plain,
spl184_200,
inference(avatar_split_clause,[],[f1457,f3561]) ).
fof(f3561,plain,
( spl184_200
<=> ! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_200])]) ).
fof(f1457,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f535]) ).
fof(f535,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f3559,plain,
spl184_199,
inference(avatar_split_clause,[],[f1433,f3557]) ).
fof(f3557,plain,
( spl184_199
<=> ! [X0] :
( element(sK84(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_199])]) ).
fof(f1433,plain,
! [X0] :
( element(sK84(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f855,plain,
! [X0] :
( ( ~ empty(sK84(X0))
& element(sK84(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f523,f854]) ).
fof(f854,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK84(X0))
& element(sK84(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f523,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f3555,plain,
spl184_198,
inference(avatar_split_clause,[],[f1217,f3553]) ).
fof(f3553,plain,
( spl184_198
<=> ! [X0,X1] :
( well_founded_relation(X0)
| ~ well_founded_relation(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_198])]) ).
fof(f1217,plain,
! [X0,X1] :
( well_founded_relation(X0)
| ~ well_founded_relation(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f782]) ).
fof(f782,plain,
! [X0,X1] :
( ( ( well_founded_relation(X0)
| ~ well_founded_relation(X1) )
& ( antisymmetric(X0)
| ~ antisymmetric(X1) )
& ( connected(X0)
| ~ connected(X1) )
& ( transitive(X0)
| ~ transitive(X1) )
& ( reflexive(X0)
| ~ reflexive(X1) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f781]) ).
fof(f781,plain,
! [X1,X0] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f666]) ).
fof(f3550,plain,
( spl184_197
| ~ spl184_23
| ~ spl184_63 ),
inference(avatar_split_clause,[],[f2625,f2491,f2296,f3547]) ).
fof(f3547,plain,
( spl184_197
<=> epsilon_transitive(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_197])]) ).
fof(f2625,plain,
( epsilon_transitive(sK177)
| ~ spl184_23
| ~ spl184_63 ),
inference(resolution,[],[f2492,f2298]) ).
fof(f3545,plain,
spl184_196,
inference(avatar_split_clause,[],[f1216,f3543]) ).
fof(f3543,plain,
( spl184_196
<=> ! [X0,X1] :
( antisymmetric(X0)
| ~ antisymmetric(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_196])]) ).
fof(f1216,plain,
! [X0,X1] :
( antisymmetric(X0)
| ~ antisymmetric(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f782]) ).
fof(f3541,plain,
spl184_195,
inference(avatar_split_clause,[],[f1215,f3539]) ).
fof(f3539,plain,
( spl184_195
<=> ! [X0,X1] :
( connected(X0)
| ~ connected(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_195])]) ).
fof(f1215,plain,
! [X0,X1] :
( connected(X0)
| ~ connected(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f782]) ).
fof(f3537,plain,
spl184_194,
inference(avatar_split_clause,[],[f1214,f3535]) ).
fof(f3535,plain,
( spl184_194
<=> ! [X0,X1] :
( transitive(X0)
| ~ transitive(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_194])]) ).
fof(f1214,plain,
! [X0,X1] :
( transitive(X0)
| ~ transitive(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f782]) ).
fof(f3533,plain,
spl184_193,
inference(avatar_split_clause,[],[f1213,f3531]) ).
fof(f3531,plain,
( spl184_193
<=> ! [X0,X1] :
( reflexive(X0)
| ~ reflexive(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_193])]) ).
fof(f1213,plain,
! [X0,X1] :
( reflexive(X0)
| ~ reflexive(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f782]) ).
fof(f3529,plain,
spl184_192,
inference(avatar_split_clause,[],[f1193,f3527]) ).
fof(f3527,plain,
( spl184_192
<=> ! [X0] :
( sP0(X0)
| sK67(X0) != sK68(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_192])]) ).
fof(f1193,plain,
! [X0] :
( sP0(X0)
| sK67(X0) != sK68(X0) ),
inference(cnf_transformation,[],[f774]) ).
fof(f3525,plain,
spl184_191,
inference(avatar_split_clause,[],[f1192,f3523]) ).
fof(f3523,plain,
( spl184_191
<=> ! [X0] :
( sP0(X0)
| in(sK68(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_191])]) ).
fof(f1192,plain,
! [X0] :
( sP0(X0)
| in(sK68(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f774]) ).
fof(f3521,plain,
spl184_190,
inference(avatar_split_clause,[],[f1191,f3519]) ).
fof(f3519,plain,
( spl184_190
<=> ! [X0] :
( sP0(X0)
| in(sK67(X0),relation_field(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_190])]) ).
fof(f1191,plain,
! [X0] :
( sP0(X0)
| in(sK67(X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f774]) ).
fof(f3507,plain,
( spl184_189
| ~ spl184_13
| ~ spl184_63 ),
inference(avatar_split_clause,[],[f2624,f2491,f2246,f3504]) ).
fof(f3504,plain,
( spl184_189
<=> epsilon_transitive(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_189])]) ).
fof(f2624,plain,
( epsilon_transitive(sK173)
| ~ spl184_13
| ~ spl184_63 ),
inference(resolution,[],[f2492,f2248]) ).
fof(f3486,plain,
( spl184_188
| ~ spl184_186
| ~ spl184_187 ),
inference(avatar_split_clause,[],[f3482,f3479,f3469,f3484]) ).
fof(f3469,plain,
( spl184_186
<=> ! [X0] : sK173 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_186])]) ).
fof(f3479,plain,
( spl184_187
<=> ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_187])]) ).
fof(f3482,plain,
( ! [X0] : set_difference(X0,sK173) = X0
| ~ spl184_186
| ~ spl184_187 ),
inference(forward_demodulation,[],[f3480,f3470]) ).
fof(f3470,plain,
( ! [X0] : sK173 = set_difference(X0,X0)
| ~ spl184_186 ),
inference(avatar_component_clause,[],[f3469]) ).
fof(f3480,plain,
( ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0
| ~ spl184_187 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f3481,plain,
spl184_187,
inference(avatar_split_clause,[],[f2066,f3479]) ).
fof(f2066,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f1696,f1249]) ).
fof(f1696,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f3471,plain,
( spl184_186
| ~ spl184_13
| ~ spl184_103
| ~ spl184_109
| ~ spl184_185 ),
inference(avatar_split_clause,[],[f3467,f3463,f2823,f2798,f2246,f3469]) ).
fof(f2798,plain,
( spl184_103
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_103])]) ).
fof(f3463,plain,
( spl184_185
<=> ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_185])]) ).
fof(f3467,plain,
( ! [X0] : sK173 = set_difference(X0,X0)
| ~ spl184_13
| ~ spl184_103
| ~ spl184_109
| ~ spl184_185 ),
inference(forward_demodulation,[],[f3466,f2880]) ).
fof(f3466,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl184_103
| ~ spl184_185 ),
inference(forward_demodulation,[],[f3464,f2799]) ).
fof(f2799,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl184_103 ),
inference(avatar_component_clause,[],[f2798]) ).
fof(f3464,plain,
( ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set))
| ~ spl184_185 ),
inference(avatar_component_clause,[],[f3463]) ).
fof(f3465,plain,
spl184_185,
inference(avatar_split_clause,[],[f1992,f3463]) ).
fof(f1992,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f1425,f1249]) ).
fof(f1425,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f245]) ).
fof(f245,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f3461,plain,
( spl184_184
| ~ spl184_13
| ~ spl184_62 ),
inference(avatar_split_clause,[],[f2618,f2487,f2246,f3458]) ).
fof(f3458,plain,
( spl184_184
<=> relation(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_184])]) ).
fof(f2487,plain,
( spl184_62
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_62])]) ).
fof(f2618,plain,
( relation(sK173)
| ~ spl184_13
| ~ spl184_62 ),
inference(resolution,[],[f2488,f2248]) ).
fof(f2488,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl184_62 ),
inference(avatar_component_clause,[],[f2487]) ).
fof(f3456,plain,
spl184_183,
inference(avatar_split_clause,[],[f1916,f3454]) ).
fof(f3454,plain,
( spl184_183
<=> ! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_183])]) ).
fof(f1916,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1156,f1912]) ).
fof(f1156,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f190]) ).
fof(f190,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f3452,plain,
spl184_182,
inference(avatar_split_clause,[],[f1286,f3450]) ).
fof(f3450,plain,
( spl184_182
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_182])]) ).
fof(f1286,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f438]) ).
fof(f438,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f327]) ).
fof(f327,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f3448,plain,
spl184_181,
inference(avatar_split_clause,[],[f1261,f3446]) ).
fof(f3446,plain,
( spl184_181
<=> ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_181])]) ).
fof(f1261,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f320]) ).
fof(f320,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f3444,plain,
spl184_180,
inference(avatar_split_clause,[],[f1260,f3442]) ).
fof(f3442,plain,
( spl184_180
<=> ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_180])]) ).
fof(f1260,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f404]) ).
fof(f404,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f194]) ).
fof(f194,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f3440,plain,
spl184_179,
inference(avatar_split_clause,[],[f1256,f3438]) ).
fof(f3438,plain,
( spl184_179
<=> ! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_179])]) ).
fof(f1256,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f400]) ).
fof(f400,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f237]) ).
fof(f237,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f3436,plain,
spl184_178,
inference(avatar_split_clause,[],[f1166,f3434]) ).
fof(f3434,plain,
( spl184_178
<=> ! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK61(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_178])]) ).
fof(f1166,plain,
! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK61(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f757]) ).
fof(f3432,plain,
spl184_177,
inference(avatar_split_clause,[],[f1162,f3430]) ).
fof(f3430,plain,
( spl184_177
<=> ! [X0] :
( ordinal(sK60(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_177])]) ).
fof(f1162,plain,
! [X0] :
( ordinal(sK60(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f753]) ).
fof(f3423,plain,
( spl184_176
| ~ spl184_23
| ~ spl184_61 ),
inference(avatar_split_clause,[],[f2613,f2483,f2296,f3420]) ).
fof(f3420,plain,
( spl184_176
<=> function(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_176])]) ).
fof(f2483,plain,
( spl184_61
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_61])]) ).
fof(f2613,plain,
( function(sK177)
| ~ spl184_23
| ~ spl184_61 ),
inference(resolution,[],[f2484,f2298]) ).
fof(f2484,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl184_61 ),
inference(avatar_component_clause,[],[f2483]) ).
fof(f3394,plain,
( spl184_175
| ~ spl184_13
| ~ spl184_61 ),
inference(avatar_split_clause,[],[f2612,f2483,f2246,f3391]) ).
fof(f3391,plain,
( spl184_175
<=> function(sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_175])]) ).
fof(f2612,plain,
( function(sK173)
| ~ spl184_13
| ~ spl184_61 ),
inference(resolution,[],[f2484,f2248]) ).
fof(f3340,plain,
( spl184_174
| ~ spl184_13
| ~ spl184_109
| ~ spl184_156 ),
inference(avatar_split_clause,[],[f3131,f3128,f2823,f2246,f3338]) ).
fof(f3338,plain,
( spl184_174
<=> ! [X0,X1] :
( sK173 = X0
| sP42(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_174])]) ).
fof(f3128,plain,
( spl184_156
<=> ! [X0,X1] :
( sP42(X1,X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_156])]) ).
fof(f3131,plain,
( ! [X0,X1] :
( sK173 = X0
| sP42(X1,X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_156 ),
inference(forward_demodulation,[],[f3129,f2880]) ).
fof(f3129,plain,
( ! [X0,X1] :
( sP42(X1,X0)
| empty_set = X0 )
| ~ spl184_156 ),
inference(avatar_component_clause,[],[f3128]) ).
fof(f3221,plain,
( spl184_173
| ~ spl184_13
| ~ spl184_109
| ~ spl184_133 ),
inference(avatar_split_clause,[],[f3038,f3035,f2823,f2246,f3219]) ).
fof(f3219,plain,
( spl184_173
<=> ! [X0] :
( sK85(X0) != sK173
| sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_173])]) ).
fof(f3035,plain,
( spl184_133
<=> ! [X0] :
( sP6(X0)
| empty_set != sK85(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_133])]) ).
fof(f3038,plain,
( ! [X0] :
( sK85(X0) != sK173
| sP6(X0) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_133 ),
inference(forward_demodulation,[],[f3036,f2880]) ).
fof(f3036,plain,
( ! [X0] :
( sP6(X0)
| empty_set != sK85(X0) )
| ~ spl184_133 ),
inference(avatar_component_clause,[],[f3035]) ).
fof(f3195,plain,
spl184_172,
inference(avatar_split_clause,[],[f2157,f3193]) ).
fof(f2157,plain,
! [X0,X1] : sP53(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f1858]) ).
fof(f1858,plain,
! [X2,X0,X1] :
( sP53(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1111]) ).
fof(f3191,plain,
spl184_171,
inference(avatar_split_clause,[],[f2156,f3189]) ).
fof(f2156,plain,
! [X0,X1] : sP52(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f1850]) ).
fof(f1850,plain,
! [X2,X0,X1] :
( sP52(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1105]) ).
fof(f3187,plain,
spl184_170,
inference(avatar_split_clause,[],[f2155,f3185]) ).
fof(f3185,plain,
( spl184_170
<=> ! [X0,X1] : sP51(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_170])]) ).
fof(f2155,plain,
! [X0,X1] : sP51(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f1842]) ).
fof(f1842,plain,
! [X2,X0,X1] :
( sP51(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1099]) ).
fof(f3183,plain,
spl184_169,
inference(avatar_split_clause,[],[f2153,f3181]) ).
fof(f3181,plain,
( spl184_169
<=> ! [X0,X1] : sP50(X1,X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_169])]) ).
fof(f2153,plain,
! [X0,X1] : sP50(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f1832]) ).
fof(f1832,plain,
! [X2,X0,X1] :
( sP50(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1092]) ).
fof(f3179,plain,
spl184_168,
inference(avatar_split_clause,[],[f2125,f3177]) ).
fof(f3177,plain,
( spl184_168
<=> ! [X0] :
( sP35(X0,relation_rng(X0))
| ~ sP36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_168])]) ).
fof(f2125,plain,
! [X0] :
( sP35(X0,relation_rng(X0))
| ~ sP36(X0) ),
inference(equality_resolution,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( sP35(X0,X1)
| relation_rng(X0) != X1
| ~ sP36(X0) ),
inference(cnf_transformation,[],[f972]) ).
fof(f3175,plain,
spl184_167,
inference(avatar_split_clause,[],[f1816,f3173]) ).
fof(f3173,plain,
( spl184_167
<=> ! [X0,X1] : relation_of2_as_subset(sK161(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_167])]) ).
fof(f1816,plain,
! [X0,X1] : relation_of2_as_subset(sK161(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,plain,
! [X0,X1] : relation_of2_as_subset(sK161(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f112,f1083]) ).
fof(f1083,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK161(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f112,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f3171,plain,
spl184_166,
inference(avatar_split_clause,[],[f1815,f3169]) ).
fof(f3169,plain,
( spl184_166
<=> ! [X0,X1] : relation_of2(sK160(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_166])]) ).
fof(f1815,plain,
! [X0,X1] : relation_of2(sK160(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,plain,
! [X0,X1] : relation_of2(sK160(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f110,f1081]) ).
fof(f1081,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK160(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f110,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f3167,plain,
spl184_165,
inference(avatar_split_clause,[],[f1743,f3165]) ).
fof(f1743,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f607]) ).
fof(f607,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f225]) ).
fof(f225,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f3163,plain,
spl184_164,
inference(avatar_split_clause,[],[f1742,f3161]) ).
fof(f1742,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f606]) ).
fof(f606,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(f3159,plain,
spl184_163,
inference(avatar_split_clause,[],[f1740,f3157]) ).
fof(f3157,plain,
( spl184_163
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_163])]) ).
fof(f1740,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f603]) ).
fof(f603,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f3155,plain,
spl184_162,
inference(avatar_split_clause,[],[f1739,f3153]) ).
fof(f3153,plain,
( spl184_162
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_162])]) ).
fof(f1739,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f602]) ).
fof(f602,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(f3151,plain,
spl184_161,
inference(avatar_split_clause,[],[f1720,f3149]) ).
fof(f3149,plain,
( spl184_161
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_161])]) ).
fof(f1720,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f599]) ).
fof(f599,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f3147,plain,
spl184_160,
inference(avatar_split_clause,[],[f1719,f3145]) ).
fof(f3145,plain,
( spl184_160
<=> ! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_160])]) ).
fof(f1719,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f598]) ).
fof(f598,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f3143,plain,
spl184_159,
inference(avatar_split_clause,[],[f1718,f3141]) ).
fof(f3141,plain,
( spl184_159
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_159])]) ).
fof(f1718,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f597]) ).
fof(f597,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f3139,plain,
spl184_158,
inference(avatar_split_clause,[],[f1717,f3137]) ).
fof(f3137,plain,
( spl184_158
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_158])]) ).
fof(f1717,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f596]) ).
fof(f596,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f132]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f3135,plain,
spl184_157,
inference(avatar_split_clause,[],[f1716,f3133]) ).
fof(f1716,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f595]) ).
fof(f595,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f127]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f3130,plain,
spl184_156,
inference(avatar_split_clause,[],[f1713,f3128]) ).
fof(f1713,plain,
! [X0,X1] :
( sP42(X1,X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP42(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f726]) ).
fof(f726,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP42(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f594,f725,f724]) ).
fof(f594,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,[],[f30]) ).
fof(f30,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(f3126,plain,
spl184_155,
inference(avatar_split_clause,[],[f1680,f3124]) ).
fof(f1680,plain,
! [X0] :
( relation(X0)
| in(sK136(X0),X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f3122,plain,
spl184_154,
inference(avatar_split_clause,[],[f1675,f3120]) ).
fof(f3120,plain,
( spl184_154
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK135(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_154])]) ).
fof(f1675,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1001]) ).
fof(f3118,plain,
spl184_153,
inference(avatar_split_clause,[],[f1674,f3116]) ).
fof(f3116,plain,
( spl184_153
<=> ! [X0] :
( epsilon_transitive(X0)
| in(sK135(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_153])]) ).
fof(f1674,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1001]) ).
fof(f3114,plain,
spl184_152,
inference(avatar_split_clause,[],[f1669,f3112]) ).
fof(f3112,plain,
( spl184_152
<=> ! [X0] :
( epsilon_connected(X0)
| in(sK134(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_152])]) ).
fof(f1669,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK134(X0),X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f3110,plain,
spl184_151,
inference(avatar_split_clause,[],[f1668,f3108]) ).
fof(f3108,plain,
( spl184_151
<=> ! [X0] :
( epsilon_connected(X0)
| in(sK133(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_151])]) ).
fof(f1668,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK133(X0),X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f3106,plain,
spl184_150,
inference(avatar_split_clause,[],[f1666,f3104]) ).
fof(f3104,plain,
( spl184_150
<=> ! [X0] :
( being_limit_ordinal(X0)
| union(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_150])]) ).
fof(f1666,plain,
! [X0] :
( being_limit_ordinal(X0)
| union(X0) != X0 ),
inference(cnf_transformation,[],[f993]) ).
fof(f993,plain,
! [X0] :
( ( being_limit_ordinal(X0)
| union(X0) != X0 )
& ( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> union(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f3102,plain,
spl184_149,
inference(avatar_split_clause,[],[f1665,f3100]) ).
fof(f3100,plain,
( spl184_149
<=> ! [X0] :
( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_149])]) ).
fof(f1665,plain,
! [X0] :
( union(X0) = X0
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f993]) ).
fof(f3098,plain,
spl184_148,
inference(avatar_split_clause,[],[f1661,f3096]) ).
fof(f3096,plain,
( spl184_148
<=> ! [X0] :
( sP40(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_148])]) ).
fof(f1661,plain,
! [X0] :
( sP40(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f723,plain,
! [X0] :
( sP40(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f585,f722,f721]) ).
fof(f585,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,[],[f584]) ).
fof(f584,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,[],[f17]) ).
fof(f17,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(f3094,plain,
spl184_147,
inference(avatar_split_clause,[],[f1650,f3092]) ).
fof(f3092,plain,
( spl184_147
<=> ! [X0] :
( sP38(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_147])]) ).
fof(f1650,plain,
! [X0] :
( sP38(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f720]) ).
fof(f720,plain,
! [X0] :
( sP38(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f583,f719,f718]) ).
fof(f583,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,[],[f582]) ).
fof(f582,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,[],[f20]) ).
fof(f20,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(f3090,plain,
spl184_146,
inference(avatar_split_clause,[],[f1637,f3088]) ).
fof(f3088,plain,
( spl184_146
<=> ! [X0] :
( sP36(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_146])]) ).
fof(f1637,plain,
! [X0] :
( sP36(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f717]) ).
fof(f717,plain,
! [X0] :
( sP36(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f579,f716,f715]) ).
fof(f579,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,[],[f578]) ).
fof(f578,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,[],[f55]) ).
fof(f55,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(f3086,plain,
spl184_145,
inference(avatar_split_clause,[],[f1628,f3084]) ).
fof(f3084,plain,
( spl184_145
<=> ! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_145])]) ).
fof(f1628,plain,
! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f714]) ).
fof(f714,plain,
! [X0] :
( sP34(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f577,f713,f712]) ).
fof(f713,plain,
! [X0] :
( ( one_to_one(X0)
<=> sP33(X0) )
| ~ sP34(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f577,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,[],[f576]) ).
fof(f576,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,[],[f67]) ).
fof(f67,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(f3082,plain,
spl184_144,
inference(avatar_split_clause,[],[f1622,f3080]) ).
fof(f3080,plain,
( spl184_144
<=> ! [X0] :
( one_to_one(X0)
| ~ sP33(X0)
| ~ sP34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_144])]) ).
fof(f1622,plain,
! [X0] :
( one_to_one(X0)
| ~ sP33(X0)
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f967]) ).
fof(f967,plain,
! [X0] :
( ( ( one_to_one(X0)
| ~ sP33(X0) )
& ( sP33(X0)
| ~ one_to_one(X0) ) )
| ~ sP34(X0) ),
inference(nnf_transformation,[],[f713]) ).
fof(f3078,plain,
spl184_143,
inference(avatar_split_clause,[],[f1621,f3076]) ).
fof(f3076,plain,
( spl184_143
<=> ! [X0] :
( sP33(X0)
| ~ one_to_one(X0)
| ~ sP34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_143])]) ).
fof(f1621,plain,
! [X0] :
( sP33(X0)
| ~ one_to_one(X0)
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f967]) ).
fof(f3074,plain,
spl184_142,
inference(avatar_split_clause,[],[f1615,f3072]) ).
fof(f3072,plain,
( spl184_142
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_142])]) ).
fof(f1615,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f569]) ).
fof(f569,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f568]) ).
fof(f568,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f3070,plain,
spl184_141,
inference(avatar_split_clause,[],[f1527,f3068]) ).
fof(f3068,plain,
( spl184_141
<=> ! [X0,X1] :
( is_well_founded_in(X1,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_141])]) ).
fof(f1527,plain,
! [X0,X1] :
( is_well_founded_in(X1,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f902]) ).
fof(f3066,plain,
spl184_140,
inference(avatar_split_clause,[],[f1526,f3064]) ).
fof(f3064,plain,
( spl184_140
<=> ! [X0,X1] :
( is_connected_in(X1,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_140])]) ).
fof(f1526,plain,
! [X0,X1] :
( is_connected_in(X1,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f902]) ).
fof(f3062,plain,
spl184_139,
inference(avatar_split_clause,[],[f1525,f3060]) ).
fof(f3060,plain,
( spl184_139
<=> ! [X0,X1] :
( is_antisymmetric_in(X1,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_139])]) ).
fof(f1525,plain,
! [X0,X1] :
( is_antisymmetric_in(X1,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f902]) ).
fof(f3058,plain,
spl184_138,
inference(avatar_split_clause,[],[f1524,f3056]) ).
fof(f3056,plain,
( spl184_138
<=> ! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_138])]) ).
fof(f1524,plain,
! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f902]) ).
fof(f3054,plain,
spl184_137,
inference(avatar_split_clause,[],[f1523,f3052]) ).
fof(f3052,plain,
( spl184_137
<=> ! [X0,X1] :
( is_reflexive_in(X1,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_137])]) ).
fof(f1523,plain,
! [X0,X1] :
( is_reflexive_in(X1,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f902]) ).
fof(f3050,plain,
spl184_136,
inference(avatar_split_clause,[],[f1509,f3048]) ).
fof(f3048,plain,
( spl184_136
<=> ! [X2,X0,X1] :
( one_to_one(X1)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_136])]) ).
fof(f1509,plain,
! [X2,X0,X1] :
( one_to_one(X1)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f893]) ).
fof(f3046,plain,
spl184_135,
inference(avatar_split_clause,[],[f1476,f3044]) ).
fof(f3044,plain,
( spl184_135
<=> ! [X0] :
( well_ordering(X0)
| ~ sP8(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_135])]) ).
fof(f1476,plain,
! [X0] :
( well_ordering(X0)
| ~ sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f866]) ).
fof(f866,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ well_ordering(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f676]) ).
fof(f676,plain,
! [X0] :
( ( well_ordering(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f3042,plain,
spl184_134,
inference(avatar_split_clause,[],[f1475,f3040]) ).
fof(f3040,plain,
( spl184_134
<=> ! [X0] :
( sP8(X0)
| ~ well_ordering(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_134])]) ).
fof(f1475,plain,
! [X0] :
( sP8(X0)
| ~ well_ordering(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f866]) ).
fof(f3037,plain,
spl184_133,
inference(avatar_split_clause,[],[f1472,f3035]) ).
fof(f1472,plain,
! [X0] :
( sP6(X0)
| empty_set != sK85(X0) ),
inference(cnf_transformation,[],[f865]) ).
fof(f3033,plain,
spl184_132,
inference(avatar_split_clause,[],[f1468,f3031]) ).
fof(f3031,plain,
( spl184_132
<=> ! [X0] :
( well_founded_relation(X0)
| ~ sP6(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_132])]) ).
fof(f1468,plain,
! [X0] :
( well_founded_relation(X0)
| ~ sP6(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f860]) ).
fof(f860,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ well_founded_relation(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f673]) ).
fof(f673,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f3029,plain,
spl184_131,
inference(avatar_split_clause,[],[f1467,f3027]) ).
fof(f3027,plain,
( spl184_131
<=> ! [X0] :
( sP6(X0)
| ~ well_founded_relation(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_131])]) ).
fof(f1467,plain,
! [X0] :
( sP6(X0)
| ~ well_founded_relation(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f860]) ).
fof(f3025,plain,
spl184_130,
inference(avatar_split_clause,[],[f1189,f3023]) ).
fof(f1189,plain,
! [X0] :
( connected(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f770]) ).
fof(f770,plain,
! [X0] :
( ( ( connected(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ connected(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f664]) ).
fof(f664,plain,
! [X0] :
( ( connected(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f3021,plain,
spl184_129,
inference(avatar_split_clause,[],[f1188,f3019]) ).
fof(f3019,plain,
( spl184_129
<=> ! [X0] :
( sP0(X0)
| ~ connected(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_129])]) ).
fof(f1188,plain,
! [X0] :
( sP0(X0)
| ~ connected(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f770]) ).
fof(f3009,plain,
( ~ spl184_128
| ~ spl184_1
| ~ spl184_123 ),
inference(avatar_split_clause,[],[f2998,f2975,f2186,f3006]) ).
fof(f3006,plain,
( spl184_128
<=> proper_subset(sK57,sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_128])]) ).
fof(f2998,plain,
( ~ proper_subset(sK57,sK56)
| ~ spl184_1
| ~ spl184_123 ),
inference(resolution,[],[f2976,f2188]) ).
fof(f3004,plain,
( spl184_127
| ~ spl184_13
| ~ spl184_109
| ~ spl184_124 ),
inference(avatar_split_clause,[],[f2983,f2979,f2823,f2246,f3001]) ).
fof(f3001,plain,
( spl184_127
<=> powerset(sK173) = unordered_pair(sK173,sK173) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_127])]) ).
fof(f2979,plain,
( spl184_124
<=> powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_124])]) ).
fof(f2983,plain,
( powerset(sK173) = unordered_pair(sK173,sK173)
| ~ spl184_13
| ~ spl184_109
| ~ spl184_124 ),
inference(forward_demodulation,[],[f2981,f2880]) ).
fof(f2981,plain,
( powerset(empty_set) = unordered_pair(empty_set,empty_set)
| ~ spl184_124 ),
inference(avatar_component_clause,[],[f2979]) ).
fof(f2991,plain,
( spl184_126
| ~ spl184_13
| ~ spl184_109
| ~ spl184_121 ),
inference(avatar_split_clause,[],[f2969,f2965,f2823,f2246,f2989]) ).
fof(f2989,plain,
( spl184_126
<=> ! [X0] :
( ~ subset(X0,sK173)
| sK173 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_126])]) ).
fof(f2965,plain,
( spl184_121
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_121])]) ).
fof(f2969,plain,
( ! [X0] :
( ~ subset(X0,sK173)
| sK173 = X0 )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_121 ),
inference(forward_demodulation,[],[f2968,f2880]) ).
fof(f2968,plain,
( ! [X0] :
( sK173 = X0
| ~ subset(X0,empty_set) )
| ~ spl184_13
| ~ spl184_109
| ~ spl184_121 ),
inference(forward_demodulation,[],[f2966,f2880]) ).
fof(f2966,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl184_121 ),
inference(avatar_component_clause,[],[f2965]) ).
fof(f2987,plain,
spl184_125,
inference(avatar_split_clause,[],[f1990,f2985]) ).
fof(f2985,plain,
( spl184_125
<=> ! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_125])]) ).
fof(f1990,plain,
! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1420,f1912]) ).
fof(f1420,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f118]) ).
fof(f118,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f2982,plain,
spl184_124,
inference(avatar_split_clause,[],[f1914,f2979]) ).
fof(f1914,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f1151,f1158]) ).
fof(f1151,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f227]) ).
fof(f227,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f2977,plain,
spl184_123,
inference(avatar_split_clause,[],[f1338,f2975]) ).
fof(f1338,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f472]) ).
fof(f472,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f301]) ).
fof(f301,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f2973,plain,
spl184_122,
inference(avatar_split_clause,[],[f1240,f2971]) ).
fof(f1240,plain,
! [X0] :
( ordinal(X0)
| in(sK74(X0),X0) ),
inference(cnf_transformation,[],[f793]) ).
fof(f2967,plain,
spl184_121,
inference(avatar_split_clause,[],[f1221,f2965]) ).
fof(f1221,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f388]) ).
fof(f388,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f271]) ).
fof(f271,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f2869,plain,
spl184_120,
inference(avatar_split_clause,[],[f1812,f2867]) ).
fof(f2867,plain,
( spl184_120
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_120])]) ).
fof(f1812,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f651]) ).
fof(f651,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f315]) ).
fof(f315,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f2865,plain,
spl184_119,
inference(avatar_split_clause,[],[f1729,f2863]) ).
fof(f2863,plain,
( spl184_119
<=> ! [X0,X1] :
( sP44(X1,X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_119])]) ).
fof(f1729,plain,
! [X0,X1] :
( sP44(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f729]) ).
fof(f729,plain,
! [X0,X1] :
( sP44(X1,X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f600,f728,f727]) ).
fof(f600,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,[],[f14]) ).
fof(f14,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(f2861,plain,
spl184_118,
inference(avatar_split_clause,[],[f1695,f2859]) ).
fof(f2859,plain,
( spl184_118
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_118])]) ).
fof(f1695,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f2857,plain,
spl184_117,
inference(avatar_split_clause,[],[f1689,f2855]) ).
fof(f2855,plain,
( spl184_117
<=> ! [X0] : element(sK143(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_117])]) ).
fof(f1689,plain,
! [X0] : element(sK143(X0),powerset(X0)),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,plain,
! [X0] :
( empty(sK143(X0))
& element(sK143(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143])],[f175,f1019]) ).
fof(f1019,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK143(X0))
& element(sK143(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f175,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f2853,plain,
spl184_116,
inference(avatar_split_clause,[],[f1456,f2851]) ).
fof(f2851,plain,
( spl184_116
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_116])]) ).
fof(f1456,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f534]) ).
fof(f534,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f2849,plain,
spl184_115,
inference(avatar_split_clause,[],[f1455,f2847]) ).
fof(f2847,plain,
( spl184_115
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_115])]) ).
fof(f1455,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f533]) ).
fof(f533,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f140]) ).
fof(f140,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f2845,plain,
spl184_114,
inference(avatar_split_clause,[],[f1454,f2843]) ).
fof(f2843,plain,
( spl184_114
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_114])]) ).
fof(f1454,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f533]) ).
fof(f2841,plain,
spl184_113,
inference(avatar_split_clause,[],[f1453,f2839]) ).
fof(f2839,plain,
( spl184_113
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_113])]) ).
fof(f1453,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f532]) ).
fof(f532,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f2837,plain,
spl184_112,
inference(avatar_split_clause,[],[f1452,f2835]) ).
fof(f2835,plain,
( spl184_112
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_112])]) ).
fof(f1452,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f532]) ).
fof(f2833,plain,
spl184_111,
inference(avatar_split_clause,[],[f1451,f2831]) ).
fof(f2831,plain,
( spl184_111
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_111])]) ).
fof(f1451,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f531]) ).
fof(f531,plain,
! [X0] :
( ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f2829,plain,
spl184_110,
inference(avatar_split_clause,[],[f1450,f2827]) ).
fof(f2827,plain,
( spl184_110
<=> ! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_110])]) ).
fof(f1450,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f531]) ).
fof(f2825,plain,
spl184_109,
inference(avatar_split_clause,[],[f1446,f2823]) ).
fof(f1446,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f529]) ).
fof(f529,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f309]) ).
fof(f309,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f2821,plain,
( spl184_108
| ~ spl184_42
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2464,f2448,f2391,f2818]) ).
fof(f2818,plain,
( spl184_108
<=> sP1(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_108])]) ).
fof(f2464,plain,
( sP1(sK183)
| ~ spl184_42
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2393]) ).
fof(f2816,plain,
spl184_107,
inference(avatar_split_clause,[],[f1443,f2814]) ).
fof(f2814,plain,
( spl184_107
<=> ! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_107])]) ).
fof(f1443,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f526]) ).
fof(f526,plain,
! [X0] :
( ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,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(f2812,plain,
spl184_106,
inference(avatar_split_clause,[],[f1442,f2810]) ).
fof(f2810,plain,
( spl184_106
<=> ! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_106])]) ).
fof(f1442,plain,
! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f526]) ).
fof(f2808,plain,
spl184_105,
inference(avatar_split_clause,[],[f1441,f2806]) ).
fof(f2806,plain,
( spl184_105
<=> ! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_105])]) ).
fof(f1441,plain,
! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f526]) ).
fof(f2804,plain,
spl184_104,
inference(avatar_split_clause,[],[f1434,f2802]) ).
fof(f2802,plain,
( spl184_104
<=> ! [X0] :
( ~ empty(sK84(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_104])]) ).
fof(f1434,plain,
! [X0] :
( ~ empty(sK84(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f2800,plain,
spl184_103,
inference(avatar_split_clause,[],[f1428,f2798]) ).
fof(f1428,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f267]) ).
fof(f267,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f2796,plain,
spl184_102,
inference(avatar_split_clause,[],[f1427,f2794]) ).
fof(f1427,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f224]) ).
fof(f224,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f2792,plain,
spl184_101,
inference(avatar_split_clause,[],[f1426,f2790]) ).
fof(f2790,plain,
( spl184_101
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_101])]) ).
fof(f1426,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f287]) ).
fof(f287,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f2788,plain,
( spl184_100
| ~ spl184_35
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2463,f2448,f2356,f2785]) ).
fof(f2785,plain,
( spl184_100
<=> sP1(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_100])]) ).
fof(f2463,plain,
( sP1(sK182)
| ~ spl184_35
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2358]) ).
fof(f2782,plain,
spl184_99,
inference(avatar_split_clause,[],[f2147,f2780]) ).
fof(f2780,plain,
( spl184_99
<=> ! [X3] : in(X3,unordered_pair(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_99])]) ).
fof(f2147,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f2146]) ).
fof(f2146,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f2085]) ).
fof(f2085,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1802,f1158]) ).
fof(f1802,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f1073]) ).
fof(f2778,plain,
spl184_98,
inference(avatar_split_clause,[],[f1915,f2776]) ).
fof(f2776,plain,
( spl184_98
<=> ! [X0] : empty_set != unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_98])]) ).
fof(f1915,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f1155,f1158]) ).
fof(f1155,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f150]) ).
fof(f150,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f2774,plain,
spl184_97,
inference(avatar_split_clause,[],[f1246,f2772]) ).
fof(f1246,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f259]) ).
fof(f259,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f2770,plain,
spl184_96,
inference(avatar_split_clause,[],[f1245,f2768]) ).
fof(f2768,plain,
( spl184_96
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_96])]) ).
fof(f1245,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f317]) ).
fof(f317,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f2766,plain,
spl184_95,
inference(avatar_split_clause,[],[f1160,f2764]) ).
fof(f1160,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f312]) ).
fof(f312,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(f2762,plain,
spl184_94,
inference(avatar_split_clause,[],[f1159,f2760]) ).
fof(f2760,plain,
( spl184_94
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_94])]) ).
fof(f1159,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f312]) ).
fof(f2758,plain,
( spl184_93
| ~ spl184_32
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2462,f2448,f2341,f2755]) ).
fof(f2755,plain,
( spl184_93
<=> sP1(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_93])]) ).
fof(f2462,plain,
( sP1(sK181)
| ~ spl184_32
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2343]) ).
fof(f2753,plain,
spl184_92,
inference(avatar_split_clause,[],[f1157,f2751]) ).
fof(f2751,plain,
( spl184_92
<=> ! [X0] : union(powerset(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl184_92])]) ).
fof(f1157,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f330]) ).
fof(f330,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f2719,plain,
( spl184_91
| ~ spl184_30
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2461,f2448,f2331,f2716]) ).
fof(f2716,plain,
( spl184_91
<=> sP1(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_91])]) ).
fof(f2461,plain,
( sP1(sK180)
| ~ spl184_30
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2333]) ).
fof(f2654,plain,
( spl184_90
| ~ spl184_27
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2460,f2448,f2316,f2651]) ).
fof(f2651,plain,
( spl184_90
<=> sP1(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_90])]) ).
fof(f2460,plain,
( sP1(sK179)
| ~ spl184_27
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2318]) ).
fof(f2601,plain,
( spl184_89
| ~ spl184_25
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2459,f2448,f2306,f2598]) ).
fof(f2598,plain,
( spl184_89
<=> sP1(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_89])]) ).
fof(f2459,plain,
( sP1(sK178)
| ~ spl184_25
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2308]) ).
fof(f2596,plain,
spl184_88,
inference(avatar_split_clause,[],[f2166,f2594]) ).
fof(f2594,plain,
( spl184_88
<=> ! [X0] : element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_88])]) ).
fof(f2166,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f1429,f1424]) ).
fof(f1424,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f1429,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f2592,plain,
spl184_87,
inference(avatar_split_clause,[],[f2145,f2590]) ).
fof(f2590,plain,
( spl184_87
<=> ! [X0] : sP49(X0,union(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_87])]) ).
fof(f2145,plain,
! [X0] : sP49(X0,union(X0)),
inference(equality_resolution,[],[f1799]) ).
fof(f1799,plain,
! [X0,X1] :
( sP49(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f1069]) ).
fof(f2588,plain,
spl184_86,
inference(avatar_split_clause,[],[f2136,f2585]) ).
fof(f2585,plain,
( spl184_86
<=> empty_set = set_meet(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_86])]) ).
fof(f2136,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f2135]) ).
fof(f2135,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f1715]) ).
fof(f1715,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f1030]) ).
fof(f2583,plain,
spl184_85,
inference(avatar_split_clause,[],[f1693,f2581]) ).
fof(f2581,plain,
( spl184_85
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_85])]) ).
fof(f1693,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f131]) ).
fof(f131,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f2579,plain,
spl184_84,
inference(avatar_split_clause,[],[f1685,f2577]) ).
fof(f2577,plain,
( spl184_84
<=> ! [X0] : in(X0,sK141(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_84])]) ).
fof(f1685,plain,
! [X0] : in(X0,sK141(X0)),
inference(cnf_transformation,[],[f1018]) ).
fof(f2575,plain,
spl184_83,
inference(avatar_split_clause,[],[f1684,f2573]) ).
fof(f2573,plain,
( spl184_83
<=> ! [X0] : element(sK140(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_83])]) ).
fof(f1684,plain,
! [X0] : element(sK140(X0),X0),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,plain,
! [X0] : element(sK140(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK140])],[f111,f1013]) ).
fof(f1013,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK140(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f111,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f2571,plain,
spl184_82,
inference(avatar_split_clause,[],[f1612,f2569]) ).
fof(f1612,plain,
! [X0] :
( sP32(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f711]) ).
fof(f711,plain,
! [X0] :
( sP32(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f563,f710,f709]) ).
fof(f563,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,[],[f21]) ).
fof(f21,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(f2567,plain,
spl184_81,
inference(avatar_split_clause,[],[f1603,f2565]) ).
fof(f1603,plain,
! [X0] :
( sP30(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f708]) ).
fof(f708,plain,
! [X0] :
( sP30(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f562,f707,f706]) ).
fof(f562,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,[],[f22]) ).
fof(f22,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(f2563,plain,
spl184_80,
inference(avatar_split_clause,[],[f1594,f2561]) ).
fof(f1594,plain,
! [X0] :
( sP28(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f705]) ).
fof(f705,plain,
! [X0] :
( sP28(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f561,f704,f703]) ).
fof(f561,plain,
! [X0] :
( ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
fof(f2559,plain,
spl184_79,
inference(avatar_split_clause,[],[f1568,f2557]) ).
fof(f1568,plain,
! [X0] :
( sP24(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f699]) ).
fof(f699,plain,
! [X0] :
( sP24(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f557,f698,f697]) ).
fof(f557,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,[],[f556]) ).
fof(f556,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,[],[f69]) ).
fof(f69,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(f2555,plain,
( spl184_78
| ~ spl184_24
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2458,f2448,f2301,f2552]) ).
fof(f2552,plain,
( spl184_78
<=> sP1(sK177) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_78])]) ).
fof(f2458,plain,
( sP1(sK177)
| ~ spl184_24
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2303]) ).
fof(f2550,plain,
spl184_77,
inference(avatar_split_clause,[],[f1558,f2548]) ).
fof(f1558,plain,
! [X0] :
( sP22(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f696]) ).
fof(f696,plain,
! [X0] :
( sP22(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f555,f695,f694]) ).
fof(f555,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,[],[f62]) ).
fof(f62,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(f2546,plain,
spl184_76,
inference(avatar_split_clause,[],[f1549,f2544]) ).
fof(f1549,plain,
! [X0] :
( sP20(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f693]) ).
fof(f693,plain,
! [X0] :
( sP20(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f554,f692,f691]) ).
fof(f554,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,[],[f553]) ).
fof(f553,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,[],[f50]) ).
fof(f50,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(f2542,plain,
spl184_75,
inference(avatar_split_clause,[],[f1540,f2540]) ).
fof(f1540,plain,
! [X0] :
( sP18(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f690]) ).
fof(f690,plain,
! [X0] :
( sP18(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f552,f689,f688]) ).
fof(f552,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,[],[f45]) ).
fof(f45,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(f2538,plain,
spl184_74,
inference(avatar_split_clause,[],[f1529,f2536]) ).
fof(f1529,plain,
! [X0] :
( sP16(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f687]) ).
fof(f687,plain,
! [X0] :
( sP16(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f550,f686,f685]) ).
fof(f550,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,[],[f59]) ).
fof(f59,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(f2534,plain,
spl184_73,
inference(avatar_split_clause,[],[f1483,f2532]) ).
fof(f1483,plain,
! [X0] :
( sP9(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f677]) ).
fof(f677,plain,
! [X0] :
( sP9(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f542,f676,f675]) ).
fof(f542,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,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(f2530,plain,
spl184_72,
inference(avatar_split_clause,[],[f1481,f2528]) ).
fof(f2528,plain,
( spl184_72
<=> ! [X0] :
( well_founded_relation(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_72])]) ).
fof(f1481,plain,
! [X0] :
( well_founded_relation(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f2526,plain,
spl184_71,
inference(avatar_split_clause,[],[f1480,f2524]) ).
fof(f2524,plain,
( spl184_71
<=> ! [X0] :
( connected(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_71])]) ).
fof(f1480,plain,
! [X0] :
( connected(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f2522,plain,
spl184_70,
inference(avatar_split_clause,[],[f1479,f2520]) ).
fof(f2520,plain,
( spl184_70
<=> ! [X0] :
( antisymmetric(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_70])]) ).
fof(f1479,plain,
! [X0] :
( antisymmetric(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f2518,plain,
spl184_69,
inference(avatar_split_clause,[],[f1478,f2516]) ).
fof(f2516,plain,
( spl184_69
<=> ! [X0] :
( transitive(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_69])]) ).
fof(f1478,plain,
! [X0] :
( transitive(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f2514,plain,
spl184_68,
inference(avatar_split_clause,[],[f1477,f2512]) ).
fof(f2512,plain,
( spl184_68
<=> ! [X0] :
( reflexive(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_68])]) ).
fof(f1477,plain,
! [X0] :
( reflexive(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f868]) ).
fof(f2510,plain,
( spl184_67
| ~ spl184_19
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2457,f2448,f2276,f2507]) ).
fof(f2507,plain,
( spl184_67
<=> sP1(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_67])]) ).
fof(f2457,plain,
( sP1(sK175)
| ~ spl184_19
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2278]) ).
fof(f2505,plain,
spl184_66,
inference(avatar_split_clause,[],[f1474,f2503]) ).
fof(f1474,plain,
! [X0] :
( sP7(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f674]) ).
fof(f674,plain,
! [X0] :
( sP7(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f541,f673,f672]) ).
fof(f541,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,[],[f39]) ).
fof(f39,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(f2501,plain,
spl184_65,
inference(avatar_split_clause,[],[f1449,f2499]) ).
fof(f1449,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f2497,plain,
spl184_64,
inference(avatar_split_clause,[],[f1448,f2495]) ).
fof(f1448,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f530]) ).
fof(f2493,plain,
spl184_63,
inference(avatar_split_clause,[],[f1447,f2491]) ).
fof(f1447,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f530]) ).
fof(f2489,plain,
spl184_62,
inference(avatar_split_clause,[],[f1445,f2487]) ).
fof(f1445,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f528]) ).
fof(f528,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(f2485,plain,
spl184_61,
inference(avatar_split_clause,[],[f1444,f2483]) ).
fof(f1444,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f527]) ).
fof(f527,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(f2481,plain,
spl184_60,
inference(avatar_split_clause,[],[f1436,f2479]) ).
fof(f1436,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f524]) ).
fof(f524,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(f2477,plain,
spl184_59,
inference(avatar_split_clause,[],[f1435,f2475]) ).
fof(f1435,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f524]) ).
fof(f2473,plain,
spl184_58,
inference(avatar_split_clause,[],[f1424,f2471]) ).
fof(f2469,plain,
( spl184_57
| ~ spl184_5
| ~ spl184_55 ),
inference(avatar_split_clause,[],[f2456,f2448,f2206,f2466]) ).
fof(f2466,plain,
( spl184_57
<=> sP1(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_57])]) ).
fof(f2456,plain,
( sP1(empty_set)
| ~ spl184_5
| ~ spl184_55 ),
inference(resolution,[],[f2449,f2208]) ).
fof(f2454,plain,
spl184_56,
inference(avatar_split_clause,[],[f1242,f2452]) ).
fof(f2452,plain,
( spl184_56
<=> ! [X0] : in(X0,sK75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_56])]) ).
fof(f1242,plain,
! [X0] : in(X0,sK75(X0)),
inference(cnf_transformation,[],[f796]) ).
fof(f2450,plain,
spl184_55,
inference(avatar_split_clause,[],[f1196,f2448]) ).
fof(f1196,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f665]) ).
fof(f665,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f366,f664,f663]) ).
fof(f366,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,[],[f161]) ).
fof(f161,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(f2446,plain,
spl184_54,
inference(avatar_split_clause,[],[f1153,f2443]) ).
fof(f2443,plain,
( spl184_54
<=> empty_set = relation_rng(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_54])]) ).
fof(f1153,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f300]) ).
fof(f300,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f2441,plain,
spl184_53,
inference(avatar_split_clause,[],[f1152,f2438]) ).
fof(f2438,plain,
( spl184_53
<=> empty_set = relation_dom(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_53])]) ).
fof(f1152,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f300]) ).
fof(f2436,plain,
spl184_52,
inference(avatar_split_clause,[],[f2133,f2434]) ).
fof(f2434,plain,
( spl184_52
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_52])]) ).
fof(f2133,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f1682]) ).
fof(f1682,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2432,plain,
spl184_51,
inference(avatar_split_clause,[],[f1692,f2430]) ).
fof(f1692,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f339]) ).
fof(f339,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f2428,plain,
spl184_50,
inference(avatar_split_clause,[],[f1691,f2426]) ).
fof(f2426,plain,
( spl184_50
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_50])]) ).
fof(f1691,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f2424,plain,
spl184_49,
inference(avatar_split_clause,[],[f1690,f2422]) ).
fof(f2422,plain,
( spl184_49
<=> ! [X0] : empty(sK143(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_49])]) ).
fof(f1690,plain,
! [X0] : empty(sK143(X0)),
inference(cnf_transformation,[],[f1020]) ).
fof(f2420,plain,
spl184_48,
inference(avatar_split_clause,[],[f1432,f2418]) ).
fof(f2418,plain,
( spl184_48
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_48])]) ).
fof(f1432,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f2416,plain,
spl184_47,
inference(avatar_split_clause,[],[f1423,f2414]) ).
fof(f1423,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f100]) ).
fof(f100,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f2412,plain,
spl184_46,
inference(avatar_split_clause,[],[f1422,f2410]) ).
fof(f2410,plain,
( spl184_46
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_46])]) ).
fof(f1422,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f120]) ).
fof(f120,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f2408,plain,
spl184_45,
inference(avatar_split_clause,[],[f1154,f2406]) ).
fof(f2406,plain,
( spl184_45
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_45])]) ).
fof(f1154,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f248]) ).
fof(f248,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f2404,plain,
spl184_44,
inference(avatar_split_clause,[],[f1911,f2401]) ).
fof(f2401,plain,
( spl184_44
<=> function(sK183) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_44])]) ).
fof(f1911,plain,
function(sK183),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,plain,
( function(sK183)
& empty(sK183)
& relation(sK183) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f172,f1146]) ).
fof(f1146,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK183)
& empty(sK183)
& relation(sK183) ) ),
introduced(choice_axiom,[]) ).
fof(f172,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f2399,plain,
spl184_43,
inference(avatar_split_clause,[],[f1910,f2396]) ).
fof(f1910,plain,
empty(sK183),
inference(cnf_transformation,[],[f1147]) ).
fof(f2394,plain,
spl184_42,
inference(avatar_split_clause,[],[f1909,f2391]) ).
fof(f1909,plain,
relation(sK183),
inference(cnf_transformation,[],[f1147]) ).
fof(f2389,plain,
spl184_41,
inference(avatar_split_clause,[],[f1908,f2386]) ).
fof(f2386,plain,
( spl184_41
<=> ordinal(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_41])]) ).
fof(f1908,plain,
ordinal(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,plain,
( ordinal(sK182)
& epsilon_connected(sK182)
& epsilon_transitive(sK182)
& empty(sK182)
& one_to_one(sK182)
& function(sK182)
& relation(sK182) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f173,f1144]) ).
fof(f1144,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK182)
& epsilon_connected(sK182)
& epsilon_transitive(sK182)
& empty(sK182)
& one_to_one(sK182)
& function(sK182)
& relation(sK182) ) ),
introduced(choice_axiom,[]) ).
fof(f173,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(f2384,plain,
spl184_40,
inference(avatar_split_clause,[],[f1907,f2381]) ).
fof(f2381,plain,
( spl184_40
<=> epsilon_connected(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_40])]) ).
fof(f1907,plain,
epsilon_connected(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2379,plain,
spl184_39,
inference(avatar_split_clause,[],[f1906,f2376]) ).
fof(f2376,plain,
( spl184_39
<=> epsilon_transitive(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_39])]) ).
fof(f1906,plain,
epsilon_transitive(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2374,plain,
spl184_38,
inference(avatar_split_clause,[],[f1905,f2371]) ).
fof(f2371,plain,
( spl184_38
<=> empty(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_38])]) ).
fof(f1905,plain,
empty(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2369,plain,
spl184_37,
inference(avatar_split_clause,[],[f1904,f2366]) ).
fof(f2366,plain,
( spl184_37
<=> one_to_one(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_37])]) ).
fof(f1904,plain,
one_to_one(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2364,plain,
spl184_36,
inference(avatar_split_clause,[],[f1903,f2361]) ).
fof(f2361,plain,
( spl184_36
<=> function(sK182) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_36])]) ).
fof(f1903,plain,
function(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2359,plain,
spl184_35,
inference(avatar_split_clause,[],[f1902,f2356]) ).
fof(f1902,plain,
relation(sK182),
inference(cnf_transformation,[],[f1145]) ).
fof(f2354,plain,
spl184_34,
inference(avatar_split_clause,[],[f1901,f2351]) ).
fof(f2351,plain,
( spl184_34
<=> one_to_one(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_34])]) ).
fof(f1901,plain,
one_to_one(sK181),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,plain,
( one_to_one(sK181)
& function(sK181)
& relation(sK181) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181])],[f177,f1142]) ).
fof(f1142,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK181)
& function(sK181)
& relation(sK181) ) ),
introduced(choice_axiom,[]) ).
fof(f177,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f2349,plain,
spl184_33,
inference(avatar_split_clause,[],[f1900,f2346]) ).
fof(f2346,plain,
( spl184_33
<=> function(sK181) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_33])]) ).
fof(f1900,plain,
function(sK181),
inference(cnf_transformation,[],[f1143]) ).
fof(f2344,plain,
spl184_32,
inference(avatar_split_clause,[],[f1899,f2341]) ).
fof(f1899,plain,
relation(sK181),
inference(cnf_transformation,[],[f1143]) ).
fof(f2339,plain,
spl184_31,
inference(avatar_split_clause,[],[f1898,f2336]) ).
fof(f2336,plain,
( spl184_31
<=> function(sK180) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_31])]) ).
fof(f1898,plain,
function(sK180),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,plain,
( function(sK180)
& relation(sK180) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f167,f1140]) ).
fof(f1140,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK180)
& relation(sK180) ) ),
introduced(choice_axiom,[]) ).
fof(f167,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f2334,plain,
spl184_30,
inference(avatar_split_clause,[],[f1897,f2331]) ).
fof(f1897,plain,
relation(sK180),
inference(cnf_transformation,[],[f1141]) ).
fof(f2329,plain,
spl184_29,
inference(avatar_split_clause,[],[f1896,f2326]) ).
fof(f2326,plain,
( spl184_29
<=> function(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_29])]) ).
fof(f1896,plain,
function(sK179),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,plain,
( function(sK179)
& relation_empty_yielding(sK179)
& relation(sK179) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK179])],[f180,f1138]) ).
fof(f1138,plain,
( ? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) )
=> ( function(sK179)
& relation_empty_yielding(sK179)
& relation(sK179) ) ),
introduced(choice_axiom,[]) ).
fof(f180,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f2324,plain,
spl184_28,
inference(avatar_split_clause,[],[f1895,f2321]) ).
fof(f2321,plain,
( spl184_28
<=> relation_empty_yielding(sK179) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_28])]) ).
fof(f1895,plain,
relation_empty_yielding(sK179),
inference(cnf_transformation,[],[f1139]) ).
fof(f2319,plain,
spl184_27,
inference(avatar_split_clause,[],[f1894,f2316]) ).
fof(f1894,plain,
relation(sK179),
inference(cnf_transformation,[],[f1139]) ).
fof(f2314,plain,
spl184_26,
inference(avatar_split_clause,[],[f1893,f2311]) ).
fof(f2311,plain,
( spl184_26
<=> relation_empty_yielding(sK178) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_26])]) ).
fof(f1893,plain,
relation_empty_yielding(sK178),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,plain,
( relation_empty_yielding(sK178)
& relation(sK178) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178])],[f179,f1136]) ).
fof(f1136,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK178)
& relation(sK178) ) ),
introduced(choice_axiom,[]) ).
fof(f179,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f2309,plain,
spl184_25,
inference(avatar_split_clause,[],[f1892,f2306]) ).
fof(f1892,plain,
relation(sK178),
inference(cnf_transformation,[],[f1137]) ).
fof(f2304,plain,
spl184_24,
inference(avatar_split_clause,[],[f1891,f2301]) ).
fof(f1891,plain,
relation(sK177),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,plain,
( relation(sK177)
& empty(sK177) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f169,f1134]) ).
fof(f1134,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK177)
& empty(sK177) ) ),
introduced(choice_axiom,[]) ).
fof(f169,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f2299,plain,
spl184_23,
inference(avatar_split_clause,[],[f1890,f2296]) ).
fof(f1890,plain,
empty(sK177),
inference(cnf_transformation,[],[f1135]) ).
fof(f2294,plain,
spl184_22,
inference(avatar_split_clause,[],[f1889,f2291]) ).
fof(f2291,plain,
( spl184_22
<=> ordinal(sK176) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_22])]) ).
fof(f1889,plain,
ordinal(sK176),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,plain,
( ordinal(sK176)
& epsilon_connected(sK176)
& epsilon_transitive(sK176) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK176])],[f168,f1132]) ).
fof(f1132,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK176)
& epsilon_connected(sK176)
& epsilon_transitive(sK176) ) ),
introduced(choice_axiom,[]) ).
fof(f168,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f2289,plain,
spl184_21,
inference(avatar_split_clause,[],[f1888,f2286]) ).
fof(f2286,plain,
( spl184_21
<=> epsilon_connected(sK176) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_21])]) ).
fof(f1888,plain,
epsilon_connected(sK176),
inference(cnf_transformation,[],[f1133]) ).
fof(f2284,plain,
spl184_20,
inference(avatar_split_clause,[],[f1887,f2281]) ).
fof(f2281,plain,
( spl184_20
<=> epsilon_transitive(sK176) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_20])]) ).
fof(f1887,plain,
epsilon_transitive(sK176),
inference(cnf_transformation,[],[f1133]) ).
fof(f2279,plain,
spl184_19,
inference(avatar_split_clause,[],[f1886,f2276]) ).
fof(f1886,plain,
relation(sK175),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,plain,
( relation(sK175)
& ~ empty(sK175) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175])],[f174,f1130]) ).
fof(f1130,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK175)
& ~ empty(sK175) ) ),
introduced(choice_axiom,[]) ).
fof(f174,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f2274,plain,
~ spl184_18,
inference(avatar_split_clause,[],[f1885,f2271]) ).
fof(f2271,plain,
( spl184_18
<=> empty(sK175) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_18])]) ).
fof(f1885,plain,
~ empty(sK175),
inference(cnf_transformation,[],[f1131]) ).
fof(f2269,plain,
spl184_17,
inference(avatar_split_clause,[],[f1884,f2266]) ).
fof(f2266,plain,
( spl184_17
<=> ordinal(sK174) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_17])]) ).
fof(f1884,plain,
ordinal(sK174),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,plain,
( ordinal(sK174)
& epsilon_connected(sK174)
& epsilon_transitive(sK174)
& ~ empty(sK174) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f178,f1128]) ).
fof(f1128,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK174)
& epsilon_connected(sK174)
& epsilon_transitive(sK174)
& ~ empty(sK174) ) ),
introduced(choice_axiom,[]) ).
fof(f178,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f2264,plain,
spl184_16,
inference(avatar_split_clause,[],[f1883,f2261]) ).
fof(f2261,plain,
( spl184_16
<=> epsilon_connected(sK174) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_16])]) ).
fof(f1883,plain,
epsilon_connected(sK174),
inference(cnf_transformation,[],[f1129]) ).
fof(f2259,plain,
spl184_15,
inference(avatar_split_clause,[],[f1882,f2256]) ).
fof(f2256,plain,
( spl184_15
<=> epsilon_transitive(sK174) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_15])]) ).
fof(f1882,plain,
epsilon_transitive(sK174),
inference(cnf_transformation,[],[f1129]) ).
fof(f2254,plain,
~ spl184_14,
inference(avatar_split_clause,[],[f1881,f2251]) ).
fof(f2251,plain,
( spl184_14
<=> empty(sK174) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_14])]) ).
fof(f1881,plain,
~ empty(sK174),
inference(cnf_transformation,[],[f1129]) ).
fof(f2249,plain,
spl184_13,
inference(avatar_split_clause,[],[f1880,f2246]) ).
fof(f1880,plain,
empty(sK173),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,plain,
empty(sK173),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173])],[f171,f1126]) ).
fof(f1126,plain,
( ? [X0] : empty(X0)
=> empty(sK173) ),
introduced(choice_axiom,[]) ).
fof(f171,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f2244,plain,
~ spl184_12,
inference(avatar_split_clause,[],[f1879,f2241]) ).
fof(f2241,plain,
( spl184_12
<=> empty(sK172) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_12])]) ).
fof(f1879,plain,
~ empty(sK172),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,plain,
~ empty(sK172),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f176,f1124]) ).
fof(f1124,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK172) ),
introduced(choice_axiom,[]) ).
fof(f176,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f2239,plain,
spl184_11,
inference(avatar_split_clause,[],[f1419,f2236]) ).
fof(f2236,plain,
( spl184_11
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_11])]) ).
fof(f1419,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f124]) ).
fof(f124,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(f2234,plain,
spl184_10,
inference(avatar_split_clause,[],[f1418,f2231]) ).
fof(f2231,plain,
( spl184_10
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_10])]) ).
fof(f1418,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f124]) ).
fof(f2229,plain,
spl184_9,
inference(avatar_split_clause,[],[f1417,f2226]) ).
fof(f2226,plain,
( spl184_9
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_9])]) ).
fof(f1417,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f124]) ).
fof(f2224,plain,
spl184_8,
inference(avatar_split_clause,[],[f1415,f2221]) ).
fof(f2221,plain,
( spl184_8
<=> one_to_one(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_8])]) ).
fof(f1415,plain,
one_to_one(empty_set),
inference(cnf_transformation,[],[f124]) ).
fof(f2219,plain,
spl184_7,
inference(avatar_split_clause,[],[f1414,f2216]) ).
fof(f2216,plain,
( spl184_7
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_7])]) ).
fof(f1414,plain,
function(empty_set),
inference(cnf_transformation,[],[f124]) ).
fof(f2214,plain,
spl184_6,
inference(avatar_split_clause,[],[f1411,f2211]) ).
fof(f2211,plain,
( spl184_6
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_6])]) ).
fof(f1411,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f115]) ).
fof(f115,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f2209,plain,
spl184_5,
inference(avatar_split_clause,[],[f1408,f2206]) ).
fof(f1408,plain,
relation(empty_set),
inference(cnf_transformation,[],[f135]) ).
fof(f135,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f2204,plain,
spl184_4,
inference(avatar_split_clause,[],[f1406,f2201]) ).
fof(f2201,plain,
( spl184_4
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl184_4])]) ).
fof(f1406,plain,
empty(empty_set),
inference(cnf_transformation,[],[f121]) ).
fof(f121,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f2199,plain,
~ spl184_3,
inference(avatar_split_clause,[],[f1150,f2196]) ).
fof(f1150,plain,
~ relation_of2_as_subset(sK59,sK58,sK57),
inference(cnf_transformation,[],[f751]) ).
fof(f751,plain,
( ~ relation_of2_as_subset(sK59,sK58,sK57)
& subset(sK56,sK57)
& relation_of2_as_subset(sK59,sK58,sK56) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59])],[f346,f750]) ).
fof(f750,plain,
( ? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(X0,X1)
& relation_of2_as_subset(X3,X2,X0) )
=> ( ~ relation_of2_as_subset(sK59,sK58,sK57)
& subset(sK56,sK57)
& relation_of2_as_subset(sK59,sK58,sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(X0,X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f345]) ).
fof(f345,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(X0,X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f215]) ).
fof(f215,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[],[f214]) ).
fof(f214,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f2194,plain,
spl184_2,
inference(avatar_split_clause,[],[f1148,f2191]) ).
fof(f1148,plain,
relation_of2_as_subset(sK59,sK58,sK56),
inference(cnf_transformation,[],[f751]) ).
fof(f2189,plain,
spl184_1,
inference(avatar_split_clause,[],[f1149,f2186]) ).
fof(f1149,plain,
subset(sK56,sK57),
inference(cnf_transformation,[],[f751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU264+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri May 3 12:04:23 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % (24505)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (24508)WARNING: value z3 for option sas not known
% 0.12/0.35 % (24506)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (24509)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (24507)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (24508)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)
% 0.12/0.35 % (24510)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)
% 0.12/0.35 % (24511)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)
% 0.12/0.35 % (24512)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)
% 0.18/0.43 TRYING [1]
% 0.18/0.44 TRYING [2]
% 0.18/0.50 TRYING [3]
% 1.58/0.58 TRYING [1]
% 1.58/0.60 TRYING [2]
% 3.68/0.86 % (24510)First to succeed.
% 3.68/0.88 TRYING [4]
% 3.68/0.90 % (24511)Also succeeded, but the first one will report.
% 3.68/0.90 % (24510)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24505"
% 3.68/0.90 % (24510)Refutation found. Thanks to Tanya!
% 3.68/0.90 % SZS status Theorem for theBenchmark
% 3.68/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/0.92 % (24510)------------------------------
% 3.68/0.92 % (24510)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.68/0.92 % (24510)Termination reason: Refutation
% 3.68/0.92
% 3.68/0.92 % (24510)Memory used [KB]: 12457
% 3.68/0.92 % (24510)Time elapsed: 0.546 s
% 3.68/0.92 % (24510)Instructions burned: 1548 (million)
% 3.68/0.92 % (24505)Success in time 0.592 s
%------------------------------------------------------------------------------